Fractions · Equivalent fractions · 2.1

Same value, new look.

Equivalent fractions name the same amount with different numbers. 1/2, 2/4, and 3/6 all shade the same part of a bar.

01 / THE IDEA

See it work.

Picture it

Shaded parts out of the whole.

4/8

Watch the method

Same value, new look

4/8 shades the same as 1/2.

1 / 2
48\frac{4}{8}
1

Find a common factor

4 and 8 both divide by 4.

gcd⁡(4,8)=4\gcd(4,8)=4
2

Divide top and bottom

Divide both by 4.

48=12\frac{4}{8} = \frac{1}{2}
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

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

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— / WHY IT WORKS

The idea underneath.

Equivalent fractions

Splitting each part into more pieces does not change how much is shaded. 1/2 = 2/4 = 3/6 = 4/8.

Why it works

Half a bar is half a bar, however many cuts you make.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Simplify 4/28

1

Find a common factor

4 and 28 both divide by 4. \gcd(4,28)=4

2

Divide top and bottom

Divide both by 4. 4/28 = 1/7

EX 2medium

Simplify 10/15

1

Find a common factor

10 and 15 both divide by 5. \gcd(10,15)=5

2

Divide top and bottom

Divide both by 5. 10/15 = 2/3

EX 3hard

Simplify 12/36

1

Find a common factor

12 and 36 both divide by 12. \gcd(12,36)=12

2

Divide top and bottom

Divide both by 12. 12/36 = 1/3

04 / COMMON TRAPS

Where students slip.

Trap

Thinking 2/4 is more than 1/2.

Fix

They are equal — the same shaded area.

Trap

Only checking the numerators.

Fix

Both top and bottom change together.

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

Simplify 4/28

Need a hint?
  • Same shaded amount = equivalent.
  • Top and bottom scale together.
C2

Simplify 24/42

Need a hint?
  • Same shaded amount = equivalent.
  • Top and bottom scale together.
C3

Simplify 24/42

Need a hint?
  • Same shaded amount = equivalent.
  • Top and bottom scale together.
C4

Simplify 5/35

Need a hint?
  • Same shaded amount = equivalent.
  • Top and bottom scale together.
Apply

Apply (4)

A1

Simplify 10/15

Need a hint?
  • Same shaded amount = equivalent.
  • Top and bottom scale together.
A2

Simplify 15/20

Need a hint?
  • Same shaded amount = equivalent.
  • Top and bottom scale together.
A3

Simplify 12/30

Need a hint?
  • Same shaded amount = equivalent.
  • Top and bottom scale together.
A4

Simplify 6/10

Need a hint?
  • Same shaded amount = equivalent.
  • Top and bottom scale together.
Extension

Extension (4)

E1

Simplify 12/36

Need a hint?
  • Same shaded amount = equivalent.
  • Top and bottom scale together.
E2

Simplify 8/12

Need a hint?
  • Same shaded amount = equivalent.
  • Top and bottom scale together.
E3

Simplify 9/15

Need a hint?
  • Same shaded amount = equivalent.
  • Top and bottom scale together.
E4

Simplify 12/30

Need a hint?
  • Same shaded amount = equivalent.
  • Top and bottom scale together.