Fractions · What is a fraction? · 1.5

Equal to one, and wholes.

When the top and bottom match, the fraction is 1 (the whole). When the top is a bigger multiple, it is a whole number of wholes: 8/4 = 2.

01 / THE IDEA

See it work.

Picture it

Shaded parts out of the whole.

8/4

Watch the method

Equal to 1 and to wholes

4/4 fills one whole; 8/4 fills two.

1 / 2
84\frac{8}{4}
1

Find a common factor

8 and 4 both divide by 4.

gcd⁡(8,4)=4\gcd(8,4)=4
2

Divide top and bottom

Divide both by 4.

84=2\frac{8}{4} = 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.

Whole-number fractions

d/d = 1. (k·d)/d = k. The fraction is a whole number when the top is a multiple of the bottom.

Why it works

Four quarters make one whole dollar.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Simplify 30/5

1

Find a common factor

30 and 5 both divide by 5. \gcd(30,5)=5

2

Divide top and bottom

Divide both by 5. 30/5 = 6

EX 2medium

Simplify 24/4

1

Find a common factor

24 and 4 both divide by 4. \gcd(24,4)=4

2

Divide top and bottom

Divide both by 4. 24/4 = 6

EX 3hard

Simplify 9/3

1

Find a common factor

9 and 3 both divide by 3. \gcd(9,3)=3

2

Divide top and bottom

Divide both by 3. 9/3 = 3

04 / COMMON TRAPS

Where students slip.

Trap

Writing 4/4 as a fraction answer.

Fix

It simplifies to 1.

Trap

Missing that 8/4 = 2.

Fix

A multiple of the bottom is a whole number.

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 30/5

Need a hint?
  • Same top and bottom = 1.
  • Divide to get the whole number.
C2

Simplify 4/2

Need a hint?
  • Same top and bottom = 1.
  • Divide to get the whole number.
C3

Simplify 12/3

Need a hint?
  • Same top and bottom = 1.
  • Divide to get the whole number.
C4

Simplify 20/4

Need a hint?
  • Same top and bottom = 1.
  • Divide to get the whole number.
Apply

Apply (4)

A1

Simplify 24/4

Need a hint?
  • Same top and bottom = 1.
  • Divide to get the whole number.
A2

Simplify 20/5

Need a hint?
  • Same top and bottom = 1.
  • Divide to get the whole number.
A3

Simplify 10/5

Need a hint?
  • Same top and bottom = 1.
  • Divide to get the whole number.
A4

Simplify 20/5

Need a hint?
  • Same top and bottom = 1.
  • Divide to get the whole number.
Extension

Extension (4)

E1

Simplify 9/3

Need a hint?
  • Same top and bottom = 1.
  • Divide to get the whole number.
E2

Simplify 12/4

Need a hint?
  • Same top and bottom = 1.
  • Divide to get the whole number.
E3

Simplify 18/3

Need a hint?
  • Same top and bottom = 1.
  • Divide to get the whole number.
E4

Simplify 30/5

Need a hint?
  • Same top and bottom = 1.
  • Divide to get the whole number.