Fractions · Simplify · 3.4

Already simplest?

Some fractions are already in lowest terms — the top and bottom share no common factor. Recognise these and leave them.

01 / THE IDEA

See it work.

Watch the method

Already simplest?

5/8: 5 and 8 share no factor, so it stays 5/8.

1 / 1

\frac{5}{8}

1

Already simplest

Top and bottom share no common factor.

\frac{5}{8}

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

… =

— / WHY IT WORKS

The idea underneath.

Coprime top and bottom

If the only shared factor is 1, the fraction is already simplest.

Why it works

5 and 8 have nothing in common to divide out.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Simplify 6/10

1

Find a common factor

6 and 10 both divide by 2. \gcd(6,10)=2

2

Divide top and bottom

Divide both by 2. 6/10 = 3/5

EX 2medium

Simplify 12/30

1

Find a common factor

12 and 30 both divide by 6. \gcd(12,30)=6

2

Divide top and bottom

Divide both by 6. 12/30 = 2/5

EX 3hard

Simplify 12/42

1

Find a common factor

12 and 42 both divide by 6. \gcd(12,42)=6

2

Divide top and bottom

Divide both by 6. 12/42 = 2/7

04 / COMMON TRAPS

Where students slip.

Trap

Forcing a reduction that isn’t there.

Fix

If nothing divides both, leave it.

Trap

Changing the value while “simplifying”.

Fix

Only divide by true common factors.

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 6/10

Need a hint?

Check for any common factor.
None? it is already simplest.

C2

Simplify 10/35

Need a hint?

Check for any common factor.
None? it is already simplest.

C3

Simplify 5/30

Need a hint?

Check for any common factor.
None? it is already simplest.

C4

Simplify 6/30

Need a hint?

Check for any common factor.
None? it is already simplest.

Apply

Apply (4)

A1

Simplify 12/30

Need a hint?

Check for any common factor.
None? it is already simplest.

A2

Simplify 8/14

Need a hint?

Check for any common factor.
None? it is already simplest.

A3

Simplify 24/36

Need a hint?

Check for any common factor.
None? it is already simplest.

A4

Simplify 2/10

Need a hint?

Check for any common factor.
None? it is already simplest.

Extension

Extension (4)

E1

Simplify 12/42

Need a hint?

Check for any common factor.
None? it is already simplest.

E2

Simplify 15/30

Need a hint?

Check for any common factor.
None? it is already simplest.

E3

Simplify 6/18

Need a hint?

Check for any common factor.
None? it is already simplest.

E4

Simplify 4/28

Need a hint?

Check for any common factor.
None? it is already simplest.