# Practical Applications of Mathematics in Everyday Life

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

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.

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 |

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).

## Read More From Owlcation

## 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 ft^{3}, 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 = 16ft^{3}

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 = 16ft^{3}/0.33ft^{3}= 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.

## 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,

**is the rate of the work being completed, and**

*r***is the time of work.**

*T*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 articles 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

**Question:** Do people need mathematics every day? Why?

**Answer:** 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.

**Question:** Could you please tell me how trigonometry is used in our everyday lives?

**Answer:** 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.

**Question:** How do you use math to calculate dinner?

**Answer:** 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.

**Question:** What are some professions that utilize mathematics?

**Answer:** 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.

**Question:** Is there a connection between math and nature?

**Answer:** Yes, there is! In fact, many of nature's process can be described mathematically, and in some cases, the equations are beautifully simple. First, the field of physics is the study of the mechanics of nature. Physics is also a math-heavy field of study. In fact, many scientific fields of study use mathematics to try and understand the processes that occur in nature.

One area where mathematics and nature collides is in the self-repeating pattern known as the fractal. Fractals can be found in leaves, river flow patterns, lightning, tree branches, seashells, etc. A lot of these can be simply described mathematically by something called the Mandelbrot set. This is an equation that results in an infinite series of numbers that depend on exponentiation of a previous number plus a constant. The study of fractals, especially those found in nature, is fascinating.

**Question:** Do you need mathematics every day? If so, why?

**Answer:** In terms of mathematics, "need" is subjective. To the average person, they may not need to use much math daily, unless it's necessary for their job or they have an intrinsic interest in numbers. However, if people learn math and put it to good use, math can help them be more efficient, saving them time and money.

I use mathematics every day. This is both in my job and in my personal/home life. In some ways, math is what you make of it. If you like mathematics and find it easy to understand, you will no doubt find more ways to use it daily.

**Question:** Is math not useful in any case?

**Answer:** I think math will always have a useful and important part to play in our life. Even things that you might believe are purely non-math will still likely have a mathematics component to it. Take philosophy for instance. At the heart of philosophy is logic. Logic is based on reasoning according to strict principles of validity. Math is highly logical and the more advanced fields of math find themselves deeply intertwined in philosophy and reasoning. As I have mentioned before, if you are unaware of mathematics, you will be unaware of its potential applications in your life. The more math you know, the more you will use it to solve life's problems.

**Question:** How are straight lines useful in our daily life?

**Answer:** Straight lines are the basis of many architectural and engineering principles. Look at all of the roadways and buildings that man has constructed. Straight lines are easier to build than curved ones. Straight lines are also very efficient. For example, cubes with straight lines are easier to transport in bulk and to construct things with then spheres. Straight roads are easier to drive on and result in less energy use when compared to a curved roadway. Straight lines also make up one of the strongest shapes used in the engineering world, triangles. In engineering, straight lines enable designers to control and direct forces such that the things we invent perform at their desired level of functionality. In addition, you've probably heard the saying that the shortest distance between any two points is a straight line. This is certainly true within the context of any finite three-dimensional space.

**© 2011 Christopher Wanamaker**

## Comments

**shivay** on March 22, 2020:

What is use of real analysis in life? Please give me answer.

**Danica** on October 14, 2019:

Is mathematics invented or created?

**Eka Rahmawati** on April 08, 2019:

Im agree with you, because a lot of people think that mathematics is a difficult lesson and have no relation with their real life. But in fact there's alot of mathematics theory always used by human everyday trough their activities. The first one is, mathematics can be used to count or manage their money. For the example if some people go to shop something and there's a lot of discount there, so they can know how much discount that they'll get so they can make sure with their money conditions is that able to buy or not. Another example is mathematics can be use to manage human outcome money being stable and controlled. Then the second example is mathematics can be used for thinking budget for renovation house. When there some people want to renovate or improve their house, they can predicted what the thing that they need and how much thing that they need to renovate their house, because if their can predict and count how much thing that they need exactly they can save a lot of money. From both of that example we can conclude that mathematics can be used to our real daily life.

Thank you.

**Harendra** on March 09, 2019:

What is the use of Calculus in real time ?

**Ebunoluwa** on February 12, 2019:

The cost of a wrist watch 5 years ago is 2000 if its discounted at 8% per annum simple interest what we be the cost now?

**Liubov Maliarchuk** on November 22, 2018:

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

**Manjula** on November 20, 2018:

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.

**Neddy707** on August 16, 2018:

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