Fractions · Mixed & improper · 5.1

Improper & mixed.

An improper fraction has a top bigger than its bottom (5/3). A mixed number shows the whole part plus a fraction (1 2/3). They are the same amount.

01 / THE IDEA

See it work.

On the number line

Where does it sit?

0121 2/3

Watch the method

Improper & mixed

5/3 is one whole and two-thirds: 1 2/3.

1 / 2
53\frac{5}{3}
1

Divide top by bottom

5 ÷ 3 = 1 remainder 2.

5÷3=1 r 25 \div 3 = 1\text{ r }2
2

Write the mixed number

Whole part, then remainder over the denominator.

1231\frac{2}{3}
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.

Two forms

When the top exceeds the bottom there is at least one whole. A mixed number pulls the wholes out.

Why it works

Five thirds fills one whole with two-thirds left over.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Write as a mixed number 7/6

1

Divide top by bottom

7 ÷ 6 = 1 remainder 1. 7 \div 6 = 1\text{ r }1

2

Write the mixed number

Whole part, then remainder over the denominator. 11/6

EX 2medium

Write as a mixed number 5/4

1

Divide top by bottom

5 ÷ 4 = 1 remainder 1. 5 \div 4 = 1\text{ r }1

2

Write the mixed number

Whole part, then remainder over the denominator. 11/4

EX 3hard

Write as a mixed number 3/2

1

Divide top by bottom

3 ÷ 2 = 1 remainder 1. 3 \div 2 = 1\text{ r }1

2

Write the mixed number

Whole part, then remainder over the denominator. 11/2

04 / COMMON TRAPS

Where students slip.

Trap

Thinking 5/3 is “wrong”.

Fix

Improper fractions are perfectly valid.

Trap

Reading 1 2/3 as 1 × 2/3.

Fix

It means 1 + 2/3.

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 as a mixed number 7/6

Need a hint?
  • Top bigger than bottom = improper.
  • Pull out the wholes for mixed.
C2

Write as a mixed number 5/3

Need a hint?
  • Top bigger than bottom = improper.
  • Pull out the wholes for mixed.
C3

Write as a mixed number 16/6

Need a hint?
  • Top bigger than bottom = improper.
  • Pull out the wholes for mixed.
C4

Write as a mixed number 15/4

Need a hint?
  • Top bigger than bottom = improper.
  • Pull out the wholes for mixed.
Apply

Apply (4)

A1

Write as a mixed number 5/4

Need a hint?
  • Top bigger than bottom = improper.
  • Pull out the wholes for mixed.
A2

Write as a mixed number 15/6

Need a hint?
  • Top bigger than bottom = improper.
  • Pull out the wholes for mixed.
A3

Write as a mixed number 5/3

Need a hint?
  • Top bigger than bottom = improper.
  • Pull out the wholes for mixed.
A4

Write as a mixed number 6/5

Need a hint?
  • Top bigger than bottom = improper.
  • Pull out the wholes for mixed.
Extension

Extension (4)

E1

Write as a mixed number 3/2

Need a hint?
  • Top bigger than bottom = improper.
  • Pull out the wholes for mixed.
E2

Write as a mixed number 5/2

Need a hint?
  • Top bigger than bottom = improper.
  • Pull out the wholes for mixed.
E3

Write as a mixed number 14/6

Need a hint?
  • Top bigger than bottom = improper.
  • Pull out the wholes for mixed.
E4

Write as a mixed number 17/6

Need a hint?
  • Top bigger than bottom = improper.
  • Pull out the wholes for mixed.