Fractions · Mixed & improper · 5.3

Mixed → improper.

To convert a mixed number to an improper fraction, multiply the whole by the denominator and add the numerator — over the same denominator.

01 / THE IDEA

See it work.

Watch the method

Mixed → improper

2 1/3: 2 × 3 + 1 = 7 → 7/3.

1 / 2
2132\frac{1}{3}
1

Whole × denominator

2 × 3 = 6.

2×3=62\times3=6
2

Add the numerator

6 + 1 = 7, over 3.

6+13=73\frac{6+1}{3} = \frac{7}{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.

Recombine the wholes

Each whole is d/d. Two wholes is 6/3; plus 1/3 gives 7/3.

Why it works

Turn the wholes back into pieces and add them in.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Write as an improper fraction 3 2/5

1

Whole × denominator

3 × 5 = 15. 3\times5=15

2

Add the numerator

15 + 2 = 17, over 5. \frac{15+2}{5} = 17/5

EX 2medium

Write as an improper fraction 3 1/3

1

Whole × denominator

3 × 3 = 9. 3\times3=9

2

Add the numerator

9 + 1 = 10, over 3. \frac{9+1}{3} = 10/3

EX 3hard

Write as an improper fraction 3 3/5

1

Whole × denominator

3 × 5 = 15. 3\times5=15

2

Add the numerator

15 + 3 = 18, over 5. \frac{15+3}{5} = 18/5

04 / COMMON TRAPS

Where students slip.

Trap

Adding before multiplying.

Fix

Multiply the whole by the bottom first.

Trap

Changing the denominator.

Fix

It stays the same.

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 an improper fraction 3 2/5

Need a hint?
  • Whole × denominator.
  • Add the numerator; keep the bottom.
C2

Write as an improper fraction 1 1/2

Need a hint?
  • Whole × denominator.
  • Add the numerator; keep the bottom.
C3

Write as an improper fraction 2 1/2

Need a hint?
  • Whole × denominator.
  • Add the numerator; keep the bottom.
C4

Write as an improper fraction 3 1/2

Need a hint?
  • Whole × denominator.
  • Add the numerator; keep the bottom.
Apply

Apply (4)

A1

Write as an improper fraction 3 1/3

Need a hint?
  • Whole × denominator.
  • Add the numerator; keep the bottom.
A2

Write as an improper fraction 3 3/5

Need a hint?
  • Whole × denominator.
  • Add the numerator; keep the bottom.
A3

Write as an improper fraction 1 1/4

Need a hint?
  • Whole × denominator.
  • Add the numerator; keep the bottom.
A4

Write as an improper fraction 2 3/5

Need a hint?
  • Whole × denominator.
  • Add the numerator; keep the bottom.
Extension

Extension (4)

E1

Write as an improper fraction 3 3/5

Need a hint?
  • Whole × denominator.
  • Add the numerator; keep the bottom.
E2

Write as an improper fraction 1 4/5

Need a hint?
  • Whole × denominator.
  • Add the numerator; keep the bottom.
E3

Write as an improper fraction 1 1/3

Need a hint?
  • Whole × denominator.
  • Add the numerator; keep the bottom.
E4

Write as an improper fraction 1 1/4

Need a hint?
  • Whole × denominator.
  • Add the numerator; keep the bottom.