Fractions · Equivalent fractions · 2.2

Make equivalent.

To build an equivalent fraction, multiply the top AND the bottom by the same number. That keeps the value the same.

01 / THE IDEA

See it work.

Watch the method

Make equivalent

1/2 with denominator 6: multiply both by 3 → 3/6.

1 / 2
12=?6\frac{1}{2} = \frac{?}{6}
1

How many times bigger?

2 × 3 = 6.

2×3=62\times3=6
2

Multiply top and bottom

Multiply both by 3 so the value stays the same.

12=36\frac{1}{2} = \frac{3}{6}
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

Type a fraction like 3/4 or 1 1/2.

streak 0
best 0
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— / WHY IT WORKS

The idea underneath.

Scale both

Multiplying numerator and denominator by k is multiplying by k/k = 1, so the value is unchanged.

Why it works

Cut every slice in two: twice as many slices, same amount.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Write 1/3 with denominator 12.

1

How many times bigger?

3 × 4 = 12. 3\times4=12

2

Multiply top and bottom

Multiply both by 4 so the value stays the same. 1/3 = 4/12

EX 2medium

Write 4/5 with denominator 10.

1

How many times bigger?

5 × 2 = 10. 5\times2=10

2

Multiply top and bottom

Multiply both by 2 so the value stays the same. 4/5 = 8/10

EX 3hard

Write 2/5 with denominator 20.

1

How many times bigger?

5 × 4 = 20. 5\times4=20

2

Multiply top and bottom

Multiply both by 4 so the value stays the same. 2/5 = 8/20

04 / COMMON TRAPS

Where students slip.

Trap

Multiplying only the bottom.

Fix

Multiply BOTH by the same number.

Trap

Adding instead of multiplying.

Fix

Equivalence comes from multiplying.

05 / QUIZ

Test yourself.

The Test

12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.

0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).
Core

Core (4)

C1

Write 1/3 with denominator 12.

Need a hint?
  • Find what the bottom is multiplied by.
  • Multiply the top by the same number.
C2

Write 1/3 with denominator 6.

Need a hint?
  • Find what the bottom is multiplied by.
  • Multiply the top by the same number.
C3

Write 1/2 with denominator 10.

Need a hint?
  • Find what the bottom is multiplied by.
  • Multiply the top by the same number.
C4

Write 4/5 with denominator 10.

Need a hint?
  • Find what the bottom is multiplied by.
  • Multiply the top by the same number.
Apply

Apply (4)

A1

Write 4/5 with denominator 10.

Need a hint?
  • Find what the bottom is multiplied by.
  • Multiply the top by the same number.
A2

Write 1/3 with denominator 9.

Need a hint?
  • Find what the bottom is multiplied by.
  • Multiply the top by the same number.
A3

Write 1/4 with denominator 8.

Need a hint?
  • Find what the bottom is multiplied by.
  • Multiply the top by the same number.
A4

Write 3/5 with denominator 20.

Need a hint?
  • Find what the bottom is multiplied by.
  • Multiply the top by the same number.
Extension

Extension (4)

E1

Write 2/5 with denominator 20.

Need a hint?
  • Find what the bottom is multiplied by.
  • Multiply the top by the same number.
E2

Write 1/2 with denominator 8.

Need a hint?
  • Find what the bottom is multiplied by.
  • Multiply the top by the same number.
E3

Write 2/3 with denominator 6.

Need a hint?
  • Find what the bottom is multiplied by.
  • Multiply the top by the same number.
E4

Write 1/2 with denominator 8.

Need a hint?
  • Find what the bottom is multiplied by.
  • Multiply the top by the same number.