Year 6: Grouping and ratio in packs
Part of the Year 6 ratio and proportion chapter. Chapter overview · whole chapter on one page
Grouping and ratio in packs
Sometimes a ratio describes what goes into each group, such as each pack, bag or table. A pack that holds 2 orange and 3 blue counters has the ratio 2:3 in it. There are 2 + 3 = 5 counters in the pack, so 5 is the size of the group.
To solve a grouping problem, first find what one group contains. Then find the number of groups. Multiply the amount in one group by the number of groups to find the total. The total must be a multiple of the group size if the groups are to fill exactly.
Key ideas
- Find what one group contains first, using the ratio.
- Number of groups = total ÷ the size of one group.
- Total for all the groups = amount in one group × number of groups.
- The groups fill exactly only when the total is a multiple of the group size.
Key words. A ratio is made of parts. Every part is the same size. The total is all the parts added together.
Method. Find how many are in one group, then multiply by the number of groups.
- Write how many red pencils are in one group. The ratio part is the number in one group.2 in one group
- Multiply by the number of groups, 6. Every group has the same amount.2 × 6 = 12
- Write the answer. 12
Check. 6 groups of 2 gives 12. ✓
Watch out. Multiply by the number of groups. Do not add the ratio parts.
Key words. A ratio is made of parts. Every part is the same size. The total is all the parts added together.
Method. Find the number of groups, then the amount in one group, then multiply.
- Find the number of groups: divide 60 by the group size, 5. The groups must fill exactly.60 ÷ 5 = 12 groups
- Find how many cherry lollies are in one group. The ratio parts add up to 5, so each group has 5 parts.5 ÷ 5 = 1 per part, and 1 × 2 = 2
- Multiply by the number of groups, 12. Every group has the same amount.2 × 12 = 24
- Write the answer. 24
Check. 12 × 5 = 60. ✓
Watch out. Check that the groups fill exactly. A group must be the whole ratio, such as 2 + 3 = 5 parts.
Key words. A ratio is made of parts. Every part is the same size. The total is all the parts added together.
Method. Find the number of groups, then the amount in one group, then multiply.
- Find the number of groups: divide 84 by the group size, 7. The groups must fill exactly.84 ÷ 7 = 12 groups
- Find how many red counters are in one group. The ratio parts add up to 7, so each group has 7 parts.7 ÷ 7 = 1 per part, and 1 × 4 = 4
- Multiply by the number of groups, 12. Every group has the same amount.4 × 12 = 48
- Write the answer. 48
Check. 12 × 7 = 84. ✓
Watch out. Check that the groups fill exactly. A group must be the whole ratio, such as 2 + 3 = 5 parts.
Watch out
Do not multiply the two ratio numbers by each other. In the example with 60 lollies, the bags hold 5 lollies each, so there are 12 bags, not 2 × 3 bags.
Exam tip
Grown-up tip. Ask: “How many are in one pack?” and “How many packs are there?” If the total does not divide exactly by the group size, the groups cannot be filled.
Exercise 7F Grouping and ratio in packs
Non-calculatorKey words. A ratio is made of parts. Every part is the same size. The total is all the parts added together.
Method. Find the number of groups, then the amount in one group, then multiply.
- Find the number of groups: divide 20 by the group size, 4. The groups must fill exactly.20 ÷ 4 = 5 groups
- Find how many red pens are in one group. The ratio parts add up to 4, so each group has 4 parts.4 ÷ 4 = 1 per part, and 1 × 3 = 3
- Multiply by the number of groups, 5. Every group has the same amount.3 × 5 = 15
- Write the answer. 15
Check. 5 × 4 = 20. ✓
Watch out. Check that the groups fill exactly. A group must be the whole ratio, such as 2 + 3 = 5 parts.
Key words. A ratio is made of parts. Every part is the same size. The total is all the parts added together.
Method. Find how many are in one group, then multiply by the number of groups.
- Write how many yellow tiles are in one group. The ratio part is the number in one group.5 in one group
- Multiply by the number of groups, 7. Every group has the same amount.5 × 7 = 35
- Write the answer. 35
Check. 7 groups of 5 gives 35. ✓
Watch out. Multiply by the number of groups. Do not add the ratio parts.
Key words. A ratio is made of parts. Every part is the same size. The total is all the parts added together.
Method. Find how many are in one group, then multiply by the number of groups.
- Write how many red counters are in one group. The ratio part is the number in one group.3 in one group
- Multiply by the number of groups, 4. Every group has the same amount.3 × 4 = 12
- Write the answer. 12
Check. 4 groups of 3 gives 12. ✓
Watch out. Multiply by the number of groups. Do not add the ratio parts.
Key words. A ratio is made of parts. Every part is the same size. The total is all the parts added together.
Method. Find how many are in one group, then multiply by the number of groups.
- Write how many blue counters are in one group. The ratio part is the number in one group.4 in one group
- Multiply by the number of groups, 8. Every group has the same amount.4 × 8 = 32
- Write the answer. 32
Check. 8 groups of 4 gives 32. ✓
Watch out. Multiply by the number of groups. Do not add the ratio parts.
Key words. A ratio is made of parts. Every part is the same size. The total is all the parts added together.
Method. Find how many are in one group, then multiply by the number of groups.
- Write how many white counters are in one group. The ratio part is the number in one group.5 in one group
- Multiply by the number of groups, 6. Every group has the same amount.5 × 6 = 30
- Write the answer. 30
Check. 6 groups of 5 gives 30. ✓
Watch out. Multiply by the number of groups. Do not add the ratio parts.
Key words. A ratio is made of parts. Every part is the same size. The total is all the parts added together.
Method. Find the number of groups, then the amount in one group, then multiply.
- Find the number of groups: divide 56 by the group size, 8. The groups must fill exactly.56 ÷ 8 = 7 groups
- Find how many chocolate cakes are in one group. The ratio parts add up to 8, so each group has 8 parts.8 ÷ 8 = 1 per part, and 1 × 3 = 3
- Multiply by the number of groups, 7. Every group has the same amount.3 × 7 = 21
- Write the answer. 21
Check. 7 × 8 = 56. ✓
Watch out. Check that the groups fill exactly. A group must be the whole ratio, such as 2 + 3 = 5 parts.
Key words. A ratio is made of parts. Every part is the same size. The total is all the parts added together.
Method. Find the number of groups, then the amount in one group, then multiply.
- Find the number of groups: divide 60 by the group size, 6. The groups must fill exactly.60 ÷ 6 = 10 groups
- Find how many fruity sweets are in one group. The ratio parts add up to 3, so each group has 3 parts.6 ÷ 3 = 2 per part, and 2 × 2 = 4
- Multiply by the number of groups, 10. Every group has the same amount.4 × 10 = 40
- Write the answer. 40
Check. 10 × 6 = 60. ✓
Watch out. Check that the groups fill exactly. A group must be the whole ratio, such as 2 + 3 = 5 parts.
Key words. A ratio is made of parts. Every part is the same size. The total is all the parts added together.
Method. Find the number of groups, then the amount in one group, then multiply.
- Find the number of groups: divide 20 by the group size, 5. The groups must fill exactly.20 ÷ 5 = 4 groups
- Find how many blue counters are in one group. The ratio parts add up to 5, so each group has 5 parts.5 ÷ 5 = 1 per part, and 1 × 3 = 3
- Multiply by the number of groups, 4. Every group has the same amount.3 × 4 = 12
- Write the answer. 12
Check. 4 × 5 = 20. ✓
Watch out. Check that the groups fill exactly. A group must be the whole ratio, such as 2 + 3 = 5 parts.
Key words. A ratio is made of parts. Every part is the same size. The total is all the parts added together.
Method. Find the number of groups, then the amount in one group, then multiply.
- Find the number of groups: divide 80 by the group size, 8. The groups must fill exactly.80 ÷ 8 = 10 groups
- Find how many girls are in one group. The ratio parts add up to 4, so each group has 4 parts.8 ÷ 4 = 2 per part, and 2 × 1 = 2
- Multiply by the number of groups, 10. Every group has the same amount.2 × 10 = 20
- Write the answer. 20
Check. 10 × 8 = 80. ✓
Watch out. Check that the groups fill exactly. A group must be the whole ratio, such as 2 + 3 = 5 parts.
Key words. A ratio is made of parts. Every part is the same size. The total is all the parts added together.
Method. Find the number of groups, then the amount in one group, then multiply.
- Find the number of groups: divide 90 by the group size, 9. The groups must fill exactly.90 ÷ 9 = 10 groups
- Find how many red pencils are in one group. The ratio parts add up to 9, so each group has 9 parts.9 ÷ 9 = 1 per part, and 1 × 4 = 4
- Multiply by the number of groups, 10. Every group has the same amount.4 × 10 = 40
- Write the answer. 40
Check. 10 × 9 = 90. ✓
Watch out. Check that the groups fill exactly. A group must be the whole ratio, such as 2 + 3 = 5 parts.
Key words. A ratio is made of parts. Every part is the same size. The total is all the parts added together.
Method. Find the number of groups, then the amount in one group, then multiply.
- Find the number of groups: divide 24 by the group size, 6. The groups must fill exactly.24 ÷ 6 = 4 groups
- Find how many boys are in one group. The ratio parts add up to 3, so each group has 3 parts.6 ÷ 3 = 2 per part, and 2 × 1 = 2
- Multiply by the number of groups, 4. Every group has the same amount.2 × 4 = 8
- Write the answer. 8
Check. 4 × 6 = 24. ✓
Watch out. Check that the groups fill exactly. A group must be the whole ratio, such as 2 + 3 = 5 parts.
Key words. A ratio is made of parts. Every part is the same size. The total is all the parts added together.
Method. Find the red sweets in one pack, then in 3 packs.
- Find the red sweets in one pack. The ratio 1:2 shares 6 sweets into 3 parts, so one part is 2 sweets.6 ÷ 3 = 2, and 1 × 2 = 2 red
- Multiply by the number of packs, 3. Every pack has the same number of red sweets.2 × 3 = 6 red sweets
- Compare with 4. Three packs have 6 red sweets, which is not 4.6 ≠ 4
- Write the answer. No. 3 packs have 6 red sweets, not 4.
Check. Each pack has 2 red sweets, so 3 packs have 3 × 2 = 6 red sweets. ✓
Watch out. Find the number in one pack first. Then multiply by the number of packs.
Key words. A ratio is made of parts. Every part is the same size. The total is all the parts added together.
Method. Find the number of groups, then the amount in one group, then multiply.
- Find the number of groups: divide 40 by the group size, 8. The groups must fill exactly.40 ÷ 8 = 5 groups
- Find how many mint sweets are in one group. The ratio parts add up to 8, so each group has 8 parts.8 ÷ 8 = 1 per part, and 1 × 3 = 3
- Multiply by the number of groups, 5. Every group has the same amount.3 × 5 = 15
- Write the answer. 15
Check. 5 × 8 = 40. ✓
Watch out. Check that the groups fill exactly. A group must be the whole ratio, such as 2 + 3 = 5 parts.
Key words. A ratio is made of parts. Every part is the same size. The total is all the parts added together.
Method. Find the number of groups, then the amount in one group, then multiply.
- Find the number of groups: divide 60 by the group size, 10. The groups must fill exactly.60 ÷ 10 = 6 groups
- Find how many boys are in one group. The ratio parts add up to 5, so each group has 5 parts.10 ÷ 5 = 2 per part, and 2 × 2 = 4
- Multiply by the number of groups, 6. Every group has the same amount.4 × 6 = 24
- Write the answer. 24
Check. 6 × 10 = 60. ✓
Watch out. Check that the groups fill exactly. A group must be the whole ratio, such as 2 + 3 = 5 parts.
Key words. A ratio compares two amounts of the same kind. We write it with a colon: 2:3 is read ‘2 to 3’. The order matters, because the first number is the first amount named.
Method. Find the total boys and girls, then simplify the ratio.
- Find the total number of boys: 10 teams with 4 boys each. Each team has 4 boys.10 × 4 = 40 boys
- Find the total number of girls: 10 teams with 6 girls each. Each team has 6 girls.10 × 6 = 60 girls
- Write the ratio of boys to girls. The order is boys first.40:60
- Simplify by dividing both numbers by their HCF, which is 20. This gives the simplest form.40 ÷ 20 = 2, and 60 ÷ 20 = 3
- Write the answer. 2:3
Check. 2 × 20 = 40 and 3 × 20 = 60. ✓
Watch out. Simplify the total ratio, not the ratio in one team. Both give 2:3 here.