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Concept 2 of 9

The Golden Rule: Creating Equivalent Fractions

1

Today's big idea

Multiply top and bottom by the same number and the amount stays exactly the same.

1/2, 2/4 and 4/8 shade the same strip, each step doubling both numbers.

2

How it works

👀 What's going on?

Cut a pizza in half and eat one piece. Now cut the same pizza into 4 and eat two of them. You ate exactly the same amount both times, but you would write the fraction differently.

💡 Here's the trick

1/2×2 / ×2 ↓2/4×2 / ×2 ↓4/8same amount, different slices

Look at the strip above. 1/2, 2/4 and 4/8 all shade the same length. Each step doubles the top and the bottom together, which cuts the slices smaller and hands you more of them. Multiply top and bottom by the same number and the amount never moves.

🪄 How to do it

  1. 1.Start from the fraction in the picture above and pick a number to scale by.
  2. 2.Multiply the top number by it.
  3. 3.Multiply the bottom number by the same thing, or the amount changes.

✍️ Try it

Scale 2/5 by 4. Then scale 2/5 by 2 instead. Should the two answers be worth the same?

Scaling by 4 gives 8/20. Scaling by 2 gives 4/10. Both are still 2/5, and doubling 4/10 lands right back on 8/20. A fraction has endless names and every one of them is worth the same.

⚠️ Watch out

You might be thinking you could add the same number to top and bottom instead. Test it on 1/2. Adding 1 to each gives 2/3, which is more than a half, so the amount did move. Only multiplying keeps it fair.

🌟 Why this matters

Recipes get doubled, prices get compared, and measurements get rewritten in other units. All of that is renaming an amount without changing what it is worth.
Exam tip: Most equivalent-fraction questions are this single move done once or twice.

3

Watch me solve one

Quanta solves it

“Watch how I think through one of these — then you try.”

THE PROBLEM

“Make 1/3 into an equivalent fraction with 12 on the bottom.”

  1. 1

    Find the bottom multiplier

    3 × ? = 12 → 3 × 4 = 12.

  2. 2

    Multiply the TOP by the same

    Golden Rule: same multiplier on top. 1 × 4 = 4.

  3. 3

    Write the new fraction

    1/3 = 4/12

  4. 4

    Equivalent ✓

    1/3 = 4/12 (same amount, different slices)

Now you try one — same steps, different story 👇

4

See it in action

⚡ Time to play!

The Golden Rule: whatever you multiply the TOP by, you MUST multiply the BOTTOM by the SAME number!

Starting fraction: 1/2

Choose multiplier for TOP (1):

5

Quick check

✅ VERIFICATION

Which fraction is equivalent to 3/4?

⚡ Finish the activity above first to answer.

Keep going!

Up next: The Pizza Combiner

Same bottom? Just add the top numbers.

Concept 3 of 9 →