Fractions · What is a fraction? · 1.3

Counting unit fractions.

Every fraction is built from unit fractions (one part). 3/4 is just three copies of 1/4. The numerator counts the unit fractions.

01 / THE IDEA

See it work.

Picture it

Shaded parts out of the whole.

3/4

Watch the method

Counting unit fractions

3/4 = 1/4 + 1/4 + 1/4 — three quarters.

1 / 1
34\frac{3}{4}
1

Count the unit fractions

3/4 is 3 copies of 1/4.

34=3×14\frac{3}{4} = 3\times\frac{1}{4}
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.

Built from unit fractions

n/d means n copies of 1/d. This is why you add fractions with the same denominator by adding the tops.

Why it works

Three quarter-slices make three-quarters.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

How many 1/3 make 2/3?

1

Count the unit fractions

2/3 is 2 copies of 1/3. 2/3 = 2\times1/3

EX 2medium

How many 1/3 make 2/3?

1

Count the unit fractions

2/3 is 2 copies of 1/3. 2/3 = 2\times1/3

EX 3hard

How many 1/2 make 2/2?

1

Count the unit fractions

2/2 is 2 copies of 1/2. 2/2 = 2\times1/2

04 / COMMON TRAPS

Where students slip.

Trap

Thinking 3/4 is one indivisible thing.

Fix

It is three 1/4 pieces.

Trap

Confusing the count with the size.

Fix

The numerator counts; the denominator sizes.

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

How many 1/3 make 2/3?

Need a hint?
  • n/d is n copies of 1/d.
  • The top is the count.
C2

How many 1/6 make 2/6?

Need a hint?
  • n/d is n copies of 1/d.
  • The top is the count.
C3

How many 1/2 make 2/2?

Need a hint?
  • n/d is n copies of 1/d.
  • The top is the count.
C4

How many 1/3 make 2/3?

Need a hint?
  • n/d is n copies of 1/d.
  • The top is the count.
Apply

Apply (4)

A1

How many 1/3 make 2/3?

Need a hint?
  • n/d is n copies of 1/d.
  • The top is the count.
A2

How many 1/5 make 2/5?

Need a hint?
  • n/d is n copies of 1/d.
  • The top is the count.
A3

How many 1/3 make 2/3?

Need a hint?
  • n/d is n copies of 1/d.
  • The top is the count.
A4

How many 1/3 make 2/3?

Need a hint?
  • n/d is n copies of 1/d.
  • The top is the count.
Extension

Extension (4)

E1

How many 1/2 make 2/2?

Need a hint?
  • n/d is n copies of 1/d.
  • The top is the count.
E2

How many 1/5 make 3/5?

Need a hint?
  • n/d is n copies of 1/d.
  • The top is the count.
E3

How many 1/2 make 2/2?

Need a hint?
  • n/d is n copies of 1/d.
  • The top is the count.
E4

How many 1/4 make 3/4?

Need a hint?
  • n/d is n copies of 1/d.
  • The top is the count.