Simplifying ratios

The Maths Habit

Which one has the same mix of shaded and white tiles as this one?

This one
A
✓ The sameB
Not the sameC
Not the same

Halve both numbers.

8 and 64 and 3
10 and 145 and 7
20 and 1210 and 6

Ratio
Compares two amounts. 2 : 3 means 2 shaded for every 3 white.
2 : 3
Order
The order matters. 2 : 3 is not the same as 3 : 2.
2 : 3
3 : 2
Simplest form
The same ratio with the smallest numbers. Only 1 goes into both.
4 : 6
2 : 3

number:number÷same:
  1. 1Pick a number that goes into both.Try 2, 3, 5 or 10. Join the tiles into groups of that number.
  2. 2Divide both numbers.Use the same number for both. Count the groups.

Write 10 : 15 in its simplest form.

1Pick a number that goes into both.
10:15
2Divide both numbers.
÷52:3

Write 8 : 10 in its simplest form.

1Pick a number that goes into both.
8:10
2Divide both numbers.
÷24:5

Write 10 : 15 in its simplest form.

1Pick a number that goes into both.
10:15
2Divide both numbers.
÷52:3
1Pick a number that goes into both.2Divide both numbers.

Write 6 : 15 in its simplest form.

1Pick a number that goes into both.
6:15
2Divide both numbers.
÷32:5

Write 10 : 15 in its simplest form.

1Pick a number that goes into both.
10:15
2Divide both numbers.
÷52:3
1Pick a number that goes into both.2Divide both numbers.

Write 20 : 30 in its simplest form.

1Pick a number that goes into both.
20:30
2Divide both numbers.
÷102:3

Write 10 : 15 in its simplest form.

1Pick a number that goes into both.
10:15
2Divide both numbers.
÷52:3
1Pick a number that goes into both.2Divide both numbers.

Write 14 : 10 in its simplest form.

1Pick a number that goes into both.
14:10
2Divide both numbers.
÷27:5

1Pick a number that goes into both.2Divide both numbers.

1Write 4 : 10 in its simplest form.

1
4:102÷22:5

2Write 9 : 12 in its simplest form.

1
9:122÷33:4

3Write 25 : 15 in its simplest form.

1
25:152÷55:3

4Write 12 : 14 in its simplest form.

1
12:142÷26:7

Is it in its simplest form?

2 : 3Yes
4 : 10No: 2 goes into both
5 : 3Yes
6 : 9No: 3 goes into both

number:number÷same:÷same:
  1. 1Pick a number that goes into both.Try 2, 3, 5 or 10. Join the tiles into groups of that number.
  2. 2Divide both numbers.Use the same number for both. Count the groups.
  3. 3Divide again if you can.Stop when only 1 goes into both. This is the simplest form.

Write 12 : 16 in its simplest form.

1Pick a number that goes into both.
12:16
2Divide both numbers.
÷26:8
3Divide again if you can.
÷23:4

Write 20 : 50 in its simplest form.

1Pick a number that goes into both.
20:50
2Divide both numbers.
÷54:10
3Divide again if you can.
÷22:5

Write 12 : 16 in its simplest form.

1Pick a number that goes into both.
12:16
2Divide both numbers.
÷26:8
3Divide again if you can.
÷23:4
1Pick a number that goes into both.2Divide both numbers.3Divide again if you can.

Write 6 : 30 in its simplest form.

1Pick a number that goes into both.
6:30
2Divide both numbers.
÷23:15
3Divide again if you can.
÷31:5

Write 12 : 16 in its simplest form.

1Pick a number that goes into both.
12:16
2Divide both numbers.
÷26:8
3Divide again if you can.
÷23:4
1Pick a number that goes into both.2Divide both numbers.3Divide again if you can.

Write 18 : 12 in its simplest form.

1Pick a number that goes into both.
18:12
2Divide both numbers.
÷29:6
3Divide again if you can.
÷33:2

Write 12 : 16 in its simplest form.

1Pick a number that goes into both.
12:16
2Divide both numbers.
÷26:8
3Divide again if you can.
÷23:4
1Pick a number that goes into both.2Divide both numbers.3Divide again if you can.

Write 14 : 28 in its simplest form.

1Pick a number that goes into both.
14:28
2Divide both numbers.
÷27:14
3Divide again if you can.
÷71:2

Simplifying ratios worksheet, page 1

Simplifying ratios worksheet, page 2

Answer sheet

Is it right?
Thumbs up: right. Thumbs down: wrong.

  1. 6 : 9 = 2 : 3 in its simplest form

    Right

  2. 10 : 20 = 5 : 10 in its simplest form

    Wrong: divide again

  3. 8 : 12 = 3 : 2 in its simplest form

    Wrong: it is 2 : 3

  4. 15 : 5 = 3 : 1 in its simplest form

    Right

  5. 12 : 18 = 2 : 3 in its simplest form

    Right

  1. Write 36 : 48 in its simplest form in one step.

    ÷ 12: 3 : 4

  2. Write 12 : 18 : 30 in its simplest form.

    ÷ 6: 2 : 3 : 5

  3. Write 20 minutes : 1 hour in its simplest form.

    20 : 60 = 1 : 3

  1. Write 12 : 20 in its simplest form.

    3 : 5
    1Pick a number thatgoes into both.1220:2Divide bothnumbers.3Divide againif you can.÷2:÷:

  2. Write 24 : 30 in its simplest form.

    4 : 5
    1Pick a number thatgoes into both.2430:2Divide bothnumbers.3Divide againif you can.÷:÷:

  3. Write 40 : 60 in its simplest form.

    2 : 3
Exit tickets to print