What is Doing the Same to Both Sides?

S1-SA5-1192

Grade Level:

Class 5

Maths, Computing, AI, Physics, Logic

Definition

What is it?

Doing the same to both sides means performing the exact same mathematical operation (like adding, subtracting, multiplying, or dividing) on both sides of an equation to keep it balanced. This rule helps us find the value of an unknown number while making sure the equation remains true.

Simple Example

Quick Example

Imagine you have a weighing scale with 5 ladoos on one side and 'x' ladoos plus 2 ladoos on the other side, and it's perfectly balanced. If you add 3 more ladoos to the first side, you must also add 3 ladoos to the second side to keep the scale balanced. This is doing the same to both sides.

Worked Example

Step-by-Step

Let's solve for 'x' in the equation: x + 7 = 15

1. Our goal is to get 'x' by itself on one side of the equation.
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2. We have '+ 7' with 'x'. To remove '+ 7', we need to do the opposite operation, which is subtracting 7.
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3. Subtract 7 from the left side: (x + 7) - 7
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4. Since we subtracted 7 from the left side, we MUST also subtract 7 from the right side: 15 - 7
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5. Now the equation becomes: x + 0 = 8
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6. So, x = 8.

Answer: x = 8

Why It Matters

This fundamental rule is crucial for solving equations in Maths, which forms the basis for understanding how computers process information (Computing), how AI models learn, and how physical laws are described (Physics). Engineers and data scientists use this every day to build amazing technology.

Common Mistakes

MISTAKE: Only performing the operation on one side of the equation. For example, in x + 5 = 10, only subtracting 5 from the left side (x = 10). | CORRECTION: Whatever operation you do to one side, you must do the exact same to the other side to maintain balance. So, x + 5 - 5 = 10 - 5, which means x = 5.

MISTAKE: Using the wrong inverse operation. For example, to remove '+ 3', a student might multiply by 3 instead of subtracting 3. | CORRECTION: Always use the inverse operation: addition undoes subtraction, subtraction undoes addition, multiplication undoes division, and division undoes multiplication.

MISTAKE: Making calculation errors after applying the operation. For example, in 2x = 10, dividing both sides by 2 but writing x = 4 instead of x = 5. | CORRECTION: Double-check your arithmetic after performing the operation on both sides to ensure accuracy.

Practice Questions

Try It Yourself

QUESTION: If you have y - 3 = 9, what should you do to both sides to find 'y'? | ANSWER: Add 3 to both sides.

QUESTION: Solve for 'a': 4a = 20 | ANSWER: Divide both sides by 4. So, a = 5.

QUESTION: Your mobile data plan gives you 15 GB per month. You have already used 8 GB. If 'd' is the data remaining, write an equation and solve for 'd' using the 'doing the same to both sides' rule. | ANSWER: Equation: d + 8 = 15. Subtract 8 from both sides: d + 8 - 8 = 15 - 8. So, d = 7 GB.

MCQ

Quick Quiz

Which operation should be done to both sides of the equation x / 5 = 6 to solve for x?

Add 5

Subtract 5

Multiply by 5

Divide by 5

The Correct Answer Is:

To undo division by 5, you need to multiply by 5. Whatever you do to one side, you must do to the other to keep the equation balanced.

Real World Connection

In the Real World

When a chef is balancing a recipe, say for making chai, if they increase the amount of milk, they also need to increase the amount of tea and sugar proportionally to keep the taste balanced. Similarly, when engineers design a bridge, they use equations that must remain balanced. If they add more weight to one side, they must add support to the other side to prevent collapse. This principle ensures stability in everything from cooking to construction.

Key Vocabulary

Key Terms

EQUATION: A mathematical statement showing that two expressions are equal, usually with an '=' sign. | BALANCE: To keep both sides of an equation equal in value. | OPERATION: A mathematical process like addition, subtraction, multiplication, or division. | UNKNOWN: A quantity whose value is not known, often represented by a letter like 'x' or 'y'. | INVERSE OPERATION: An operation that reverses the effect of another operation (e.g., addition is the inverse of subtraction).

What's Next

What to Learn Next

Great job understanding how to balance equations! Next, you can explore solving equations with multiple steps or variables on both sides. This will build on the balancing rule you just learned and help you tackle even more complex problems.