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Have you ever wondered how Algebra may be applied to solve real-life problems?
We regularly see people using Algebra in many parts of everyday life; for instance, it is utilized in our morning schedule each day to measure the time you will spend in the shower, making breakfast, or driving to work.
The absence of "X" or "Y" doesn't imply that algebra is not around us; algebra’s actual occurrences are uncountable. This exact and compact numerical language works wonderfully with practically all different subjects and everyday life.
In this article, we will grasp instances in real life where applications of algebra are needed and examples of applications of algebra in real life.
- How to factorise a polynomial?
What is Algebra?
Algebra is a part of mathematics that deals with symbols and the standards for controlling those symbols. The more basic parts of algebra are called elementary algebra, and the more abstract types are called Abstract Algebra or modern algebra.
Algebraic Expression
Let us consider the pattern below. It has been created using marbles. Here we see that the first column has 2 marbles, the second column has 3 marbles, the third column has 4 marbles and so on.
Thus we observe that every new column increases by 1 marble. We can write the representation as
The number of marbles used in a column =
position of the column + 1
or as
the number of marbles used in a column = n + 1.
Here n represents the position of the column. So ‘n’ is an example for a variable that can take any value 1,2,3… so on. Thus n + 1 is the algebraic expression formed with n as variable and constant 1.
A variable is a number that does not have a fixed value. The picture and the list below show some real-life examples, where the value of a variable changes with the change in place and time.
- The temperature in different places also change.
- The height of a growing child changes with time.
- The speed of a car changes with time.
- The age of people keeps on increasing year by year.
Constant
The value remains fixed for specific numbers that represent quantities or ideas that will not change. For example, the date of birth of a particular person, the normal human body temperature and capacity of a given container.
Framing algebraic expressions with given conditions
Now we will see how to frame an algebraic expression. The rules are that variables are to be represented with alphabetic letters, say lower case a-z and constants in numeric form.
1. Amanda has 10 storybooks more than Alex. Express the number of storybooks Amanda has in terms of the number of storybooks Alex has.
Let the number of storybooks Alex has = y
Therefore the number of storybooks Amanda has = y + 10
2. Sweets from a big box are equally distributed in 10 small boxes. Express the number of sweets in one small box in terms of the total number of sweets.
Let x be the total number of sweets.
Number of sweet boxes = 10
Therefore, the number of sweets in one box is = x/10
Solving Equations
Let us see how practical applications of algebra can be used to solve equations. You will often see equations like 3x + 4 = 5, where you want to find x.
Consider a situation from our daily life.
The cost of a book is £5 more than the cost of a pen. Let us take the cost of the pen as £x. Then the cost of the book is £ (x + 5) . If the cost of the book is £20, what is the cost of the pen?
We know that the book’s cost is x + 5 and it is given that x + 5 = 20. This is an equation in the variable x.
A table is prepared as shown below for various values of x:
It is clear from the table that x + 5 = 20 only for x = 15. So, the cost of the pen is £15.
In general we say that x = 15 is the solution of the equation x + 5 = 20. This is the trial and error method where we substitute different values for the variable that satisfies the given equation.
An equation has two parts which are connected by an equal to sign. The two parts or sides of an equation are denoted as LHS (Left Hand Side) and RHS (Right Hand Side). If LHS = RHS we get an equation. 2x = 6 is an
algebraic equation, whereas 3x > 10 or 4x < 12 are not equations.
Solving an equation using the Principle of Balances
Consider the balance given in the figure.
Four circles balance one square and a circle on the other side. The idea is we have to find out how many circles will balance a square. If we remove the circle from the left pan, we have only the square there. Since we removed a circle from the left pan, we have to remove the circle from the right pan also. Then there will be three circles in the right pan.
Now the balance looks like the one shown on the right. This is called the principle of balances. Using balancing equations, we can solve equations in a systematic way.
Solve using the principle of balances:
Benjamin's mother is three times as old as Benjamin. If Benjamin's mother is 39 years old, find Benjamin's age.
Let Benjamin's age be x.
Benjamin’s mother's age 3x = 39
3x/3 = 39/3 {Dividing by 3 on both the sides }
So, Benjamin’s age = 13.
The same quantity can be added or subtracted to both sides of the equation. If the same amount is multiplied or divided on both the sides of an equation, it remains the same.
Forming an equation to find the unknown
Translating verbal descriptions into algebraic expressions is an essential initial step in solving word problems. So let’s see another real-life example in the form of a puzzle.
Detailed Solution:
Our first supposition is that Uma buys at least one ball of each kind. Now let’s say she buys x footballs, y cricket balls, and z table-tennis balls.
The question requires x + y + z = 100 [ 1 ]
It also requires 15 x + 1y + z/4 = 100 [ 2 ]Since we have 3 variables but only 2 equations we’ll have to use the trial and error method to get at the solution.
Let’s vary x the number of footballs and see what we get:
Suppose x = 1, then
y + z =99 and y + z/ 4 = 83z/4 = 14 3z = 56 z = 56/3 which is not a whole number.
Trying for x = 2 also fails and now
If x = 3, then z = 97 and y + z / 4 = 55 3z/4 =42 3z= 168 z = 168/3 = 56 which is a whole number!
And if z = 56 then y = 97 - z = 97 - 56 = 41
So the set of balls Uma buys is { 3 footballs, 41 cricket balls and 56 table tennis balls }
Algebra in Geometry
In Algebraic Geometry we study geometric objects and their assortment that are characterized by polynomial equations.
Examples of algebraic varieties’ most studied classes are plane algebraic curves, including lines, circles, parabolas, ellipses, hyperbolas. There are also cubic curves like elliptic curves and quartic curves like lemniscates and Cassini ovals.
In real life, algebraic geometry can be used to study the dynamics properties of robotics mechanisms.
Source: Pinterest
A robot can move in continuous space with an infinite set of possible actions and states. When the robot has arms and legs that must also be controlled and the search space becomes many-dimensional. Robot’s kinematics can be formulated as a polynomial equation system that can be solved using algebraic geometry tools.
Algebraic geometry is also widely used in statistics, control theory, and geometric modelling. There are also connections to string theory, game theory, graph matchings and integer programming.
Algebra in Computer Programming
The mathematical languages unite fields such as science, technology, and engineering into itself. That is why an individual intrigued by the field of computer programming and coding should figure out how to comprehend and control mathematical logic.
Strong comprehension of algebra incorporates characterizing the connections between objects, critical thinking with restricted factors, and analytical skill development to help execute decision making.
One such use of Algebra can be seen in Inference procedures used in Knowledge engineering. Variables and constant symbols are used as terms representing objects in real life.
The knowledge engineer adds a set of facts and specifies what is true, and the inference procedure figures out how to turn the facts into a solution to the problem.
Besides, because a fact is true regardless of what task one is trying to solve, knowledge bases can be reused for various tasks without modification.
Example for the task of inference
Take a sentence,
Everyone likes ice cream.
It is represented in First-order logic as
x Likes ( x, ice cream )
where x is the variable and is the universal quantifier that generalizes to all persons liking icecream.
If another sentence found in the knowledge base is as follows:
John likes ice cream
It is represented as Likes( John, ice cream)
The inference procedure will reason out from x Likes ( x, ice cream ) with the substitution {x/John} and infers Likes(John, ice cream) and concludes that John likes icecreams.
Biostatistics University of Florida
Other uses of algebra in programming are Ontology, error correction algorithms, Natural language processing, Neural networks, designing artificial intelligence programming languages such as LISP and PROLOG and theorem provers such as OTTER.
Algebra in Real Life
In real life there are a plethora of instances where Algebra is being used. It’s utility is being universally quantified in all walks of our lives. For instance, take a shopping domain where we need to be budgeted with the cart items and some algebraic formulation is applied.
The economy of every country is analysed with the help of economists taking the help of algebra to solve the problems related to debts or loans.
Tom Evans's ANALOGY program (1968) solved geometric analogy problems that appear in IQ tests such as the one shown below.
Source: Artificial Intelligence by Stuart Russell
The use of algebra is multipurpose, and it goes handy in every sphere of our lives. It isn't just mathematicians, however, even most academicians, educationists, researchers, and experts from all different backgrounds collectively
agree with the adaptability of algebra.
Real-World Applications of Linear Algebra
What is linear algebra.
Linear algebra is the branch of mathematics concerning linear equations such as linear maps and their representations in vector spaces and matrices.
The concept of classification can be simulated with the help of neural network structures that use a linear regression model. Here the training set is compared with the test data so that the learning algorithms generate outcomes to predict data related to decision making, medical diagnosis, statistical inferences, etc.
Applications
The most generally utilized use of linear algebra is certainly optimization, and the most broadly utilized sort of advancement is linear algebra. You can upgrade spending plans, your eating regimen, and your course to work
utilizing linear algebra, and this uniqueness starts to expose a lot of applications.
Other real-world applications of linear algebra include ranking in search engines, decision tree induction, testing software code in software engineering, graphics, facial recognition, prediction and so on.
In real life, algebra can be compared to a universally handy device or a sorcery wand that can help manage regular issues of life. Whenever life throws a maths problem at you, for example when you have to solve an equation or work out a geometrical problem, algebra is usually the best way to attack it.
Written by Jesy Margaret, Cuemath teacher
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13 Examples Of Algebra In Everyday Life
Almost every student exclaims “I’m never going to use this math in real life!” while solving algebraic equations. Isn’t it? However, this is not always the situation. We often see people using algebra in most aspects of daily life; for example- people in the market make use of algebraic operations to calculate profit and loss incurred. Just because we do not see any “X” or “Y” does not mean that algebra has failed to prove its existence; still, the real-life examples of algebra are uncountable. This precise and concise mathematical language entwines beautifully with almost all other subjects and even daily life.
The word “Algebra” comes from the Arabic word “al jabr,” which translates to “reunion of broken parts.” Muhammad ibn Musa al-Khwarizmi, a 9th-century Persian mathematician, geographer, and astronomer, is regarded as “the father of algebra.”
Let’s look into the examples of algebra in everyday life.
1. Early Life
In the early stages of development, an infant makes use of algebra to calculate trajectories and you might be surprised to know how! A 16-week baby can assess the direction of an object approaching and is even able to determine the position where the object will land. Babies easily estimate the distance between them and the toy and are also able to track the objects. What do you think is playing a role here? Of course, it’s Algebra! Even though the infants have no theoretical knowledge of algebraic operations, they can make efficient use of it.
2. Professional Advancement
In whatever field you want to strive ahead, algebra is going to be needed. When a student goes from school to college, chances are that algebra will find a way in whatever subject a student opts for. Most of the time, physical and chemical sciences employ the basics of algebraic equations. In the case of computer sciences, the algorithms are based on algebraic operations only. Moreover, algebra is involved in the field of art and architecture to calculate the correct proportions to put forth a masterpiece. Basic knowledge of algebraic operations also prepares a person for the work front.
3. Morning Routine
Right from the time a person wakes up in the morning, algebra comes into play. Take for example- a person has a meeting in the morning, what is that person likely to do? He/she will set up an alarm for waking up in the morning to get ready and assemble all the essential documents. What is happening here? The person knowingly or unknowingly makes use of algebra to calculate the time required to bathe, have breakfast or collect coffee, gather all important paperwork, and reach the office on time. Now, this particular situation involves time, money, and distance and their accurate calculations to make it to the meeting on time.
4. Making It To The Trash Can
How do you think you make a perfect shot at the trash can? Yes, you guessed it right! You apply algebra in this case as well. While aiming at the trash can, you unconsciously calculate the distance between yourself and the trash can, air resistance, the weight of the trash you want to throw away, the required trajectory, and the force required so that the piece of trash lands into the trash can. Your application of algebra while aiming at the trash can does not end here. You also estimate the strength of the nerve impulse which has to be sent to each muscle at the right time to contract or relax it. In case, you still miss your shot, you did not do your algebra well.
5. Business & Finance Management
Algebra is as crucial in business as in other fields. A business owner makes use of algebraic operations to calculate the profits or losses incurred. A business person will employ algebra to decide whether a piece of equipment does not lose it’s worthwhile it is in stock. Also, the business owner needs to calculate the lowest price at which an item can be sold to still cover the expenses. As for the people working in the finance area, exchange rates and interest rates are often represented algebraically; therefore, good knowledge of algebraic operations is necessary to carry out finances accurately.
Also, to understand the terms and conditions of a loan or an investment account, a sound knowledge of numbers, especially algebra, is required. Moreover, the growth in the business market is often exponential, which also requires a good knowledge of basic algebraic operations.
Algebra does not even leave behind sports to make use of it. If you look closely, the players of almost all sports, unintentionally, apply algebra. The cricketers can hit sixes only because they can calculate the force required to hit the ball and basketball players calculate the trajectory to score a point. Similarly, footballers calculate the force and distance to score a goal and sprinters estimate the speed required to cover the distance to reach the endpoint; therefore, every sport involves algebra in one way or the other.
Moreover, you might be surprised to know that even dogs employ algebra to calculate the time and distance to catch hold of a boomerang or a food morsel mid-air.
You might think that algebra has no role to play in the kitchen, especially while cooking. However, the truth might not be stranger to the kitchen or even cooking. Algebra finds its way while cooking, baking, measuring ingredients, etc. The ones who are beginners in the kitchen often consult recipe books while preparing a particular dish. The temperature in the recipe book might be given on a Celsius scale and one might have to convert it to other scales depending on the dial involved. Also, take the following example: while preparing Thanksgiving Dinner, the turkey has to be cooked as per its weight. Let’s say a turkey takes 24 hours per 5-pound to thaw and you have a 15-pound turkey in hand, how much time will the turkey take to thaw? You can very well calculate the same using algebraic operations.
8. Technology
Had it not been for algebra, you might not be having flat-screen TVs or smartphones. The computer games that you play endlessly, mobile phones that you use, and cars that you drive, it is because of the people who are adept at algebra that such situations are made possible. In algebra, specific numbers are replaced by symbols. While playing a computer game, you see a character; that character is nothing but a string of symbols. A computer programmer uses his knowledge of algebra to put forth a string of symbols. Also, a set of rules are followed to make the symbols interact in the right way which also requires algebra.
9. Logical Thinking
The study of algebra helps in logical thinking and enables a person to break down a problem first and then find its solution. Although you might not see theoretical algebraic problems daily, exposure to algebraic equations and problems at some point in life will train your mind to think logically. This ability to think logically will not only help you at home but also in your workplace and enable you to make mindful decisions at any time.
10. Home Improvement
Repairing and remodeling of homes require the knowledge of numbers. To get this job done efficiently, algebra is needed. The basics of algebra and numbers will help you in determining the amount of particular material required to get the desired project finished; for example- an electrician will figure out the number of electrical circuits, a tile installer will estimate the number of tiles required to cover the floor of a particular room, a painter will determine the quantity of paint required to paint the walls, and so on. In each example, you might have noticed that algebra is involved in one way or the other.
11. Health & Fitness
A knowledge of algebra can even prove beneficial for your health. While losing weight, you might have noticed that you first calculate your Body Mass Index (BMI), then watch out for food intake, and hence, monitor your calories. Now, the calculation of BMI is done with the help of some equations. Similarly, in case you want to calculate your body fat percentage, some other equations might be involved. It’s quite surprising that while on a weight-loss journey, several equations are helping you in one way or the other. In the gym, while lifting weights, a trainer determines the amount of weight that a person can lift depending upon the latter’s weight.
12. Outdoor Landscaping
Landscaping is yet another area that requires a person to not only be good with numbers but also with basic algebraic operations. While designing a planter box, you will notice that algebra is required. First, you will measure the length, breadth, and height of the box, you will calculate the volume, the amount of soil or manure required, and the underlying cost of this whole project. Undoubtedly, almost every step will involve some algebraic equations.
Suppose you just brought a new home and you want a pool in your backyard. What are you going to do? You will first calculate the area of your backyard and then you will determine in how much area you want your pool to be spread. Right? You might have observed that it is only with the help of some algebraic equations that you can carry out the aforesaid steps. After the determination the area of the pool, you will calculate the amount of water to fill in the pool and also the time which will be taken to fill the pool to its brim or half the volume; which again requires algebra.
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73 comments.
I’m sorry but this article has failed to give even the simplest practical use of Algebra. Catching and throwing balls is done with practice. You can’t say a small child is using something that they are not even aware of. Like common sense, this writer is not aware of it and no amount of Algebra is going to fix that.
I believe that these are ratios used in kitchen not Algebra.
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13 Common Examples & Applications of Algebra in Real Life
Last Updated on February 24, 2022 by Editorial Team
Do you know who is the father of Algebra? Well, it is Muhammad ibn Musa al-Khwarizmi, a mathematician. And do you know why he is called so? Because for the first time, he introduced a system of making calculations where the numbers were replaced by variables. He employed this system of calculating for the justified appropriation of property among heirs, to improve maps by enriching them with longitudinal and latitudinal data, and also for making contributions to trigonometry, geometry, geography, etc. So, if you are thinking about why to study Algebra, the answer will be – to become proficient in matters related to everyday life.
Here are some of the most common uses of Algebra in real life that can surely help you understand how it helps you do basic activities like throwing a ball into a basketball net or cooking with the correct amount of ingredients.
Common examples & applications of algebra use in daily life
You will be surprised to know that Algebra enters your life at a very early stage. Though unknowingly, Algebra use starts right at the kindergarten stage when the kids start playing. Let’s briefly overview the examples of Algebra by picking some common examples.
1. Catch the ball game played by 4-5-year-old kids
The concept of choosing the correct trajectory so that the ball reaches the hands of the receiver comes from a kid’s knowledge of Algebra. By making use of variables like force, angle, and speed, the thrower tries to find the correctness of the throw of the ball. They may not have realized it, but there is no denying the fact that algebra knowledge works behind the successful landing of a ball into the hands of a receiver.
Thus, a player can find the probability of scoring a point by doing these calculations in mind. If you are missing the target too often, the best option is to revisit the Algebra concepts and learn the needful.
2. Making a schedule of activities
When you are making a schedule of activities, you actually are dividing the whole day and summing up the times taken to complete the intended activities. So, the simple process of finding whether you will reach the office on time or not if you have chosen to set the alarm at 6 am, is an algebraic calculation that you do mentally. Hours, times taken in various activities, and some new unforeseen tasks are Algebraic variables in real life, that you have to work upon to be on time at the office or any meeting.
Scheduling is common to all. And, Algebra knowledge makes you the true master of your day because of which you know how to use variables and put them in an equation. Thus, you get all things done right and on time due to Algebra playing its role.
3. Preparing the food or doubling or halving the recipe
The kitchen is one of the places where Algebra is used in an interesting manner. Especially, when you are making items like cake, vegetable soups, etc, where the correct combination of the ingredients is very crucial, Algebra comes to your rescue and helps you find the correct quantity of ingredients to make the food sufficient for different sizes of servings.
All quantities of the ingredients and the number of servings make the variables. The cook uses Algebraic intelligence to ensure that not only the food is available in sufficient quantity, but also it is tasting great. Such is the extent of Algebra use in cooking!
4. A kid developing spatial intelligence
When kids have just started to learn to walk or stand, they need to find the safe height or distance of any object that they can choose to rely upon for standing or walking. Even while using a walker, they are actually using Algebra mentally to find how far the walker will take them before hitting any object, by propelling it at a particular speed. Similarly, Algebra comes into action when the kid is trying to find whether the shape of an object is wieldable or not.
Also, Algebra is there in action when the kids are trying to play spatial reasoning games. They visualize the shapes and patterns and solve puzzles only because of certain Algebraic equations that they may come to know about in later stages of their education. So, though without cognition, kids gather spatial intelligence by applying Algebra.
5. Finding the tax liability
On growing up as an adult, people work to earn. They may require to find their tax liability. The process involves doing calculations like finding the tax rebate cap and proportioning the earnings to find how the income is to be divided into various investment options.
This process of finding tax liability is based on doing algebraic calculations where the variables are income, the qualifying amount for the rebate, etc. Algebra helps the workers to structure their income and expenses and get the taxable salary figure in hand.
6. Astrological calculations
Astrologers predict various events on the basis of planetary movements. they try to establish the relationship between the planet’s revolution speed, its position after a period of chosen duration, and so on.
All these calculations are nothing but Algebra whose concept of linear or quadratic equation balancing comes into play when these predictions are made. The Father of Algebra mentioned in the first half of this section did make use of Algebra to contribute to various findings related to astronomy and astrology in his time.
7. Technological developments
Any innovations around us could not be possible without Algebra. If you decode the functioning of an LED TV and dig into its internal atmosphere, you will find that these TVs are making use of planes, angles, and axes as variables and apply algebraic concepts in the development of various types of screens.
Thus, developmental aspects are a sum total of the materials and their placement within the TV’s environs, allowing users to have a variety of monitors, and other functionalities. The variations in monitor sizes without the problem of distortion of the picture are achieved with the help of Algebra knowledge that allows designers to fiddle with a variety of dimensional options.
8. Budgeting
Running a family’s or business’s expenses involves a budgeting process. We all are budget planners in some or the other capacity.
And, apparently, we make use of Algebra in structuring the budget so that all expenses, intended investment aims, and the overall cash in hand can be fixed and altered.
The changing conditions like inflation, an increase in the number of family members, etc. are the variables that remind of algebraic calculations. This is when you may appreciate the learning of Algebra, and its use in daily life.
9. Shopping
Who doesn’t love shopping? It is the most common activity that anybody does. And, it does involve Algebra quite deeply. Though you may not realize that you have used it, the fact still holds true.
For example, when you are trying to find the correct quantity of purchase of rice, you try to find its per pound cost to know about the real savings you are likely to make. Similarly, when you are choosing between various weights of the product and trying to match them with the appropriate vehicle that could carry it comfortably, you are making use of Algebra in a real-life situation.
10. Doing Interiors and Landscape designing
Not only interiors planning or landscape designing, in fact, but the whole of Architecture stream employs Algebra. When the designers are trying to find the correct elevation or try to arrive upon the collection of things required to do a space, they make use of data like measurements of the space and that of the items to fit in.
This is the Algebra use in real life that helps to understand how things are going to amplify the looks of the space and will contribute to the overall appearance of the space.
Similarly, in an office environment, the decisions like moving to larger spaces to accommodate people or designing cabins are some of the premises where Algebraic calculations come into play.
11. Computer Programming
While coding, the programmer is making use of datasets, strings, and variables. They assign conditions in the use of these strings and establish relationships, which ultimately result in an action on the front end.
This activity of coding, assigning values, and pre-defining the functions is actually you applying the knowledge of Algebra that helps you create the codes that work amazingly and help you meet your coding objectives.
Computer programming is done mostly in terms of data sets and variables. The conditions become the variable and the front end result is the outcome. Establishing a relationship between the two is Algebra happening in your mind.
12. Real Estate Project Planning
Realtors have to find various factors like time, labor hours, the number of people required, and of course, the money needed, to find if the project is going to be available for possession in time or not.
All these factors like labor hour vs. total project time, labor cost, etc. are actually the Algebraic variables, which the realtors apply in the equations to find the meaningful and crucial outcomes like overall profits or losses to expect from the project and other surrounding issues. Algebra can help them prepare for contingencies too.
13. Professional Sports
Sports is one profession where various departments employ Algebra. A sports analytics department works on data like Player form, weather conditions, home ground or foreign ground, etc. that are quite similar to Algebra variables. Using the Algebraic expressions, the possibility of who has higher chances of winning is predicted. Players also are doing little Algebra in their minds when they are strategizing on how to score a goal. When they choose a certain shot, it is because of Algebra that they are able to convert it into a goal.
Not only the outdoor sports, but the indoor games like Carrom, and various card games utilize the concepts of Algebra throughout the gameplay. When you are trying to make a winning hand, it is the Algebraic calculation of hands value that determines the probable outcome. Similarly, the use of Algebra decides how a carrom player is going to score on any board.
Wrapping Up,
Algebra is your trusted tool that helps you carry out various activities of daily importance. There is hardly any line of work that does not employ the concept of Algebra. So, next time, when you look at the variables and equation, you surely will not be wondered about why you need to learn these. In a nutshell, Algebra prepares you for handling all aspects of life and stays with you right from your infanthood to your adulthood.
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Algebra in Everyday Life
We use algebra quite frequently in our everyday lives, and without even realizing it! We not only use algebra, we actually need algebra, to solve most of our problems that involves calculations.
Examples of using algebra in everyday life
Here are some simple examples that demonstrate the relevance of algebra in the real world.
Going shopping
`(text(10 items))/(text (3 items/bag))` = `3.33` bags ≈ `4 bags `, explanation :.
The figure below illustrates the problem: The different shapes inside the bags denote different items purchased. The number depicts the item number.
We use simple algebraic formula `x/y` to calculate the number of bags.
x = Number of items purchased = 10
y = Capacity of 1 bag = 3
`10/3` = `3.33` bags ≈ `4` bags
So,we need 4 shopping bags to put 10 items.
Calculating grocery expense
The figure below shows the three items in different shapes and colors.
This will help your mind to calculate faster.
We will use algebra to solve the problem easily and quickly.
The prices are
a = Price of two dozen eggs = $10
b = Price of one bread = $5
c = Price of one bottle of juice= $8
=> Money needed = a + 3b + 5c
=> Money needed = $10 + 3($5) + 5($8) = $10 + $15 + $40 = $65
Filling up the gas tank
`5 ` gallons.
In the below diagram, each block represents $1, and each row is a bundle of $3, which is used to buy 1 gallon of gas.
We use simple algebraic formula,`x/y` to calculate the total gallons that can be bought.
x = Money in your pocket= $15
y = Price of 1 gallon of gas= $3
`($15)/($3)` = 5 gallon
So, with $15 we can buy 5 gallons of gas.
Word problems
Life's many problems are disguised in the form of math equations, and if we know the math, it's fairly simple to solve those problems.
Find three consecutive numbers whose sum is 216.
71, 72 and 73.
1. Understand the problem
The task is to find three consecutive numbers whose total is 216.
2. Write the variable
Let "`x`" represent the first number
So, `x` = first number
`x+1` = second number
`x+2`= third number
3. Write the equation
When you add up all the numbers, you are supposed to get 216
`x + (x + 1) + (x + 2 )`= 216
`3x + 3 `= 216
4. Solve the equation
Subtract 3 from both sides
`3x + 3 - 3 `= 216 - 3
`3x ` = 213
Divide each side by 3
`(3x) / 3 `= 213 ÷ 3
5. Check your answer
First number + Second number + Third number = 216
`x + (x + 1 )+ (x + 2)`
71 + (71 + 1) + (71 + 2)
71 + 72 + 73 = 216
So the three numbers whose sum is 216 are 71, 72 and 73
A group of 5 boys goes to the theatre for an evening show. The total cost of ticket is $55 and popcorn is $25. What is the cost per person?
A group of 5 boys goes to the theatre. The cost of ticket and popcorn is $55 and $25 respectively. What is cost per person?
Let’s say, `x` = cost of ticket/person and `y` = cost of popcorn/person
If 5 tickets cost $55, then cost of one ticket is,
`x ` = `55 / 5`
If 5 bags of popcorn cost $25, then the cost of each bag is,
`y ` = `25 / 5`
Total cost of the movie (ticket + popcorn) per person = `x + y `
Cost of ticket/person
`x` = `55 / 5`
Cost of popcorn/person
Cost of ticket/person + Cost of popcorn/person = Total cost
11 + 5 = 16
If we add up 16 five times (since there are 5 boys), the result is,
16 + 16 + 16 + 16 + 16 = 80
$80 is the total cost.
The area of a rectangle is 72`cm^2`, in which the width is twice its length. What is the dimension of the rectangle?
the length is 6 cm and the width is 12 cm.
The area of a rectangle is 72 cm. The width is twice its length. What is the length and width of the rectangle?
Let "`x`" be the length and "`2x`" be the width
Length `×` Width = Area
`x ` x `(2x)` = `2x^2 `= Area
`2x^2` = Area
`2x^2` = 72
`x^2` = `72 / 2`
`x ` = Length
So, the length is 6 cm
The width is twice its length
`2x` = 2 x 6 = 12
So, the width is 12 cm
The length is 6 cm and width is 12 cm
The perimeter i.e. the distance around the edges is the sum of lengths and widths. Since rectangle has two lengths and two breadths hence the equation is,
2 x (length + width)
2 x (6 + 12) = 2 x 18 = 36 cm
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14 Real Examples of Algebra in Everyday Life | Free PDF
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Algebra in Real Life
Be honest. When you were in middle school and high school, trying to learn algebra, even if you didn’t say it out loud, you thought it. “I’m never going to use this in real life!” Guess what? We do use algebra. Sure, not all parts, every day.
But, algebra is everywhere. In fact, it’s so common that you might not even realize it’s there. Algebra shows up in all kinds of places, from paying bills to balancing a checkbook to reading a price tag at the grocery store.
It’s easy to take these everyday activities for granted, but an understanding of the basics—and the additional details that come with them—can make life much easier in the long run. So what is algebra? And how can you use this knowledge every day? Here are a few examples of algebra that you might not be aware of.
What even is algebra?
Algebra is defined as “the part of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulae and equations.”
One of the more common applications of algebra is high school math. High school algebra helps students learn how to use equations and graphs to solve problems, so they can get a better understanding of what their answers mean.
At its core, high school algebra focuses on two major concepts: linear equation solving and quadratic equation solving.
Linear equations are used to solve for one variable while quadratic equations are used to solve for two or three variables.
You might recall using linear equations when you were in middle school or ninth grade, but this is just a small taste of the types of problems that high school algebra can help you with.
We may not always use a computer or pen and paper to document these algebraic equations or algebraic expressions, but they take place in our brains. So often we are using algebra in the real world or everyday life, and we’re not even thinking about it.
In high school, we were given boring word problems or math problems, and we all thought it was a waste of time, right?
In addition to the examples below, we use algebra all the time–at the grocery store, the home improvement store. We all have everyday problems to figure out, so, enter algebra!
Small Business : As a small business owner, I use algebra all the time to figure out my annual and monthly expenses. Some vendors that I use give me a significant discount for paying annually, but I still have to figure out the monthly costs.
Showing our Dogs Some Love : Paying bills is an unfortunate part of life, but it doesn’t have to be difficult. If you’re constantly balancing your checkbook and always seem to spend more than you make on your dogs, try using algebra.
You can create equations and total up costs of owning a dog. Figure out how much you spend on toys, treats, food and vet bills each year. Then divide that by months (12) to figure out what you are truly spending. How does that figure into your household budget? Adjust and adapt as necessary, to shower your dog with treats and love , but not overdraw your bank account.
Buying School Supplies : When children are preparing for school, they often find it difficult knowing how much they’ll need for clothes, school supplies, and books. If they want to get through the school year without going over their budget, they can use algebra too!
You could even teach them how to figure out how many items they need based on their size before buying clothes or supplies from the store. This will help them stay within budget while still having fun shopping with Mom or Dad
Kobe: The late beloved Kobe Bryant was well known to shoot trash in his trash can and socks in his hamper, dreaming of NBA days as a kid. Kobe was also well known to be highly intelligent, and likely used algebra to calculate those shots. When he was aiming at the trash can, he likely calculated the distance between himself and trash can, possible air resistance, the weight of the paper or sock, required trajectory or path, and the force required so that the item would land into the trash can or hamper. No, he likely did not write this down, formulate it and figure it out on paper first.
These are split-second calculations that go on in our heads without even consciously thinking about it. And when the paper or sock lands on the floor instead of our intended target, we recalculate and try again. Algebra!
Planning Your Summer Vacation : If you’re planning your summer vacation, you might want to prepare for gas prices beforehand. Using algebra again can help you save some money on gas by estimating how much gas costs per mile traveled at different speeds for up-to-date prices near your destination city or state rather than waiting until you arrive at the airport or train station and cross fingers that gas prices haven’t gone
Getting Ready for School : When we are leaving for school or work in the morning, we all have things we need to do first. Shower, dress, bathroom stuff, eating, packing lunches, feeding pets…some days the list seems endless!
But, you can use algebra and create a formula to determine exactly how much time you need in the morning to get out the door on time.
Paying your bills : An example of this is balancing a checkbook, or paying your bills. When you get to the end of the month and have to pay your bills, you need to divide up all of the money that you’ve accumulated into individual checks for each bill.
You might be able to save some money by making larger payments on certain bills, but if you don’t make enough money by splitting it evenly among them, then you’ll need to do more work. This is where algebra comes in handy.
You can use algebraic equations in order to figure out just how much each bill will cost and how much you can afford. If it turns out that there’s not enough money left over for certain bills, then you’ll want to talk about possible solutions with your family members and adjust your spending habits.
If you want to take it a bit further, you can call different utility providers and ask for the lowest prices for things like phones, electricity, water and sewer. Calculate how much your family uses, and how you might save money if you switched.
Sports and Algebra
Algebra appears in sports all the time!
Using the Kobe example above, it’s not necessarily something we consciously use or plot out on paper every time.
Sports Coaches : Whether you’re hitting a ball with a bat, serving a volleyball with your hand, shooting a basket or hopefully throwing that game winning touchdown….you’re using algebra. And, the best coaches know how to break it down and adjust for winning skills.
Baseball Cards : Have a card collector at home? I do! He collects basketball and football cards. There are all kinds of things you can do to monitor your card spending and card collection value using algebra. Sometimes my tween struggles to understand that he’s not always going to see the money-value return on the cards that he spends. Or, he overestimates how much his collection is worth.
You can do both with algebra. Keep track of how much you’re spending on sports cards, and separately keep track of how much your more valuable cards are worth. Using formulas, you can determine your gains and losses as you collect sports cards and memorabilia. But, hey, can’t put a price on fun and passion.
Your Savings Account : Your checking account balance is $50,000. What percent of your money do you have saved? What are your monthly expenses, and are you on track for retirement? How much do you need to save going forward to hit your target retirement date?
Other Algebraic Examples
- You want to know how much it would cost for two people to go on a vacation but don’t have enough money.
- You’re calculating how many ounces of ice cream you need to buy for an ice cream party you’re having.
- You’re preparing your taxes and want to know the total tax owed after fees and credits are applied.
- You’re working at a job that pays based on commission, so your paycheck depends on how many sales you make during the day.
Everyday Algebra Examples
So, the next time your child or student tells you, “I’m never going to use this!” you can give so many examples of how we are using algebra and math knowledge to solve many everyday problems.
Algebra and Learning Disabilities
It’s important to note that if a child has some learning disabilities, they likely will struggle with algebra. And I’m not just talking about tests for dyscalculia . There are many skill deficiencies that will affect algebraic thinking.
Algebra requires:
- Visualizing and application
- abstract thinking
- executive functioning
And much more. If a child is really struggling to grasp algebraic concepts, you may want to consider assessing their executive functioning skills . A student who lacks any of those skills will struggle with not only learning algebra, but applying it to everyday life.
Linear Relationships Printable
Here you go–some basic algebra linear equation worksheets
Lisa Lightner is an award-winning and nationally-known Special Education Advocate and Lobbyist who lives in suburban Philadelphia. She has or is serving on the Boards of numerous disability and education related organizations including the Epilepsy Foundation and PA Education Voters. She also has testified before State House and Senate committees relating to special education issues and education funding issues.
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