Fractions · Mixed & improper · 5.2

Improper → mixed.

To convert an improper fraction to a mixed number, divide top by bottom: the quotient is the whole part, the remainder goes over the denominator.

01 / THE IDEA

See it work.

Watch the method

Improper → mixed

7/2: 7 ÷ 2 = 3 remainder 1 → 3 1/2.

1 / 2
72\frac{7}{2}
1

Divide top by bottom

7 ÷ 2 = 3 remainder 1.

7÷2=3 r 17 \div 2 = 3\text{ r }1
2

Write the mixed number

Whole part, then remainder over the denominator.

3123\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.

streak 0
best 0
… =
— / WHY IT WORKS

The idea underneath.

Quotient and remainder

Top ÷ bottom gives the whole part; the leftover is the new numerator over the same denominator.

Why it works

How many whole groups, and what is left?

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

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

EX 2medium

Write as a mixed number 11/5

1

Divide top by bottom

11 ÷ 5 = 2 remainder 1. 11 \div 5 = 2\text{ r }1

2

Write the mixed number

Whole part, then remainder over the denominator. 21/5

EX 3hard

Write as a mixed number 4/3

1

Divide top by bottom

4 ÷ 3 = 1 remainder 1. 4 \div 3 = 1\text{ r }1

2

Write the mixed number

Whole part, then remainder over the denominator. 11/3

04 / COMMON TRAPS

Where students slip.

Trap

Forgetting the remainder.

Fix

The leftover becomes the fraction part.

Trap

Putting the remainder over the wrong number.

Fix

Keep the original denominator.

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 3/2

Need a hint?
  • Divide top by bottom.
  • Remainder over the denominator.
C2

Write as a mixed number 5/2

Need a hint?
  • Divide top by bottom.
  • Remainder over the denominator.
C3

Write as a mixed number 3/2

Need a hint?
  • Divide top by bottom.
  • Remainder over the denominator.
C4

Write as a mixed number 10/4

Need a hint?
  • Divide top by bottom.
  • Remainder over the denominator.
Apply

Apply (4)

A1

Write as a mixed number 11/5

Need a hint?
  • Divide top by bottom.
  • Remainder over the denominator.
A2

Write as a mixed number 8/6

Need a hint?
  • Divide top by bottom.
  • Remainder over the denominator.
A3

Write as a mixed number 10/3

Need a hint?
  • Divide top by bottom.
  • Remainder over the denominator.
A4

Write as a mixed number 20/6

Need a hint?
  • Divide top by bottom.
  • Remainder over the denominator.
Extension

Extension (4)

E1

Write as a mixed number 4/3

Need a hint?
  • Divide top by bottom.
  • Remainder over the denominator.
E2

Write as a mixed number 18/5

Need a hint?
  • Divide top by bottom.
  • Remainder over the denominator.
E3

Write as a mixed number 19/6

Need a hint?
  • Divide top by bottom.
  • Remainder over the denominator.
E4

Write as a mixed number 14/5

Need a hint?
  • Divide top by bottom.
  • Remainder over the denominator.