Quantity Measurements. Choosing the Correct Procedure.

Quantity Measurement is Important

Quantity is a pretty easy concept to grasp.  But, it isn’t always easy to measure.  Quantity is basically an amount of something.  But different substances are easier to measure than others.  For example, if you have a cup full of marbles, you may be able to pour them out and count them individually.  What if you have a cup full of rice?  How many grains of rice do you have?  There are ways of measuring quantity other than just counting.  The two most common ways are by using a volume measurement, or a weight measurement.

If you go to the grocery store most of the packaged food is going to be measured by either weight, or volume.  Some of the more common weight measurements on packages for sale in the US would be ounces and pounds.  Some of the common volume measurements would be cups, pint, quarts and gallons.  So, what type of measurement do you use when trying to determine quantity?  It really depends on the physical attributes of the substance you’re measuring.

Quantity, How Much Is In The Jar?

When you are measuring a non-liquid substance, you will normally use weight at a measurement tool to determine quantity.  The reason you don’t use volume with a group of solid substances is because you can’t account for the tiny space in between the individual units.  For example, if you fill one cup with water, and one cup with ice cubes, you’ll notice that the ice cubes have space in between them, while the water completely fills the entire container.


When using weight as a measurement for quantity, you will typically weigh a sample of the substance individually, then measure the entire group.  If you take the weight of the entire group and divide it by the weight of the individual sample piece, you can approximate how many total pieces there are.

Typically, when measuring the quantity of a liquid, you’re going to use volume.  Because a liquid will completely fill the container, you can fairly accurately determine the quantity of the liquid by the volume filled in the container.

For online calculators for volume or weight go to CalcuNATION.com.

Online Calculators for Weight Measurements

Online Calculators for Volume Measurements

Online Calculators for Volume and Area Measurements

CalcuNATION is a website featuring online calculators and educational resources for mathematics.  Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)

Math Education Should be Exciting for Students

Math Education is Difficult

Math education is a very challenging curriculum for teachers.  In general, many students have a tendency to avoid math.  Whether they think it is a tedious exercise, or fail to see the usefulness of mathematics in the real world, this stigma creates a barrier that math teachers have to cross to successfully reach students and influence them on how important math education really is.

Math Education to Me

I know that when I was younger, math was a very dry, boring subject to me.  Other subjects offered some level of entertainment.  Reading and grammar had stories, geography taught about exciting places in the world and history had exciting characters.  Math pretty much had numbers and long, drawn out formulas to memorize.  Even now, it doesn't seem too exciting.  Math education didn't become important to me until I learned how to use it in the applications of science.

Making Math Exciting

For the most part, students aren't shown the actual uses of math at an early age.  Most young students are only taught the fundamentals of math.  I even think that can be tedious and boring.  I think that if students are not only educated on the fundamentals of math, but are immersed in the real world applications of math in a fun way, there would be more of an interest in math education at an early age.

In science and physics, I was able to apply math to understand how simple machines were designed.  This started to pique my interest in math and how it is applied in the real world.  Fast forward 20 years and that is now what I do for my "real life" job.  I use math every day to apply drive systems.  My day includes simple math like trying to calculate the hypotenuse of a triangle, or more applied math like torque for the track drive on a bulldozer, or calculating the mechanical horsepower of a drive system.  I get to work on some pretty large and impressive machines.

My hat goes off to math teachers everywhere for trying to break down that math stigma barrier.

For more information on math education and online calculators, go to CalcuNATION.com.

CalcuNATION is a website featuring online calculators and educational resources for mathematics.  Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)

Rates Are Great For Comparing Performance

Rates are all around us.  We use rates to determine our vehicle speed, track our work performance, rank our favorite sports teams, and even keep tabs on our personal cash flow.  Once you know what a rate is, and how to recognize rates, you can effectively use rates to compare performance within a system.

The key to all rates is time.  Rates are used to track a measurement per given unit of time.  As an example, the speed or your car is calculated in miles per hour, or kilometers per hour.  This rate is set as a length of distance per unit of time.  Other speed rates may be feet per second, feet per minute, kilometers per minute, meters per second, etc.  It really depends on what speed rate would best describe the performance.  After all, it would be much more complex if we measured the speed rates of vehicles in feet per hour.

In the investment world a key phase is "rate of return" or "return on investment (ROI)".  This rate is used to compare how quickly you either gain money, or lose money on an investment.

Right now I'm in a hotel.  If you pass by many hotels or motels as you travel, you might notice that they advertise rates.  The rate is how much it costs to stay at the hotel and is usually an amount of money per night, or per week.

There are other rates than just measuring distance per time unit (speed) and money per time unit.  Other rates can be volumes per time unit (flow), beats per second (heart rate), frames per second  (photography/videography),  weight per time unit, etc.  As stated before, rates are basically any measurement relative to a unit of time.

So the next time you are in the car, watching sports, reading the newspaper, or watching TV, see how many
different rates and rating systems you can identify.

For more on rates and other online calculators, try some of the links below.

Mobile Home Mortgage Calculator

Motorcycle Loan Calculator

APY Interest Calculator

CalcuNATION is a website featuring online calculators and educational resources for mathematics.  Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)

Efficiency, It Gets in the Way of Good Math.

Efficiency is often overlooked as a factor in math.  We use math as a tool for our daily lives, but rarely does a mathematical equation work perfectly when applied in real life.  There are so many variables that can play a factor in any application of mathematics that affect the outcome.  Efficiency is one of the most common variables that affect math in applications.  It is especially common when math is applied to a mechanical system.

The core purpose of a mechanical system is to transfer, convert or apply power in a useful way.  The laws of energy state that energy is never created or destroyed.  Energy is merely transferred.  Unfortunately, every time you transfer, convert, or apply energy, there will be efficiency issues.

In mechanical systems friction and the resulting heat are a major issue that causes efficiency issues.  Can you think of a motor, whether in your car, or in an appliance, that does not get warm as it runs?  Every surface within a system that comes in contact and moves against another surface will have friction.  This friction converts some of the input energy of motion into heat energy.  Think about the heat that is created when you rub your hands together.  Every metal surface that makes contact with another metal surface creates heat from friction in a similar way.

So, efficiency is a factor in many systems.  If you take a car, you can see where energy is transferred from one system, to the next, and where the efficiency losses affect the system.  Start with the fuel, the potential energy in the fuel is converted to mechanical motion in the cylinder.  But, this process isn't perfect, some of the fuel will end up not burnt and exit through the exhaust.  Even the piston that moves down creates friction with the cylinder wall and the crankshaft.  As power is transferred to the transmission, all of the gears and bearings rub and wear against each other, creating more friction and heat.  As power moves out of the transmission and into the final gear drive to the wheels, energy is lost to more friction to the gear sets in the final drive.  Even the tires will create heat from the friction between the tire and road.

There are many ways that we fight this friction by properly maintaining the systems of our vehicles.  Fresh oil, proper tire inflation, and regular tune-ups help each system transfer power more efficiently.

So, when applying math to real world applications, it is always important to be aware of the energy losses and efficiency issues that could be a factor.

For more information on some of the calculations used in gear drive systems and other mechanical calculators, follow the links below.

Menu of Machinery and Engineering Calculators

Gear Reducer Output Calculator

Gear Increaser Output Calculator

Chain and Sprocket Output Calculator

Belt Drive Output Calculator

Mechanical Horsepower Calculator

CalcuNATION is a website featuring online calculators and educational resources for mathematics.  Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)

Carpenters, Using Math to Build and Construct.

Carpenters would have a hard time building anything without math.  Without the knowledge and application of math skills houses may end up looking like something from a fun park.  Constructing a solid piece of furniture, a level counter top, or a comfortable room with plumb walls requires many different math skills.  A good carpenter will have a strong understanding of general mathematics, measurements and geometry.

If you've ever been involved with carpenters, or carpentry in general, you may have heard the phrase "measure twice, cut once".  This is a key phrase in carpentry.  Being accurate in measurements helps to eliminate making mistakes when cutting lumber.  This helps to eliminate wasted time and money associated with these mistakes.  Fractions are a constant math function in a carpenter's life.  Also, being able to add, subtract, multiply and divide is critical to know what your measurements should be as well as accurately estimating costs.  Many carpenters will have sharp math skills and don't be surprised if they can quickly calculate these general math functions in their head.

In addition to accurate math skills for measurements.  Carpenters need to be able to convert measurements.  Not everything is measured with one length or weight unit.  Being able to convert between measurement units is key.  Converting between inches, feet, yards, pounds, ounces, and even metric units is important.

To be sure that walls are straight, cabinets are level, and furniture is built solid, carpenters use geometry.  Being able to calculate area, volume, side lengths, circumference and hypotenuse lengths, are key math skills needed for a carpenter.  Knowing the equations for these basic geometry functions are important to building solid structures.

The next time you look at a piece of furniture, a cabinet, or a house, think about some of the math used to build that structure and how important it is to your daily life.

For more on some of the math calculations a carpenter uses, try the online calculators at CalcuNATION.

Measurements and Conversions Calculators

Length Conversion Calculators

Geometry Calculators

CalcuNATION is a website featuring online calculators and educational resources for mathematics.  Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)

Water Conservation. Are You Flushing Your Money Down the Toilet?

Water conservation is a hot topic these days.  One of the most wasteful places that we use water is the bathroom.  I've posted thoughts and calculations on wasting water in the bath and shower, but I've never discussed one of the other fixtures that uses a lot of water.  The toilet.

"Flushing your money down the toilet." is a fairly common phrase for wasting money.  In some ways, it is literally true.  I don't condone anyone making it a habit to not flush the toilet, even though some people do.  Even if that habit is meant to save money and promote water conservation, it's still kind of gross.  However, we can look at just how much water is used when you hit the handle and how much money that costs per flush.

To figure this out, we first need to find out how much water is actually used to flush a toilet.  Many toilets have a different amount of water that is used per flush.  This rating is usually tagged somewhere on the fixture.  Some new toilets are designed with water conservation in mind.  These units will have fewer gallons per flush ratings than older models.  The toilet in my house uses 1.6 gallons per flush.

Now, we need to know how much the costs are for not only water service to your house, but sewer service also.  My most recent water bill charges a price of $20.00 for up to 2,500 gallons of water per month.  Every 1000 gallons of water over that is an additional $4.72.  The sewer costs are also set at $20.00 for up to 2,500 gallons of water and $4.72 for every additional 2,500 gallons.
As long as my total water and sewer usage is under 2,500 gallons per month, my combined cost of water and sewer together is $.016 per gallon.

So, if my toilet flushes at a rate of 1.6 gallons per flush, and my cost per gallon is $.016, then multiply the two numbers to come up with $.0256 per flush.  Just under 3 cents to flush the toilet.

So the next time someone tells you that you're throwing your money down the toilet, you can tell them how much it truly costs to flush that money away and lecture them on the importance of water conservation.

I know it's dirty math, but someone has to do it.

For more on how to calculate volumes, flow and pressure, try some of the online calculators at CalcuNATION.

Volume Conversion Calculators

Flow Measurement Calculators

US Gallon Volume Conversion Calculator

CalcuNATION is a website featuring online calculators and educational resources for mathematics.  Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)

Bald Versus Non-Bald. The Challenges of the Dome.

Being bald is more than a hair style, or in some cases, a non-hair style.  It turns into a way of life.  If you are fortunate enough to embrace your own baldness, you can find the positive aspects of being bald.  One of the most common references to baldness is that being bald is "low maintenance".  For those that aren't lucky enough to be bald, it's not as "low maintenance" as you might think.  It may save some money at the barber shop, but there are other hassles and expenses that need to be recognized.

If you're reading this and you have a full head of hair, then good for you.  For the average joe with a mop on his head, we can make a few assumptions.  For your daily maintenance, you probably spend some time washing your hair, and combing your hair.  Your expenses for keeping your flowing locks in check probably amount to the cost of some hair products like shampoo and maybe some hair gel.  Of course we can't forget the costs of going to the barber maybe once every two weeks?  So, in a given month, a well follicled male would probably spend around $20-$40 on hair products, depending on how fancy he is.  And, at the barber shop, we'll assume for the sake of this example, he might spend $30 per month.  That comes out to about $50-$70 per month to maintain the lifestyle of the rich and hairy.

Now let's look at your average good looking bald guy.  He doesn't have the expenses of going to the barber shop, or having to purchase shampoo or hair gel.  However, there are other expenses.

If our hair challenged friend uses a razor on his head daily to keep that shiny top looking good, he has extra costs on shaving cream and razor blades.  And, razor blades aren't cheap either.  At least not good ones.  If you do use bad razor blades, you risk cuts on your noggin.  This is where the added cost of band-aids comes in.  If your baldness is something you're not ashamed of, then you will be out in public with your chrome dome.  I don't know many people that aren't aware of the dangers of sunburns, but I can assure you that the top of your head is sensitive and not a great place to be peeling.  Now, we're adding the cost of sunscreen....good sunscreen...applied a lot.

So, from personal experience, I can assure you that there are some monthly costs associated with maintaining a bald dome.  It also takes some time every day to make sure you aren't looking scruffy...in spots.

In summation, I don't really see much of a difference in cost or time when it comes to maintaining a nice head of hair, or a nice head of nothing.

This post was written to help support CalcuNATION.  Here are some examples of health related calculators.

Nutrition and Health Calculators

Caloric Needs Calculator

Caloric Energy Calculator

CalcuNATION is a website featuring online calculators and educational resources for mathematics.  Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)

Old MacDonald Uses Math on His Farm. E-I-E-I-O. Part 2

Old MacDonald uses math on his farm to be the best farmer he can be.  Being a farmer, he takes on multiple roles in his business that are usually split up between many employees in other businesses.  He takes on the responsibilities of accountant, executive management, workforce, and maintenance.  In part 1, we looked at some of the simple ways that he has to look at finances when running a farm as a business.  Old MacDonald has to be constantly vigilant to keep costs down and his revenue stream up.  One way that he keeps costs down is to do his own maintenance and mechanic work whenever he can.

Many of the machines on a farm play critical roles.  Without tractors, combines, trucks and implements, Old "Mac" wouldn't be able to perform the day-to-day functions necessary to produce a profit.  It's very important that the equipment functions properly when needed.  And many times, especially when weather is involved, he may need the equipment to perform flawlessly in a short window of time.  A great example would be trying to harvest when a storm is brewing.

Because of the importance of his machinery, Old "Mac" constantly maintains and repairs his own equipment.  This ensures him that everything is ready when it's needed and it helps keep his costs down from having someone else work on it.  Because of this, he has a general knowledge of mechanics and hydraulics.

Many of the machinery on the farm uses hydraulics.  Most of his machines have pumps, motors and cylinders.  It helps Old "Mac" to know how the items function.  Being able to "backyard engineer" some of the equipment saves time and money.

It would be handy if Old MacDonald was familiar with the math of cylinder force, speed, and hydraulic horsepower.  I'd bet he would give some engineers a run for their money on machine design.

Of course, there are the costs of duct tape and baling twine that have to be accounted for.

For more information on mechanical and hydraulic math, try some of the online calculators at CalcuNATION.

Machinery and Engineering Calculators Menu

Hydraulic Calculators Menu

Cylinder Force Calculator

Cylinder Extension Speed Calculator

Cylinder Retraction Speed Calculator

CalcuNATION is a website featuring online calculators and educational resources for mathematics.  Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)

Inflation. It's the Enemy of Your Savings Account.

Inflation may not sound like an evil word, but if you value your money and how much you save, it can be evil.  Like many people, I was taught to save money for a rainy day.  I'll admit that I didn't always do as good of a job that I should have, but I do at least recognize the importance of saving money and earning interest.  What many aren't taught at a young age is the lesson of inflation and how it will affect the value of your savings.

Okay, so you may not be all that familiar with inflation.  Inflation is basically the erosion of value per unit of currency as a result in a generally increase in price for goods over time.  I'll try to give you an example.  The price for gas, energy, groceries and other goods slowly increase in price over time.  As these prices increase, it takes more money to purchase these items.  As time goes by, you will be able to purchase fewer goods per dollar you spend.  The value per dollar slowly erodes.  That is inflation.

So, if you have a great job and earn $100,000/year, think about what you can purchase with that $100,000. 
Next year, you'll be able to purchase about 3-3.5% less items because of the inflation.  The next year you'll be able to purchase about 3-3.5% even less.  Many companies offer a "cost of living" increase each year to combat inflation and keep the value of your compensation close to your purchasing power.

So how is this the enemy of my savings account?  The average inflation rate in the US is about 3-3.5% per year.  Every year, the value of the dollar goes down by 3-3.5%.  If you think about the money you save and the interest rate you're earning, most likely you aren't earning anywhere close to 3% in a savings account.  If you are earning less than the inflation rate, then you are actually losing value in your savings.  Even with the interest you're earning in your savings, the purchasing power of your savings is dwindling if you're not earning more interest than the inflation rate.

I hope this gives you some perspective of inflation and interest and how they react against each other.  I'm definitely not against having a savings account, but it is important to invest wisely and to be smart about where you put your money.

For more information on interest and how interest is calculated, try some of the online calculators at CalcuNATION.

Compound Interest Investment Calculator

Return on Investment Calculator (ROI)

Business and Finance Calculators

CalcuNATION is a website featuring online calculators and educational resources for mathematics.  Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)

Water Conservation. The Classic Question of Bath or Shower.

Water conservation is a hot topic these days.  And the amount of water we use in our homes makes up a significant amount of our daily water usage.  Whether you're using water to cook, clean, wash clothes, or bathe, water usage can be significant.  One of the places where we use the most water in the house is the bathroom.  And obviously, we use a lot of water to bathe.  The classic question is:  Do we use more water taking a shower, or bath?

I am going to make the assumption that most people at least know what a bath is and what a shower is.  If not, then we need to have a blog post about hygiene.  It's obvious that a shower and a bath differ in how you bathe.

A shower consists of a constant flow of water, and a bath is a set volume of water.  To determine how which wastes the most water, we need to know a few things.  For a bath, we simply need to know how much volume of water is used.  To determine the amount of water volume is used in a shower, we need to know the amount of flow coming out of the shower head, and how much time is being spent in the shower.
The amount of the flow of water in a shower depends a lot on the design of the shower head.  For this post, we will assume that the shower head will flow 2.5 gallons per minute.  A new shower head in the US will have a flow restrictor that limits flow to 2.5 GPM.

When I think of a standard bath tub, I think of a 30"x60" bath tub unit.  These units have a total volume capacity of around 40 gallons.  So, for this example, we will assume that a bath tub will be filled half way full for use.  That leaves us with a total volume of 20 gallons.

So now that we know the flow rate of the shower and the amount of volume used in a bath, we can do some math to compare.  A bath will use 20 gallons of water and a shower will use 2.5 gallons per minute.  How many minutes in the shower will it take to use more than the 20 gallons of water used in a bath?
Simply divide 20 by 2.5 to find out how many minutes it will take. 

Calculated out, this gives us 8 minutes.  So, if you take a shower for more than 8 minutes, you are using more water than if you took a bath in 20 gallons of water.

Now you've learned a new way of using math to conserve water.  And you're clean too.

For more on flow and volume calculators, try the online calculators at CalcuNATION.

Flow Measurement Calculators

Gallons Per Minute Conversion Calculator

Volume Conversion Calculators

CalcuNATION is a website featuring online calculators and educational resources for mathematics.  Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)

CalcuNATION and The Importance of Math Education.

I've spent the last few months developing the website CalcuNATION.  The website is my way of supporting math education and creating a different way for students of all ages to use math and recognize it's importance.  Up until now, I haven't really blogged about the website.  I guess I'll take a moment to explain how I came up with the idea, and why it's important to me.

Math has always been a big part of my life.  I grew up with parents that emphasized math education and how important it is to have a strong understanding of math.  My mother was a teacher and my father owned a small business.  My father always had a story or example that would emphasize math.  One that I remember was about my great-grandfather during the depression and how he was able to parlay his good math skills to be successful.  Which says a lot considering he was a farmer in central Kansas during the depression.

Now that I'm an adult, I find myself in a career that utilizes math.  I help develop and sell drive systems for heavy machinery.  It involves a lot of math.  A whole lot of math.  But, it is fun to see how calculations are used to develop a large machine.  Many of the machines that I help with are used in construction, mining, agriculture and the military.

I was having a conversation with a customer a few months ago about how to calculate the traction needed to develop a tracked rock-grinding machine when I thought about creating a simple calculation website where he could put in his machine information and it would give him an answer.  I put a lot of thought into what a calculation website would need to be for my customer and then it dawned on me to develop the website to show examples of calculations that are used daily.  That is where the idea for online calculators and CalcuNATION came in.

I thought more about who would use a website like CalcuNATION and who would get the most benefit from a collection of online calculators with formulas.  I decided to develop the website with students and teachers in mind.  The classic "Where will I use math in real life?" comment kept running over and over in my head.
So now it's been four months since I started the website.  I try to get as much feedback and involvement from students, teachers and friends to continue to make improvements.  I average one new calculator per day and I try to blog about math as much as possible.

The website has been very successful.  I get a lot of positive comments on it, and it has been used a lot.  Every month, the amount of visitors to the website doubles and that is encouraging to me.

So, if you read this and want to help me promote math, feel free to submit a new calculator idea, or register for the blog and write some posts about math.  Your help would me much appreciated.

CalcuNATION is a website featuring online calculators and educational resources for mathematics.  Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)

Old MacDonald Uses Math on His Farm, E-I-E-I-O. Part 1

Old MacDonald was a business man on the farm, and used math.

Farming isn't all about growing plants, and raising animals.  It's a business with all of the math that is associated with running a business.  Because it is a farm, not only are you using business math concepts, but there are other concepts involved in the operation of the farm to be successful.  And being a successful farmer is difficult these days, so being good at math is definitely an advantage to running a profitable farm operation.

There are so many aspects of farming that require math skills that I'm going to concentrate on one aspect per post.  This blog post is about the business math associated with farming.

Farming involves equipment, buildings, and inventory.  I say inventory as a business term, but in farming this would be the cattle and crops that are being raised and grown to sell.  The equipment is used to maintain and cultivate the inventory, and the buildings are for storage and protection of inventory and equipment.  A farmer always needs to be mindful of the concept of ROI (Return On Investment).  For every dollar that a farmer spends, how is that going to help make money?

The ROI concept is important to a farmer on the large expenditures and the small expenditures.  Keeping track of costs on small costs like feed, pesticide, herbicide, vet costs and fuel can add up.  However, if it offers a long-term benefit that outweighs the cost, it would be worth the expense.  For example, many times a farmer has a choice between a low-quality, cheaper feed for cattle versus a higher-quality, more expensive feed.  If the more expensive feed will allow the farmer to raise higher quality cattle and can receive more money for the cattle at market, it may be worth the expense of using the higher-quality feed.  It all depends on the total cost of the feed and the amount of extra revenue the farmer can get for the cattle at market.

On the bigger level, equipment and buildings can be very expensive.  It is fairly common for a tractor or combine to cost as much as a house.  That's why a farmer will weigh out the cost of the machine with how much increased productivity the farmer will receive from using the machine.  The cost of the machine isn't limited to the up front cost.  There are also costs for maintenance, fuel and the loan on the machine that can hit on the farmer's bottom line.  Buildings also fall into a similar issue, they require maintenance and may have a loan as well.

Keeping a vigilant eye on ROI is a constant part of life for a farmer.  It isn't just a job, it's a lifestyle.  It involves very hard, laborious work, and a savvy business sense.  Watching markets, costs, prices, and trends are a daily ritual for a successful farmer.

For more on some of the math discussed in this post, try some of these online calculators:

Return on Investment Calculator

Vehicle Loan Total Cost Calculator

Vehicle Loan Monthly Payment Calculator

Business and Finance Calculators

Fuel Mileage Calculator

CalcuNATION is a website featuring online calculators and educational resources for mathematics.  Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)

Math Should Be as Easy as Riding a Bike.

Math should be almost second nature in many aspects of your life.  You probably use math on a regular basis and don't even realize it.  Even when you ride a bicycle you are using math concepts.  So, as the saying goes, "It's as easy as riding a bike".  That is how easy math should be for you.

Before you groan and make a comment about ruining the enjoyment of riding a bike by bringing math into the picture, let's look at where you are already using math when riding your bike.  You may not realize it, but concepts of speed, pressure, ratio, circle circumference, weight and power are in constant use when riding a bike.

Let's look at ratio.  When you pedal a bicycle, you are driving a chain and sprocket setup that turns the rear wheel.  The front sprocket is most likely a different size that the rear sprocket.  This offset in size is a ratio.  What the ratio difference does is allow you to pedal at a different speed than the rear wheel will turn.  This change in speed also changes the amount of force applied.  If you are pedaling twice as fast as the rear wheel turns, then your force from the rear wheel will be twice as much as the force on the pedals.  The same is true in the other direction.  If you are pedaling and the rear wheel is turning twice as fast as the rate you pedal, then you will have half of the force on the rear wheel compared to the front wheel.

This ratio difference is why mountain bikes have a low ratio gear for climbing, they want as much multiplication of the force on the pedals as possible to help them climb a steep grade.  To get this multiplied force, they sacrifice speed.

You are also constantly adjusting for pressure.  Of course you have the pressure in your tires, but you also have the pressure from wind resistance.  Have you ever tried to go fast down a hill, or racing someone?  Chances are you tucked your body in to help with your aerodynamics.  By tucking your body in, you reduce the amount of area that is working against the wind, and reducing the amount of air pressure buildup in front of you.

Speaking of tires, have you ever had to pump up your tire?  Did you use one of those piston type hand pumps that have a handle you move up and down?  That's basically an air cylinder that allows you to force air into a tire.  That's another science that uses a lot of math, pneumatics.

These are just a few math concepts associated with riding a bike.  What other math concepts can you think of?

For more information on some of the concepts discussed in this post, try some of the online calculators below.

Chain and Sprocket Drive Ratio Calculator

Mechanical Horsepower Calculator

Pressure Measurement Calculators

Speed Measurement Calculators

CalcuNATION is a website featuring online calculators and educational resources for mathematics.  Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)

Ratio Math and Mechanical Advantage. It's Pretty Helpful.

Ratio math may not sound like an exciting subject to discuss in a blog, but it is very important to recognize the relevance of ratios.  Much of the machinery we use everyday take advantage of ratios to offer us some benefit.

So what exactly is a ratio?  A ratio is a measurement of mechanical advantage in a drive system.  An easy example is to think about a bicycle.

The pedals on a bicycle are attached to a toothed disc called a sprocket.  Attached to this sprocket is a chain that drives a sprocket attached to the rear wheel.  If both sprockets are the same size, the rear wheel will turn 1 revolution for every 1 revolution you pedal.  However, if we make the sprocket twice as large on the rear wheel, you now have to make two revolutions on the pedal to turn the rear wheel once.  It's easier on the person pedaling, but it moves the rear wheel slower.  Increasing the amount of force output at the sacrifice of speed.  This example is a 2:1 ratio.

If you think of a truck that is trying to tow a heavy load, you can imagine the mechanical advantage a ratio can offer.  Vehicles that haul heavy loads often times have a wide range of ratio options through a transmission.  To get the heavy load moving, they will put the transmission in low gear (numerically high).  It's called low gear because it is the very first gear ratio in the transmission and will result in very slow movement of the truck.  By putting the transmission in low gear, the engine will make more revolutions for every single rotation on the output of the transmission.  This results in an output on the transmission that has more force than the engine output, but will move slower than the engine output.  This allows the truck to move a heavy load, at slower speeds.

Other places where ratios are used are in belt and pulley systems, chain and sprocket systems, hydraulic cylinders, transmissions, planetary gearboxes and other gear drive systems.

For more information on the math behind ratios, try some of the online calculators at CalcuNATION.com.

Machinery and Engineering Calculators

Hydraulic Cylinder Force Calculator

Belt and Pulley Drive Ratio Calculator

Chain and Sprocket Drive Ratio Calculator

Gear Reducer Calculator and Gear Increaser Calculator

CalcuNATION is a website featuring online calculators and educational resources for mathematics.  Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)

To Be A Pilot? You Better Have Top Gun Math Skills.

When I was a kid I wanted to be a pilot.  I never imagined how much math was involved in flying.  I would go to airshows and imagine what it would be like to fly high and fast.  I'm sure many people share a similar story, but I would bet that many don't recognize the mathematics that pilots have to be familiar with.  At least when it comes to flying safely.

If you have a basic understanding of how an airplane functions, all of the systems involved, and the atmospheric conditions that you have to monitor, it can be almost overwhelming when you think about the math involved for a pilot.

An airplane functions on a pressure difference between the air below the wing, and the air above the wing.  The shape of the wing creates an area of low pressure above the wing as it moves through the air.  Because high pressure air tries to flow towards low pressure areas, it creates a lifting force on the bottom of the wing.  The atmospheric conditions can affect this pressure difference and how affective the lifting force is.  Temperature, altitude, and humidity can affect the atmospheric pressure and the effective lift on the wing.  Obviously, this is one of the most critical functions that a pilot has to be aware of.

One of the most important subsystems in an airplane is the engine.  Whether it's an internal combustion engine, turbine engine, or even electric, the pilot must have an understanding of how the engine works and functions to properly monitor this subsystem within an aircraft.  After all, it's the amount of air that flows over the wing that creates lift.  To move the wing through the air, you need forward thrust from the engine.  No thrust...no air movement...no lift.

When you look at the guages on some of the most basic aircraft, you'll get an idea of the different measurements that a pilot will use, and the math skills associated with those measurements.  Measurements in altitude, air speed, air pressure, temperature, fuel, frequency, and climb rate can be found.

For more information on just a few of the math skills a pilot uses when flying, try a few of them with the online calculators at CalcuNATION.com.

Transportation and Navigation Calculators Menu

Measures and Conversion Calculators Menu

Knots to MPH Conversion Calculator

Earth Gravity Acceleration Calculator

CalcuNATION is a website featuring online calculators and educational resources for mathematics.  Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)

No Pressure, But You Should Know More About Pressure

Pressure is a concept that can be confusing for some.  There are the pressures and stress associated with daily tasks like school work, homework, jobs and chores.  There are also the pressures associated with science.  We're going to look at the science aspect of pressure.

Pressure is mostly simply described as an amount of force applied to a given amount of area.  Pressure can be used to describe many different applications.

In the U.S. we typically use PSI units to describe pressure.  PSI is an acronym for Pounds per Square Inch.  The unit itself is fairly explanatory as to how much force per unit of area is applied.  Imagine a five pound force being applied to a one square inch area.  That would be equal to 5 PSI.  If you have 10 pounds applied to a 1 square inch area, that would be 10 PSI.  If you increase the amount of area that the force is applied to but keep the amount of force the same, the pressure decreases.  If you have 10 pounds of force that is applied to 2 square inches, you now have a pressure of 5 PSI.

Many times, pressure refers to an application that involves gaseous liquids.  Although PSI can be used to describe pressure in these applications, you most likely will see a unit of pressure called a Pascal, or a derivative of Pascal like KiloPascals.  Sometimes the unit of Bar may be used to describe gaseous pressures.

In regards to atmospheric pressure, there are also many ways to describe air pressure.  Atmospheric pressure depends on many factors like temperature, humidity and altitude.  Sometimes atmospheric pressure will be measured in PSI or Inches of Mercury.  Inches of Mercury is a traditional way to measure how dense the air in the atmosphere really is.

This was just a quick mention of some of the ways that pressure is measured.  For more information on how to convert between units, try some of the calculators at CalcuNATION.

PSI Conversion Calculator

Pascal Conversion Calculator

Inches of Mercury Conversion Calculator

Bar Conversion Calculator

Measures and Conversion Calculators Menu

CalcuNATION is a website featuring online calculators and educational resources for mathematics.  Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)

Do You Like to Buy Things? Then Math is Your Friend.

I know a lot of people who like to shop.  Not many people realize how much math is involved in shopping.  Even if you're not a shopper, the ability to purchase things that you want is part of our society.  I try to shop for deals when I can.  There are many different ways that stores offer incentives to purchase items.  There are discounts, sales, membership clubs, etc.

There is a pitfall to watch out for.  Many times, the sale, or discount, isn't in the store's system correctly.  When I go to check out and pay for my items, the system doesn't show the correct pricing.  Many times, the clerk relies on the system rather than trying to do the math to calculate the correct price.  I find this really annoying.  I keep a mental note of the cost of each item I'm purchasing so I know about how much I will be spending.  It really upsets me to work with a cashier who refuses to acknowledge anything other than what the system says the price is.  I show them the sale, and what the correct price should be and they either look confused, or shrug their shoulders.   ARGH!

The reason I bring this up is to show the importance of basic math when shopping.  Being able to calculate percentages and fractions will help when figuring out the correct price on a sale item.  Being able to do basic addition will help you with the total amount of money that you should be spending on the items at the checkout.  I typically round up the estimated price to the nearest dollar.  I don't want to keep track of all of the pennies for multiple items.

Remember that in many cases there will be a sales tax percentage added on to the final total.  That is another case where knowing how to calculate percentages will come in handy.

So the next time you're out shopping, practice up on you math skills and save some money.  Don't let stores get more money from you than is necessary.  After all, the more you save, the more you can afford later.

For more information on how to calculate some of the math skills listed, try these online calculators.

General Math Calculators

Finance Calculators

Profit Markup Calculator and Profit Margin Calculator

CalcuNATION is a website featuring online calculators and educational resources for mathematics.  Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)

Driving a Car. Yep...You Use Math There, Too.

I'm a firm believer that math can be as easy, or as challenging, as we choose it to be.  But, we have to recognize the importance of math and how it helps us in our day-to-day activities.  That being said, I developed a website called CalcuNATION to help show examples of math calculations that help us.  Because of this, I tend to keep my eye out for examples of how we use math in our everyday lives.

I recently got married and we decided to get away for the weekend on a short trip to the mountains in Tennessee.  I annoy my wife from time-to-time with my mathematical observations.  So, I have a blog and website I can focus these observations on so I don't annoy her too much.

When driving, math is being utilized both in a general understanding, and in actual use.  You use math to make calculations and adjustments as you drive.  You need to understand math skills to know how your vehicle is operating and how the environment is changing around you as you drive.

When I think of using math, the first thing I think of is speed.  I'm almost unconsciously adding and subtracting as I adjust my speed to the posted speed limits.  A mathematical understanding of speed rates and distances is important to know as well.  As you drive you adjust your speed not only for the posted limits, but for warnings of obstacles and other vehicles ahead.  If you see a sign that there is a sharp curve 2 miles ahead, you may not slow down very quickly.  If the same sign says 1/4 mile ahead, you most likely will adjust speed immediately.  Do you see what I'm saying?

Another easy example of math would be with fuel.  Understanding the concept of fuel mileage, volumes, distances, and even the financial part of fuel purchasing is important.  I'm always keeping an eye on my fuel mileage so that I can get the most distance for every dollar I spend on the road.

Where do you see other examples of math in use while you drive?  How about engine temperature?  Even tire pressure can be important.  What else is there?

For more information on some of the math principles listed, try some of these online calculators:

Motorcycle Loan Calculator

Fuel Mileage Calculator

Speed Calculators

Length Conversion Calculators 

Vehicle Loan Total Cost Calculator

CalcuNATION is a website featuring online calculators and educational resources for mathematics.  Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)

Torque. It's Not a New Twist on Power

Torque can be a difficult force to describe.  If I had to use another word to describe torque, I would use the word twist.  Without understanding what torque is, and how it is used, we can't really understand many other mechanical functions, like horsepower.

When I think of an example of torque, I think about arm wrestling.  It's hard to imagine someone not knowing what arm wrestling is, so I'll assume you know.  When you look at one of the opponents, he is trying to twist the other person's arm down.  This twisting motion is torque.  If you think about it, he is applying force at his elbow, and then his arm is a lever.  Those are the two factors that describe torque, a force for a given length of lever arm.

Maybe I got ahead of myself.  Let's look at how torque is described in science.  In the US we used units of torque measurement called inch-pounds, or foot-pounds.  Sometimes these are described as in/lbs, or ft/lbs.  Basically the unit is self-descriptive.  For foot-pounds, imagine a 1 foot wrench on a bolt.  If you apply one pound of pressure at the opposite end of that wrench, you are applying 1 ft/lbs of torque on that bolt.  If the imaginary wrench was 1 inch long, you would be applying 1 in/lbs of torque.

I like using the imaginary wrench comparison to try to explain torque.  It also works with a wheel that has a radius of 1 foot.  If you put one pound of force tangent to the circumference of the wheel, you would be applying one ft/lb of torque.

If you have a 3 foot imaginary wrench and you apply 10 pounds of force to the end of that wrench, how many ft/lbs of torque are you applying?  3 x 10 = 30 ft/lbs.

Torque is one of the variables used to calculate mechanical horsepower.  The other is RPM.
What other places do you see torque applied?  Remember to look for twisting motion.  Can you estimate how much torque is being applied?

For more calculations of torque, try these online calculators:

Torque Conversion Calculators

Mechanical Horsepower Calculator

Gear Increaser Calculator

Gear Reducer Calculator

CalcuNATION is a website featuring online calculators and educational resources for mathematics.  Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)

Cooking Up Some Good Points About Math In Your Life

Math is so important in our daily lives and I don't think it gets the credit it deserves.  Why is it that many students will groan when it is time to do their math homework?  When you ask a student what their favorite subject is, most of the time you won't hear "math".  Do they not understand how they use math every day?

Let's take a normal activity that many people use during their day and see where math was involved.  I think a good activity to look at would be cooking.  I don't care if you're a five-star chef, or you can barely cook macaroni and cheese, you're going to use math.  For our example, let's use mac and cheese.  Now I'm getting hungry.

Before you even think about opening a box of mac and cheese, you're already doing math.  Most likely quantity related.  How many people are going to eat this?  How much can you eat?  Now you may look at the box to see how many servings are in it.  When you are trying to judge servings, amounts, and the amount of people eating, you are using volume formula's and division.  I know!  Crazy!

As you move into the directions, you'll probably see some cooking directions, now you're getting into temperature calculations and time.  That's more math!

In addition to normal cooking instructions, it might even have some high altitude instructions.  Careful, this is for advanced mac and cheese mathematics only.  You adjust temperature based on your elevation because of the air pressure difference.  The mac and cheese company already did the difficult math for you to tell you what temperature you need to adjust for.

Now let's review.  You have to understand the basic math principles of time, volume, division and temperature to be able to make mac and cheese.  What other mathematical problems could arise when cooking a simple meal?

I can't believe you thought you could get by eating lunch without math.  Face it, it's everywhere.

For more information and online calculators on time, volume, division and temperature, try some of these links:

Division Calculator

Temperature Conversion Calculators

Time Conversion Calculators

Volume Calculators

CalcuNATION is a website featuring online calculators and educational resources for mathematics.  Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)