Maths Library

Dividing in a Ratio: Grade 6 math

This topic covers dividing a quantity into parts according to a given ratio. Students practise calculating total parts, finding the value of one part, and scaling up each share.

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What this covers

Dividing in a Ratio is taught in Grade 6 (age 11 to 12) as a topic to introduce. It sits in the Ratio strand.

Worked example

Share £60 in the ratio 2 : 3

  1. Calculate total parts: 2 + 3 = 5 parts
  2. Find value of one part: 605 = £12
  3. Multiply each part: 2 x 12 = £24 and 3 x 12 = £36

Answer: £24 : £36

Difficulty scale

The sheet generator offers five difficulty settings for this topic.

  1. Two-part ratio sharing small whole numbers, sum of parts <= 10
  2. Two-part ratio with larger whole numbers and money quantities
  3. Three-part ratio sharing integer amounts
  4. Given the difference between parts or one part's value rather than the total
  5. Multi-step word problems involving ratios changing or combining parts

Common mistakes

  • Dividing the total amount by each ratio digit directly rather than the sum of parts
  • Misidentifying which person receives which share when names are assigned

Curriculum links

Indicative matches to Common Core State Standards. Check wording and codes against the official document.

  • 6.RP.A.3 Solve real-world and mathematical ratio, rate, and percentage problems using various representations.

Sample sheet and answers

Six questions at the level's usual difficulty. Open the editor to change, add or regenerate any of them.

Dividing in a Ratio

Grade 6 math

Qs
6
Marks
18
NameDateScore / 18
1.
Chloe shares 96 sweets in the ratio 3 : 5. How many sweets are in each share?
[3]
2.
Isla shares 21 sweets in the ratio 5 : 2. How many sweets are in each share?
[3]
3.
Ella shares 24 sweets in the ratio 5 : 1. How many sweets are in each share?
[3]
4.
Priya shares 77 sweets in the ratio 5 : 2. How many sweets are in each share?
[3]
5.
Noah shares 72 sweets in the ratio 2 : 6. How many sweets are in each share?
[3]
6.
Farid shares 110 sweets in the ratio 5 : 5. How many sweets are in each share?
[3]

Answer key

  1. 36 and 60Total parts: 3 + 5 = 8; One part is 96 ÷ 8 = 12; Shares: 3 × 12 = 36 and 5 × 12 = 60
  2. 15 and 6Total parts: 5 + 2 = 7; One part is 21 ÷ 7 = 3; Shares: 5 × 3 = 15 and 2 × 3 = 6
  3. 20 and 4Total parts: 5 + 1 = 6; One part is 24 ÷ 6 = 4; Shares: 5 × 4 = 20 and 1 × 4 = 4
  4. 55 and 22Total parts: 5 + 2 = 7; One part is 77 ÷ 7 = 11; Shares: 5 × 11 = 55 and 2 × 11 = 22
  5. 18 and 54Total parts: 2 + 6 = 8; One part is 72 ÷ 8 = 9; Shares: 2 × 9 = 18 and 6 × 9 = 54
  6. 55 and 55Total parts: 5 + 5 = 10; One part is 110 ÷ 10 = 11; Shares: 5 × 11 = 55 and 5 × 11 = 55