What is Subtracting from Both Sides?

S1-SA5-0139

Grade Level:

Class 4

All STEM domains, Finance, Economics, Data Science, AI, Physics, Chemistry

Definition

What is it?

Subtracting from both sides means taking away the same amount from both sides of an 'equals' sign in a mathematical equation. We do this to keep the equation balanced, just like a weighing scale. This helps us find the value of an unknown number.

Simple Example

Quick Example

Imagine you have 5 laddoos and your friend has 5 laddoos. If you eat 2 laddoos, your friend also eats 2 laddoos to keep things fair and equal. In math, if you have 'x + 2 = 5', and you want to find 'x', you subtract 2 from both sides to keep the balance.

Worked Example

Step-by-Step

Let's say Rohan has some cricket cards (let's call this 'x') and his father gives him 7 more cards. Now Rohan has a total of 20 cards. How many cards did Rohan have initially?

Step 1: Write down the problem as an equation.
x + 7 = 20

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Step 2: To find 'x', we need to remove the '+ 7' from the left side. To do this, we subtract 7.
x + 7 - 7 = 20

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Step 3: Remember, whatever you do to one side, you must do to the other side to keep the equation balanced. So, subtract 7 from the right side too.
x + 7 - 7 = 20 - 7

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Step 4: Simplify both sides.
x + 0 = 13

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Step 5: So, x = 13.

Answer: Rohan initially had 13 cricket cards.

Why It Matters

This concept is fundamental for solving almost any equation you will encounter in higher classes. It's crucial for understanding how to balance budgets in finance, calculate distances in physics, or even design algorithms in computer science. Engineers, scientists, and economists use this every day to solve problems.

Common Mistakes

MISTAKE: Subtracting only from one side of the equation. For example, x + 5 = 10 becomes x = 10 - 5 (subtracting only from the right). | CORRECTION: Always subtract the same amount from BOTH sides to maintain equality. If you subtract 5 from the left, you must subtract 5 from the right.

MISTAKE: Subtracting a different number from each side. For example, x + 3 = 7 becomes x = 7 - 2. | CORRECTION: The number you subtract must be exactly the same on both sides of the equals sign.

MISTAKE: Getting confused when the unknown (x) is on the right side. For example, 15 = 5 + x, and then subtracting 15 from both sides. | CORRECTION: Identify the number connected to 'x' (in this case, 5) and subtract that number from both sides. So, 15 - 5 = 5 + x - 5.

Practice Questions

Try It Yourself

QUESTION: Solve for 'y': y + 12 = 30 | ANSWER: y = 18

QUESTION: The price of a chai (P) plus a samosa (Rs 15) is Rs 40. What is the price of the chai? Write an equation and solve it. | ANSWER: P + 15 = 40; P = 25. The chai costs Rs 25.

QUESTION: If 25 + m = 50, and then 5 more is added to 'm' on both sides, what will be the new equation and the value of 'm'? | ANSWER: The new equation will be 25 + m + 5 = 50 + 5, which simplifies to 30 + m = 55. If 25 + m = 50, then m = 25.

MCQ

Quick Quiz

Which operation should be performed to solve for 'k' in the equation: k + 9 = 21?

Add 9 to both sides

Subtract 9 from both sides

Multiply both sides by 9

Divide both sides by 9

The Correct Answer Is:

To isolate 'k', we need to undo the '+ 9'. The opposite of adding 9 is subtracting 9. To keep the equation balanced, we must subtract 9 from both sides.

Real World Connection

In the Real World

When you manage your monthly mobile data, if you start with 'X' GB and use 5 GB, and now you have 10 GB left, you can use 'X - 5 = 10' to find out your initial data. Or, if you are tracking your spending using a UPI app, and you want to know how much money you had before buying groceries for Rs 500, this concept helps you figure it out quickly.

Key Vocabulary

Key Terms

EQUATION: A mathematical statement showing two expressions are equal, separated by an equals sign (=) | BALANCE: To keep both sides of an equation equal in value | UNKNOWN: A quantity whose value is not known, often represented by a letter like 'x' or 'y' | ISOLATE: To get the unknown variable by itself on one side of the equation

What's Next

What to Learn Next

Great job understanding how to subtract from both sides! Next, you should learn about 'Adding to Both Sides'. It's another important technique that uses the same balancing idea, but for different types of equations. Mastering both will make you a pro at solving basic algebra problems!