What is Adding to Both Sides of an Equation?

S1-SA5-1193

Grade Level:

Class 5

Maths, Computing, AI, Physics

Definition

What is it?

Adding to both sides of an equation means performing the same addition operation on both the left side and the right side of the 'equals' sign. This keeps the equation balanced, just like a weighing scale, ensuring that both sides remain equal in value.

Simple Example

Quick Example

Imagine you have a cricket match score: Team A has 100 runs and Team B also has 100 runs. If Team A scores 5 more runs, to keep the scores equal (in your imagination), Team B must also score 5 more runs. So, 100 + 5 = 100 + 5.

Worked Example

Step-by-Step

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

Step 1: Our goal is to get 'x' by itself on one side of the equation.
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Step 2: To remove the '- 7' from the left side, we need to add 7.
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Step 3: Since we added 7 to the left side, we must also add 7 to the right side to keep the equation balanced. So, x - 7 + 7 = 15 + 7
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Step 4: Simplify both sides. On the left, -7 + 7 becomes 0, leaving 'x'. On the right, 15 + 7 becomes 22.
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Step 5: The equation now becomes x = 22.
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Answer: x = 22

Why It Matters

This concept is fundamental for solving problems in Maths, Physics, and even Computing. Engineers use it to calculate forces, AI developers use it in algorithms, and scientists use it to understand data. Mastering this helps you build a strong foundation for future studies and exciting careers like a Data Scientist or an ISRO Engineer.

Common Mistakes

MISTAKE: Adding a number to one side but subtracting it from the other side. | CORRECTION: Always perform the exact same operation (e.g., add 5) on both sides of the equation.

MISTAKE: Forgetting to add to the constant term on the other side, only adding to the variable term. | CORRECTION: Remember that the number you add must be added to the entire side, affecting all terms.

MISTAKE: Adding a number that doesn't cancel out the existing term next to the variable. | CORRECTION: To isolate the variable, add the opposite of the number currently with the variable (e.g., if it's -3, add +3).

Practice Questions

Try It Yourself

QUESTION: Solve for 'y': y - 9 = 12 | ANSWER: y = 21

QUESTION: If a + 15 = 30, what is the value of 'a'? | ANSWER: a = 15

QUESTION: Riya had some sweets. After eating 5, she had 18 left. How many sweets did she have initially? Write an equation and solve it. | ANSWER: Equation: x - 5 = 18. Solution: x = 23 sweets.

MCQ

Quick Quiz

Which operation should be performed to solve 'x - 4 = 10' for 'x'?

Subtract 4 from both sides

Add 4 to the left side only

Add 4 to both sides

Multiply both sides by 4

The Correct Answer Is:

To isolate 'x' from '- 4', you need to add 4. To keep the equation balanced, you must add 4 to both the left and right sides. This makes x - 4 + 4 = 10 + 4, which simplifies to x = 14.

Real World Connection

In the Real World

When you're tracking your daily steps on a fitness app, if the app calculates your total steps by adding steps from morning and evening walks, it uses equations. If you realize your morning steps were undercounted by 100, you'd add 100 to that side of the calculation, and to keep the total accurate, you'd effectively be adding 100 to the overall total, balancing the 'equation' of your step count.

Key Vocabulary

Key Terms

EQUATION: A mathematical statement that shows two expressions are equal | BALANCE: To keep both sides of an equation equal in value | VARIABLE: A symbol (like x or y) that represents an unknown number | ISOLATE: To get a variable by itself on one side of an equation

What's Next

What to Learn Next

Great job understanding this! Next, you should learn about 'Subtracting from Both Sides of an Equation'. It's another crucial step in solving equations and uses the same balancing idea, just with a different operation.