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What is Subtracting From Both Sides of an Equation?
Grade Level:
Class 5
Maths, Computing, AI, Physics
Definition
What is it?
Subtracting from both sides of an equation means taking away the same number or variable from both the left side and the right side of the equals sign. This keeps the equation balanced, just like a weighing scale, and helps us find the value of an unknown number.
Simple Example
Quick Example
Imagine you have a box of laddoos (let's say 'x') plus 5 extra laddoos, and this total is equal to 12 laddoos. So, x + 5 = 12. If you eat 5 laddoos from both sides (both the box side and the 12 laddoos side), the box will still have the same amount relative to the other side. You'll find out how many laddoos were originally in the box.
Worked Example
Step-by-Step
Let's solve for 'y' in the equation: y + 8 = 15
Step 1: Write down the equation.
y + 8 = 15
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Step 2: Our goal is to get 'y' alone on one side. To remove the '+ 8', we need to subtract 8.
y + 8 - 8 = 15
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Step 3: Remember, whatever we do to one side, we must do to the other side to keep the equation balanced. So, subtract 8 from the right side too.
y + 8 - 8 = 15 - 8
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Step 4: Perform the subtraction on both sides.
y + 0 = 7
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Step 5: Simplify.
y = 7
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Answer: y = 7
Why It Matters
This concept is super important for solving problems in Maths, Physics, and even Computing. Engineers use it to design bridges, scientists use it to understand how things work, and coders use it to write programs that make apps run smoothly. It's a basic building block for many exciting careers!
Common Mistakes
MISTAKE: Subtracting from only one side of the equation. For example, x + 3 = 10 becomes x = 10 - 3 (correct) but then they forget to subtract 3 from the left side. | CORRECTION: Always subtract the same amount from BOTH sides of the equals sign to keep the equation balanced.
MISTAKE: Confusing subtraction with addition when trying to isolate a variable. For example, in x - 5 = 7, they subtract 5 from both sides instead of adding 5. | CORRECTION: To remove a number that is being subtracted, you need to ADD that number to both sides. To remove a number that is being added, you SUBTRACT that number.
MISTAKE: Making calculation errors when subtracting. For example, 15 - 8 is mistakenly calculated as 6. | CORRECTION: Double-check your basic subtraction facts. Use mental math or rough work to ensure accuracy.
Practice Questions
Try It Yourself
QUESTION: Solve for 'a': a + 10 = 25 | ANSWER: a = 15
QUESTION: If the total cost of a cricket bat and a ball is Rs 850, and the ball costs Rs 120, what is the cost of the bat? (Let 'b' be the cost of the bat, so b + 120 = 850) | ANSWER: b = Rs 730
QUESTION: The number of students in Class 5 is 's'. If 7 new students join, there will be 42 students in total. How many students were there initially? Write an equation and solve it. | ANSWER: Equation: s + 7 = 42. Solution: s = 35 students.
MCQ
Quick Quiz
Which operation should be performed to solve for 'p' in the equation: p + 12 = 30?
Add 12 to both sides
Subtract 12 from both sides
Multiply both sides by 12
Divide both sides by 12
The Correct Answer Is:
B
To isolate 'p' from 'p + 12', we need to do the opposite of adding 12, which is subtracting 12. This must be done to both sides to keep the equation balanced.
Real World Connection
In the Real World
When you use a banking app like Google Pay or Paytm to check your account balance, the app uses equations. If your initial balance (x) plus a deposit (Rs 500) equals your new balance (Rs 2500), the app quickly solves x + 500 = 2500 by subtracting Rs 500 from both sides to show you your starting balance. This is happening millions of times every day in India!
Key Vocabulary
Key Terms
EQUATION: A mathematical statement showing that two expressions are equal, separated by an equals sign (=) | BALANCE: To keep both sides of an equation equal in value | VARIABLE: A letter (like x, y, a) that represents an unknown number | ISOLATE: To get a variable by itself on one side of an equation | EXPRESSION: A combination of numbers, variables, and operation signs (e.g., x + 5)
What's Next
What to Learn Next
Great job understanding this! Next, you should learn about 'Adding to Both Sides of an Equation' and 'Multiplying/Dividing on Both Sides'. These concepts are the other tools you'll use to solve even more complex equations and become a true math wizard!
