Mathematics has various branches and one of them is “ Algebra”. Algebra uses letters and symbols, known as variables, to represent a number. It helps to determine problems or equations in mathematical expressions. Any expression with one or more variables is considered to be an algebraic expression.
An algebraic expression is a mathematical statement that shows the relationship between two or more variables. It is a combination of variables, constants, and mathematical operations, such as addition, subtraction, multiplication, and division.
Algebraic expressions are used to represent real-life situations where the value of one or more variables is unknown or can be any numerical value. These expressions allow us to analyze and understand complex situations by using mathematical relationships.
Let’s check out some examples to understand the essence of algebra in simple as well as complex situations
Intriguing examples of real-life use of algebraic expressions
A lot of times, algebra, geometry, and arithmetic leave an individual perplexed. However, all these three are very different in nature from one another. Numerous disciplines, including physics, engineering, and economics, use algebraic expressions in their fields. But, we also use algebraic expressions to resolve problems in our everyday lives. Here are ten instances of real-world algebraic expressions you might wonder unknowingly using all day :
1. Finding a distance covered by a car
Considering you are traveling at 60 mph at “x” time and you have covered y distance. The distance traveled by car can be represented by the expression of the distance formula if d is equal to velocity multiplied by time ie y= x multiply 60. If your x is 1-hour y will be 60kms.
2. Finding the run rate of a cricket match
You were watching a cricket match. Think of a cricket game in which the Indian team scores are y and over are x. To find the assumption of the run rate in the next over you will use the algebraic expression run rate = y/x.
3. Calculating daily expenses
Let’s take a more relatable example. Remember, we go to the store, we often need to find the total cost of our purchases. To do this, we need to use algebra to figure out how much money we will spend on each item. Taking a, b, and c as different products and the quantity you need is 2, 3, and 5 then you need 2a, 3b, and 5c products.
You add the real cost of all to find: 2a + 2b +5c = Total bill
Similarly, if The total cost of these x items at a cost of $5 it will be represented by the algebraic expression: The total cost will be 5x
4. The cost of renting a flat
Your friend has to rent a flat in a building for some days and the monthly rent is 10,000. Your friend need help to find per day cost of living for the next 150 days. Here per day can be represented by the expression: x= 10,000/ 150 and your x will be 66.6.
5. Find the amount of money earned in a day
You are a daily part-timer. You need to find out how much you will earn in a day. As your manager said you will be provided with 5000 bucks. The amount of money earned in a day can be represented by the expression:
Money earned = 10x + 5.
In the expression, the amount of money earned in a day, where “x” is the number of tasks completed and “Money earned” is the total amount of money earned. The constant 10 represents the amount of money earned for each task completed, and the constant 5 represents a fixed amount of money earned every day, regardless of the number of tasks completed.
6. Assuming total loan with the interest
The amount of money a person has after investing $1000 at an interest rate of 5% for 3 years can be represented by the algebraic expression:
1000(0.05)^3 = amount of money
The expression calculates the amount of money a person has by first calculating the interest earned on the initial investment of $1000. The interest rate of 5% is expressed as a decimal by dividing the interest rate by 100 (0.05 = 5/100). The expression then raises the decimal representation of the interest rate to the power of 3 to account for the 3 years of interest.
7. Painting a wall in the room
Imagine You Want to paint the walls of your room and you need to calculate how much paint you need. The amount of paint needed to cover a wall can be represented by the expression
A = (w * h)/a
where “A” is the amount of paint, “w” is the width of the wall, “h” is the height of the wall, and “a” is the coverage area of the paint.
8. Calculating the tip in a restaurant
You are in a restaurant, you received a bill of 300 bucks and now you have to tip 10% of the bill to the waiter. The tip x would be x= 300 * 10% which will be 30 bucks! Bingo that’s simple.
9. Finding the area of the plot
To find the area of your plot, we consider the area to be x, and we know length y is 2 times the width. The area of a rectangular field can be represented by the expression:
Area = Length * Width. ( x= 2y* y)
10. Finding the time that would be required to complete a task
Another way that we use algebra in our lives is when we are trying to figure out how much time it will take us to do something. The amount of time it takes to complete a task can be represented by the expression:
Time = 60 x + 30.
For instance, if task “x” takes 60 minutes to complete at a rate of 1 task per hour, and it takes an additional 30 minutes to set up or clean up, the total time required to complete the task would be 60 minutes + 30 minutes = 90 minutes.
In conclusion, an algebraic expression is a powerful tool that can be used in a variety of ways in real life. This allows us to represent and solve problems in a concise and efficient manner. This is perhaps the most important benefit of algebraic expressions in real life. By understanding how to manipulate algebraic expressions, we can solve all sorts of problems, from simple arithmetic to complex physics equations. At the same time, using algebraic tiles in the form of activities, DIYs, games, etc can help with a better understanding of the concept as a whole.
Furthermore, we use algebra to represent the relationship between two variables in a real-world situation. By representing a situation in a mathematical way, we can break it down into smaller, more manageable pieces. This can make it easier to see how the different parts of the situation interact with each other.