Practical Applications of Mathematics in Everyday Life

Updated on December 1, 2018
CWanamaker profile image

Chris has a Master's degree in engineering and uses his knowledge to write about a variety of topics from an analytical perspective.

The Universal Language of Math
The Universal Language of Math | Source

Historically, mathematics has been a subject that many students struggle with. How often have you heard a young learner utter the words, "I'm never going to use this stuff!?" as they are struggling to solve some algebra or calculus problems? For many parents and teachers, the utterance of this phrase (or ones like it) is too often a common occurrence in the classroom. Most people will respond to the students by saying that they may need it or a future job or that it improves the critical thinking ability of the brain. While these responses are good, and well intended, they don't serve the practical and immediate needs of the child. So perhaps next time that you hear a student struggling with math, you can gently remind them of these practical applications of math in our everyday life.

Furthermore, it's interesting to note that if you lack knowledge of mathematics then you won't know how it can be used in your life. In other words, learning mathematics will help your mind come up with useful ways that math can be used. People often don't know what they don't know and until you fully grasp a new concept you won't realize what power it has.

Financial Management

Probably the single most cited practical application for math in our everyday life is for money management. If you can't add or subtract correctly, its going to be very difficult for you to survive in our dollar driven society. Ok, so I know what your thinking, "The typical person who manages their own money has no need for math knowledge beyond the basic concepts of arithmetic, right?" Well this is in fact incorrect.

To be able to adequately understand the terms of a loan or an investment account, a basic understanding of higher math such as Algebra is required. You see, the interest (growth or payment terms) pertaining to these types of money markets utilize the concepts of exponential growth. For example, a typical mortgage will use the compound interest formula to determine how much interest needs to be paid each month. If you lack knowledge of the mathematics behind how compound interest works (or rather, how loans and debt work), you could stand to lose a lot of money!

If you're serious about managing your money, you could even use higher math to develop future projections of your spending habits. There is great value in this information; you can use it to plan future expenditures or even set goals for yourself. Below is a graph of my bi-weekly spending on groceries for the past year and a half.

Source

What you'll notice in the above graph is that there is a nearly linear downward trend of my grocery spending. I can use the logarithmic equation to formulate an educated guess of my future spending habits. Since the best predictor of the future is the past, there is a good chance that this downward trend will continue for some time into the future (assuming nothing major in my life changes). As time progresses I am always adjusting the equations so that they reflect the best possible chance to accurately predict the future. With this information, I can understand my spending habits and I can even forecast my future spending which can help me to plan better.

Home Improvement

Anyone that repairs or remodels homes will tell you that math has helped them get the job done efficiently. Some basic math skills will enable you to determine how much material you need to purchase to finish the project right. For example, a tile installer will need to calculate the floor area of a room to determine how many tiles he needs to bring to the job site. An electrician uses math to figure out how much wire they need to install new electrical outlets. Carpenters will also be able to determine how much wood they need to build a structure. You will likely rely on some form of math even when you are doing something as simple as painting a room. Understanding basic math concepts will help any do-it-yourselfer save time and money.

For instance, if you plan on laying tile in a room you need to know about the basics of geometry in order to get perfectly straight lines and a good layout while also ensuring that you buy enough tile (but not too much) to cover the floor. You don't want to end up having many tiles or making multiple trips to the store to buy when a little math could have saved you both time and money.

In terms of home improvement, math can also help the homeowner answer other questions as well. For instance, if you have a dripping faucet, you could measure the drip rate and determine how much water you would lose in any given amount of time. This could be equated to a dollar amount.

Another way math is useful around the house is with your electrical usage. With a little math and some numbers from your utility bill, you can easily calculate how much money you spend leaving the lights on all the time. You can also compute the cost of microwaving your leftovers or playing computer games. For fun, I thought I would do a quick comparison of the cost of using a few different light bulbs to illuminate a room.

 
Incandescent
CFL
LED
Brightness (lumens)
750
800
650
Power (watts)
60
13
9
Cost Per 100 Hours*
$0.67
$0.15
$0.10
Cost Per 10 Hours
$0.05
$0.0116
$0.0081
Cost Per Year (6hrs/day)
$14.72
$3.19
$2.21
*Using the average cost of 11.2 cents per kwh for electricity

The power of math enabled me to determine that the LED light has the lowest hourly cost associated with it (this does not account for the initial purchase price of the bulbs).

Exercise, Health, and Fitness

How can a little knowledge of math help with exercise, health and fitness? Well, there are plenty of places in this category for numbers to go. If you have ever tried to reduce your Body Mass Index by going on a diet, you've probably realized that counting calories was a good way to monitor your food intake. There are also several equations that you can use to calculate your body fat percentage on any given day. Obviously math can play a significant role in how someone progresses towards their weight loss goals.

If you have ever lifted weights, you have most likely used some math to determine how much weight you are lifting. Imagine how difficult the task of loading a barbell with weight would be if you could not add or multiply numbers. Most avid weight lifters like to keep records of all of their important numbers with regards to pumping iron. Most will be able to tell you what their one rep max is, as well has how much they can lift for a variety of sets and repetitions.

Outdoor Landscaping

Math is also a great tool that can be used to help with landscaping projects. There are a variety of scenarios where this is the case, however, I will focus on one example in this article. Let’s say that you are trying to build a raised planter box that measures 8 feet long by 2 feet wide and 1 foot deep. You plan on purchasing a bagged soil mix from the home center. Each bag can fill a volume of 0.33 ft3, weighs 30lbs, and costs $2.50. How much dirt do you need to fill this planter box and how much is it going to cost? Additionally, you don’t have a truck and would need to transport the dirt in a back of a Honda Civic. The maximum payload for a Honda Civic is 850lbs. Considering your own weight (assume 200lbs for this example) how many bags of soil mix can you carry in the car and how many trips to the home center will you need to make.

There are several steps needed in order to solve this problem and answer the questions. First, calculate the volume of the dirt needed to fill the planter box:

Volume = 8ft x 2ft x 1ft = 16ft3

Next, divide that number by the volume of dirt provided in each bag to get the number of bags needed for the project:

Number of Bags = 16ft3/0.33ft3 = 48 Bags

Note that this calculation does not consider the effects of compaction (shrinkage) of the soil which would decrease its volume. Many soils could lose as much as 10-20% of its volume due to settlement, shrinkage, and compaction. The amount of compaction will depend on the soil type and is beyond the scope of this article.

Now that you know the number of bags needed, compute the total weight of the soil needed to fill the planter box:

Weight of Soil Needed = 48 Bags X 30lbs = 1,440lbs

Now we need to figure out how many bags of soil mix you can carry in your car on each trip. First, calculate the maximum weight of the soil that the car can hold given the payload capacity and the weight of the driver

Max soil = max payload – weight of driver = 850lbs – 200lbs = 650lbs

Next, divide the total soil weight needed for the project by the maximum payload that you can carry to get the minimum number of trips:

Number of trips = 1,440lbs/650lbs = 2.21

Since you cannot make 2.21 trips, you need to round up to a total of 3 trips. Since 3 trips are needed anyways, it makes sense to just buy 1/3 of the total number of bags on each of the trips. Therefore:

48 bags/3 trips = 16 bags per trip

Finally, to figure out the total price of the soil, multiply the number of bags times the price for each one:

Total Price = 48 Bags X $2.50 per bag = $120

Filling a Pool with Water

You just bought a new pool (or had one built) and are wondering how long it’s going to take to fill it up. Obviously, you want it filled with water sooner rather than later however you don’t want it to overflow while you are sleeping or at work. How can you ensure that the pool will reach the optimum level at a time when you are available to turn the water off? Using some math we can predict when the pool will be finished filling. We could also use math to set the fill rate such that it finishes filling at a specified time. Here are some example problems:

Your brand new below ground pool holds 11,000 gallons and you want to know how long it will take to fill up. To figure this out, you need to measure the flow rate of your nearby hose.

First, grab a 5 gallon bucket, a 1 gallon jug, and a stopwatch (or your phone). Use the 1 gallon jug to fill the bucket in 1 gallon increments, marking the inside at each 1 gallon interval. Once you’ve marked out 5 gallons, next grab a stopwatch and time how long it takes to fill the bucket to the 5 gallon mark. Do this 2 or 3 times and then compute the average of the measures.

For this sake of this article, let’s assume that it takes an average of 55 seconds to fill a 5 gallon bucket with water. Now you can compute the flowrate:

(5gallons/55seconds) X (60seconds/minute) = 5.45gallons per minute or 5.45gpm

Since the pool volume is 11,000 gallons, we can compute the fill time:

11,000gallons/5.45gpm = 2018.35 minutes

Convert to hours:

2018.35/60 = 33.6 hours

Now that you know how long the pool will take to fill, you can start filling it when it is convenient so that it doesn’t overflow. Alternatively, since you know the pool's volume you can specify a fill time and then calculate the flowrate need to achieve this.

In the Office

If you work in an office you may think that you don't need to know much math. However, this is not the case. Here is another example from my past employment in an office:

Our team was tasked with printing public notices for an upcoming project. In this case, 30,000 pages needed to be printed (with information on both sides), folded, sealed and mailed out by 4:00pm (in about 8 hours). Before we started printing out the notices, it was important to figure out how long it would take to print the notices in-house. If we could not get it done in less than 4 hours, then we would need to outsource the work to a contractor who could (at a much greater cost).

Our office had 4 copy machines, 3 of which are newer and can print about 40 double-sided pages a minute. The fourth copier is older and can manage about 18 double-sided pages a minute. Can our copier setup handle printing 30,000 double-sided pages in less than 4 hours?

To solve this problem simply add up the printing rates for each of the copy machines to get the total possible print output per minute:

[(40ppm) X (3 Copiers)] + [(18ppm) X (1 Copiers)] = 120ppm + 18ppm = 138ppm

Therefore, our copier setup can print, at best, 138 pages per minute. Next, divide the total number of pages that need to be printed by the printing rate to determine the printing time:

30,000 pages/138ppm = 217.39 minutes

Next, convert this to hours:

217.39min / 60 min/hr = 3.62 hours

Therefore, with our 4 copy machines, we could indeed print out all 30,000 public notices in less than 4 hours.

Source

What about Algebra?

One thing that I often hear from the youngsters is that they think that Algebra is useless. Fortunately, this is incorrect. Not only does knowing Algebra help with your critical thinking skills, you can actually use it in everyday life as well. Here's an example from my personal life:

My car was low on coolant so I decided that I needed to fill up the reservoir with some more. I had a partially full jug of coolant that had been marked as a 70/30 mixture of anti-freeze and water (70% anti-freeze and 30% water). This was a problem as in most cases coolant mixtures should be 50% water and 50% anti-freeze. So exactly how much distilled water should I add to the jug to make the resulting mixture 50/50? Here's where some critical thinking and Algebra comes in handy:

I weighed the water/coolant mixture and found that it weighed 6.5lbs. Now I can set up an algebraic equation to solve for the amount of water in pounds needed to reach a 50/50 mix. The equations are shown below:

(6.5lbs)(30% water) + (Xlbs)(100% water) = (6.5lbs + Xlbs)(50% Water)

Reducing the equation:

(195)+(100X)=(6.5+X)(50)

195 + 100X = 325 + 50X

Rearranging,

100X - 50X = 325 - 195

50X = 130

X = 130/50 = 2.6lbs

Therefore, I needed to add 2.6lbs of distilled water to the 70/30 mixture to convert it to a 50/50 mixture. With a little math I was able to solve the problem - No guessing or trips to the store were needed!

More Algebra - Classic Work-Rate Problems

Another practical use of basic algebra is solving classic work-rate problems. We often encounter these types of problems in the real world. They can appear challenging to solve, however, once you understand the way to solve it, it becomes easy! I'll give you an example from my past employment working in an office:

Example: Management told us that we were to move into a new building within 3 months and that it was time to start planning for the transition. The new building had smaller offices with less storage space so we realized it was about time to scan all of the remaining paper files in the filing room and purge ourselves from the mountain of paper.

Our office had 4 secretaries that were assigned various tasks as needed. The challenge was that all of them worked at different rates and varying responsibilities. No single person could get the job done by themselves since there were over 5,000 files to scan. We asked each employee to give us an estimate for how long it would take them to scan all of the files if they were to take on the job by themselves. Sasha said she could scan and verify all of the files in 90 days if she did nothing but scan the files. Kerry said she could complete the job in 100 days. Megan estimated that she could probably complete the job within 120 days. And finally, Marsha was the busiest and estimated it would take her 180 days to get the job done. (Note, I rounded these numbers to make the math easier to show).

If all 4 employees worked together, how long would it reasonably take to scan all the files?

To solve this problem we first recognize that it is a work-rate problem which takes the form of Q=rT. In this equation, Q is the quantity of work done, r is the rate of the work being completed, and T is the time of work.

First set up the following Table where the quantity is the product of work rate and the time to work together:

Employee
Rate
Time
Quantity (Rate X Time)
Sasha
1/90 days
T
T/90
Kerry
1/100 days
T
T/100
Megan
1/120 days
T
T/120
Marsha
1/180 days
T
T/180

The time, T, is the total time it would take all the employees to scan the files together. The work rate, r, in the table is the reciprocal of the time it would take the employee to complete the task by themselves. This may not make sense initially but think of it like this: Since Sasha can complete one task (scanning all of the files) by herself in 90 days, her work rate is 1 task per 90 days which is the same as saying she can complete 1/90th of the task in one day.

Now that this table is set up, we add all of the quantities together, set it equal to 1, and solve for the time, T. We get the following equation which can only be solved by using algebra:

Next, find a common denominator for the fractions and multiply both sides by it. In this case, the lowest common denominator is 1800.

Reducing the problem further:

Which becomes:

Combine like terms:

Solve for T:

Therefore, if all 4 employees worked together, all of the files could reasonably be scanned in less than 30 days.

Is that It?

The uses of math for the layperson are essentially endless. I could probably write several more hubs on how math is used in everyday life. Personally I use math on a daily basis to measure, track, and forecast many things. Whether it's computing the gasoline efficiency of my vehicles (or the efficiency of an electric vehicle for that matter), determining how much food to make for dinner, or calculating the power requirements of a new car stereo system, math is like a second and universal language that helps me make sense of the world.

Questions & Answers

  • Do people need mathematics every day? Why?

    The answer depends on a variety of factors, however, in general, most people use some math every day. For example, knowledge of basic mathematics is needed to buy and sell goods, follow recipes, or do many small projects around the house. In a lot of cases, people do this kind of mathematics without thinking too much about. On the other hand, advanced mathematics topics are usually not needed on a daily basis by most people. These types are things are great for scientists, engineers, programmers, etc.

    One other thing to note is that people don’t know what they don’t know. In other words, if you’ve never studied advanced mathematics before, you will never know what you could use that knowledge for since you haven’t learned it. Also, you won’t understand the opportunities to apply that types of mathematics to your life.

  • Could you please tell me how trigonometry is used in our everyday lives?

    Trigonometry is the branch of mathematics that deals with angles and sides of triangles. Trigonometry has many practical uses especially in the surveying, construction, and engineering industries. For the layman, they may not find the need to use trigonometry on a daily basis however if you have knowledge of this type of mathematics and what it can be used for it can make accomplishing many things easier. I'll provide a few examples for my personal life below to show you how trigonometry can be used in everyday life.

    My first example has to do with one of my hobbies which involves making props and decorations for plays, movies, and parties. Whenever I am crafting and making these things, I often have to measure things out and cut and shapes and objects to an exact dimension in order to get the look and structural integrity that is needed. In addition, I have to use my tools to make precise angular cuts in a variety of materials in order to maintain the desired level of precision. Instead of trying to measure an angle directly, I can use trigonometric functions to calculate the angles based on lengths of the sides of a triangular instead.

    Another time that I use trigonometry is when I was building an addition onto my house. I needed to use trigonometry to calculate the pitch of the roof and the length of the ridge line that I needed in order to maintain the same roof slope on the addition as the house. I made lots of measurements and did some calculations just to be 100% sure of the angles. I took this information to a local truss fabricator who created the trusses that I needed for the home addition.

    In addition to these things I also use trigonometry very often in my day job as an engineer.

  • What are some professions that utilize mathematics?

    Most jobs will require the use of some mathematics to be successful. However, the typical job may not ever require anything more advanced than multiplication or division.

    With that said, mathematics is very important in engineering and design-type jobs as well as in the banking, finance, and insurance industries. Also, many science and technology jobs also require the use of mathematics.

  • How do you use math to calculate dinner?

    Recipes - Almost all recipes require the use of standardized measurements to ensure repeatability as well as to maintain proper taste and seasoning levels. Units of measure such as the cup, the tablespoon, teaspoon, and things like ounces, gallons, pounds, etc. all play a role in recipe development. Without measurements like this and the use of mathematics, how would you double or half the recipe? How would you communicate the recipe to a friend or family member?

    Calories Counting - One of the most common dieting methods is counting calories. Among other things, this utilizes mathematics to accomplish correctly. In this way, you can compute the calories provided by a meal such as a dinner and make adjustments as needed to fit your diet situation.

    Macronutrient Monitoring - Just like counting calories, you can count or monitor your macronutrient intake. Bodybuilders, diabetics, and any curious person may want to know how many grams of carbohydrates, fat, or protein that they consumed. You can also compute the number of calories you obtained from each macronutrient as well. Every gram of carbohydrate and protein has about four calories of energy in it. Every gram of fat has about nine calories in it.

    How Much Food to Make? - Just like figuring out a recipe, you will often need to know how much food to prepare for a meal. You may be hosting a party or having guests at your home so it would be wise figure out how much food you need to buy and prepare. Using a little bit of math can help you cook the right amount of food, so no one is left hungry.

© 2011 CWanamaker

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    • profile image

      Liubov Maliarchuk 

      3 weeks ago

      What everyday examples could we show to students from 6 to 10, to increase their interest in Math? Thank you.

    • profile image

      Manjula 

      3 weeks ago

      Ya it's very useful I was waiting for this answers long back,.plz post more applications of mathematics,...I keep on waiting for ur more applications of mathematics.thq so much for this information.

    • profile image

      Neddy707 

      4 months ago

      looking for some everyday examples of how we use the properties of real numbers to share with my students to help them to understand that they do this regularly .... also trying to show them how the properties can help them do mental math and ditch the calcuator

      Thanx

    • profile image

      dazzling sweety 

      4 months ago

      ya its useful can u post some more interesting applications about math

    • profile image

      raj 

      6 months ago

      please post an article about how maths is applied in the field of aviation and navigation .

    • profile image

      tejaswi 

      6 months ago

      applications of maths in some more fields is what I want

    • profile image

      AKASH KRISHNA S 

      7 months ago

      Very useful

    • CWanamaker profile imageAUTHOR

      CWanamaker 

      10 months ago from Arizona

      Hello Mathsarehard,

      You are correct in your assessment of the light bulb calculations. I've updated the table with the correct information. Thank you for checking.

      -Cwanamaker

    • profile image

      mathsarehard 

      10 months ago

      I think you made a mistake in the light bulb calculations. For instance, a 60W bulb used for 100 hours would cost $0.672 not $6.72.

      You listed $0.112 as the cost per KWH not WH.

      If I'm wrong please explain so I know why. Thanks.

    • profile image

      Iqbal Nasron 

      21 months ago

      I have always believe Maths is useless and I'm guilty of telling my nephews n nieces Tht higher Maths is of no use in ur adulthood. Well after reading this article, I'm going to change all Tht. I got into some spending problems n bad debts myself. From today onwards, I'm gg to apply Maths to my life. Thnk u so much for this article. U made me a better person.

    • profile image

      Dhana lekshmi 

      23 months ago

      This article was good . The example given would surely make everyone to think practical applications of mathematics. & here i'm proud to be a maths student.

    • CWanamaker profile imageAUTHOR

      CWanamaker 

      2 years ago from Arizona

      Smyles,

      Yes we are all good at somethings and most people seem to have trouble with math. It's a bit abstract but the more you learn about it the more you understand it's universal nature.

    • profile image

      Smyles Buco 

      2 years ago

      I love math, it's how I make a living.. and I'm glad not everybody is good in math. God made it that way so that we would need each other

    • CWanamaker profile imageAUTHOR

      CWanamaker 

      2 years ago from Arizona

      David - Thanks for reading. Math is certainly essential in today's world and I am glad people are starting to see why.

    • profile image

      david igbru 

      2 years ago

      thanks a lot for this article. it will contribute greatly on a math business club am working on for schools which includes graphics stories, visual art and dram, social studies, emotional education and financial literacy. am so passionate about this project so i wish to get practical math questions on subsequent article from you. thanks again.

    • profile image

      Heta 

      2 years ago

      Nice

    • profile image

      Abhishek 

      2 years ago

      Don't like or hate maths

      Just feel it........

    • profile image

      feodz 

      2 years ago

      Good day! I would like to use this article for my research. May I know the author's name for the citation? Thanks a lot.

    • CWanamaker profile imageAUTHOR

      CWanamaker 

      2 years ago from Arizona

      Love it or hate it, math has allowed us to have the sophisticated world that we live in!

    • profile image

      tayyab qazzafi 

      2 years ago

      i hate math

    • profile image

      faiqa 

      2 years ago

      i like math because i love math

    • profile image

      niaz 

      2 years ago

      The main problem which is arosed here in Pakistan that how we use integration and diffirential rather than area calculator or other common addition and substraction.

    • profile image

      zahir 

      3 years ago

      but it is difficult to satisfy some one that how can we use mathematics in our daily life and allot of people asked about the practical use of mathematics .if some one explain it so please

    • profile image

      hajra 

      3 years ago

      Mathematics is wallah wallah

    • profile image

      Sonaa 

      3 years ago

      I like mathematices very much ..

    • JoyLevine profile image

      JoyLevine 

      4 years ago from 3rd Rock from the Sun

      I am so glad you wrote this article. I cringe every time I hear someone scoff at math and say "Do we really need all this stuff?" or like you said in the article when they say, "I'm never going to use this stuff!" Drives me crazy! I use math every day of my life in so many situations from simple tasks such as cooking to figuring out complex engineering problems, and everything in between.

      That shirt is on sale, 30% off retail of $20.00. What's your price at the register?

      I need to cut this recipe in half. How much is half of 3/4?

      How much force do I need to propel this basketball 15 ft through the air at the right angle to hit the goal, taking into consideration parabolic motion? (Ok granted they probably aren't going to try to figure that one out. They'll just keep practicing, lol).

      I shake my head every time I hear someone say they hate math. It is TRULY the universal language.

      Super article. Thumbs UP!

    • CWanamaker profile imageAUTHOR

      CWanamaker 

      5 years ago from Arizona

      Ss - I'm glad you enjoyed this article. I hope you stick with your major in college. It will be a tough road but trust me, it will be worth it. Some of the most successful people I personally know majored in math in college. Good luck!

    • profile image

      SS 

      5 years ago

      I am horrible at maths, but I have decided to major in it - B.A./B.Sc. in Maths!

      And I wish you'd been my math teacher/pal/whatev in school - maybe I would have been inspired to do better.

      Wish me luck.

      And this is a really great, articulate, and inspiring article. Thanks a lot.

    • profile image

      Dua tanveer 

      6 years ago

      I just love maths it is very useful in daily life!!!

    • CWanamaker profile imageAUTHOR

      CWanamaker 

      6 years ago from Arizona

      TrojanHorse666 - I sure hope that people find it useful. If it helps even one person, it was worth writing. Thanks for reading!

    • TrojanHorse666 profile image

      TrojanHorse666 

      6 years ago from India

      Good one! May be, someday people might have a look at this post & at least a few will get some benefit! :)

    • profile image

      TrojanHorse666 

      6 years ago

      Good one! May be, someday people might have a look at this post & at least a few will get some benefit! :)

    • CWanamaker profile imageAUTHOR

      CWanamaker 

      7 years ago from Arizona

      alezafree - I agree. I am sure that a lack of basic math skills plays a key role in our society's debt problem. It's really sad actually. Perhaps someday education will become a priority in the eyes of our leaders. Thank you for reading.

    • alezafree profile image

      Aleza Freeman 

      7 years ago from Las Vegas, NV

      Math is definitely treated like a red headed stepchild in our society. It's unfortunate, because as you said, it is essential to everyday functioning. I imagine a lack of basic math knowledge accounts (at least in part) for all those people drowning in debt with high interest credit cards.

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