Fractions · Equivalent fractions · 2.3

To a target denominator.

Need a specific denominator? Find what to multiply the bottom by to reach it, then multiply the top by the same.

01 / THE IDEA

See it work.

Watch the method

To a target denominator

2/3 as twelfths: 3 × 4 = 12, so 2 × 4 = 8 → 8/12.

1 / 2
23=?12\frac{2}{3} = \frac{?}{12}
1

How many times bigger?

3 × 4 = 12.

3×4=123\times4=12
2

Multiply top and bottom

Multiply both by 4 so the value stays the same.

23=812\frac{2}{3} = \frac{8}{12}
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.

Reach a denominator

Divide the target by the current denominator to find the multiplier, then apply it to the numerator.

Why it works

How many of the new pieces equal one old piece?

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Write 1/3 with denominator 9.

1

How many times bigger?

3 × 3 = 9. 3\times3=9

2

Multiply top and bottom

Multiply both by 3 so the value stays the same. 1/3 = 3/9

EX 2medium

Write 1/2 with denominator 10.

1

How many times bigger?

2 × 5 = 10. 2\times5=10

2

Multiply top and bottom

Multiply both by 5 so the value stays the same. 1/2 = 5/10

EX 3hard

Write 1/2 with denominator 4.

1

How many times bigger?

2 × 2 = 4. 2\times2=4

2

Multiply top and bottom

Multiply both by 2 so the value stays the same. 1/2 = 2/4

04 / COMMON TRAPS

Where students slip.

Trap

Forgetting to scale the numerator.

Fix

Whatever you do to the bottom, do to the top.

Trap

Using a multiplier that doesn’t hit the target.

Fix

Target ÷ bottom gives the multiplier.

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 9.

Need a hint?
  • Target ÷ bottom = the multiplier.
  • Multiply the top by it too.
C2

Write 2/4 with denominator 12.

Need a hint?
  • Target ÷ bottom = the multiplier.
  • Multiply the top by it too.
C3

Write 1/2 with denominator 10.

Need a hint?
  • Target ÷ bottom = the multiplier.
  • Multiply the top by it too.
C4

Write 2/4 with denominator 20.

Need a hint?
  • Target ÷ bottom = the multiplier.
  • Multiply the top by it too.
Apply

Apply (4)

A1

Write 1/2 with denominator 10.

Need a hint?
  • Target ÷ bottom = the multiplier.
  • Multiply the top by it too.
A2

Write 4/5 with denominator 20.

Need a hint?
  • Target ÷ bottom = the multiplier.
  • Multiply the top by it too.
A3

Write 4/5 with denominator 15.

Need a hint?
  • Target ÷ bottom = the multiplier.
  • Multiply the top by it too.
A4

Write 1/2 with denominator 10.

Need a hint?
  • Target ÷ bottom = the multiplier.
  • Multiply the top by it too.
Extension

Extension (4)

E1

Write 1/2 with denominator 4.

Need a hint?
  • Target ÷ bottom = the multiplier.
  • Multiply the top by it too.
E2

Write 2/4 with denominator 8.

Need a hint?
  • Target ÷ bottom = the multiplier.
  • Multiply the top by it too.
E3

Write 1/4 with denominator 8.

Need a hint?
  • Target ÷ bottom = the multiplier.
  • Multiply the top by it too.
E4

Write 1/2 with denominator 6.

Need a hint?
  • Target ÷ bottom = the multiplier.
  • Multiply the top by it too.