What is Multiplying Both Sides?

S1-SA5-0140

Grade Level:

Class 4

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

Definition

What is it?

Multiplying Both Sides means multiplying the same number on both sides of an equal sign in an equation. This keeps the equation balanced, just like a weighing scale remains balanced if you add the same weight to both sides.

Simple Example

Quick Example

Imagine you have a small box of ladoos, and you know that 'x' ladoos are equal to 5 ladoos (x = 5). If you decide to double the number of ladoos on one side, you must also double the ladoos on the other side to keep the equation true. So, if you multiply 'x' by 2, you must also multiply '5' by 2.

Worked Example

Step-by-Step

Let's say a cricket team scored 'y' runs in the first inning. We know that y / 3 = 10. We want to find out how many runs 'y' is.
---
Step 1: Write down the equation: y / 3 = 10
---
Step 2: To get 'y' alone, we need to remove the division by 3. The opposite of dividing by 3 is multiplying by 3.
---
Step 3: Multiply BOTH sides of the equation by 3: (y / 3) * 3 = 10 * 3
---
Step 4: Simplify both sides: y = 30
---
So, the cricket team scored 30 runs in the first inning. If you put 30 back into the original equation (30 / 3 = 10), it is true.

Why It Matters

Multiplying both sides helps us solve equations and find unknown values in many real-life situations. Engineers use it to design buildings, and scientists use it to understand how things work. Even in finance, people use this idea to calculate investments and profits.

Common Mistakes

MISTAKE: Multiplying only one side of the equation. For example, in x/2 = 5, writing x = 5 * 2 but not multiplying the left side. | CORRECTION: Always multiply the same number on BOTH sides of the equal sign to keep the equation balanced.

MISTAKE: Multiplying by the wrong number. For example, in x/4 = 3, multiplying by 3 instead of 4. | CORRECTION: Multiply by the number that will 'undo' the operation on the side with the variable. If it's x/4, multiply by 4.

MISTAKE: Forgetting to multiply all terms on one side if there's more than one term. For example, in (x+1)/2 = 5, only multiplying x by 2. | CORRECTION: When multiplying a side with multiple terms, use brackets to ensure the multiplier applies to *everything* on that side, like (x+1)/2 * 2.

Practice Questions

Try It Yourself

QUESTION: Solve for 'a': a / 5 = 7 | ANSWER: a = 35

QUESTION: If the price of 4 samosas is 'p' rupees, and we know that p / 2 = 25, what is the total price 'p'? | ANSWER: p = 50 rupees

QUESTION: A car travels 'd' kilometers in 3 hours. If d / 3 = 40 km/hr, what is the total distance 'd' traveled by the car? | ANSWER: d = 120 km

MCQ

Quick Quiz

If x / 6 = 4, what should you do to find the value of x?

Add 6 to both sides

Subtract 6 from both sides

Multiply both sides by 6

Divide both sides by 6

The Correct Answer Is:

To undo division by 6, you must multiply by 6. Doing this on both sides keeps the equation balanced and helps solve for x.

Real World Connection

In the Real World

When a chef is scaling up a recipe, if a recipe calls for 'x' cups of flour to make 10 rotis, and the chef wants to make 30 rotis (3 times more), they must multiply 'x' cups by 3. This ensures all ingredients are scaled correctly to keep the taste balanced, just like multiplying both sides of an equation.

Key Vocabulary

Key Terms

EQUATION: A mathematical statement showing two expressions are equal, usually with an '=' sign | VARIABLE: A letter (like x or y) that represents an unknown number | BALANCE: To keep both sides of an equation equal in value | SOLVE: To find the value of the unknown variable in an equation

What's Next

What to Learn Next

Great job understanding how to multiply both sides! Next, you can learn about 'Dividing Both Sides'. It's another important step in solving equations and will help you tackle even more complex problems.