Warm-up
Three quick questions from earlier lessons.
Discover
Trail mix uses raisins and nuts in the ratio 2 : 3. What fraction of the mix is raisins?
Key idea
Ratios compare parts; the whole is the sum of the parts.
In a ratio of two parts, the whole has parts. To share a total: total ÷ gives one part; then multiply. The fraction of the whole for the first part is .
Worked example
Share 35 stickers in the ratio 3 : 4.
7 parts
3 + 4 parts.
5 per part
35 ÷ 7.
15 and 20
3 × 5 and 4 × 5.
Your turn, guided
Your turn: 24 marbles in the ratio 1 : 3. The smaller share.
24 ÷ 4.
Practice ★
- Green paint is mixed 1 parts blue to 3 parts yellow. How many cups of blue are in 24 cups of green paint?
- Green paint is mixed 5 parts blue to 3 parts yellow. How many cups of blue are in 24 cups of green paint?
- Juice and water are mixed in the ratio 9 : 1. What fraction of the drink is juice?
Watch out!
Practice ★★
- The ratio of boys to girls in a club is 5 : 6. There are 36 girls. How many students are in the club?
- The ratio of boys to girls in a club is 3 : 4. There are 20 girls. How many students are in the club?
- Boss problem. Lemonade uses lemon juice and water in the ratio 4 : 5. You want 18 cups of lemonade.
Exit ticket
Three questions to check you have got it.
- Green paint is mixed 1 parts blue to 3 parts yellow. How many cups of blue are in 24 cups of green paint?
- Green paint is mixed 5 parts blue to 3 parts yellow. How many cups of blue are in 24 cups of green paint?
- Green paint is mixed 5 parts blue to 4 parts yellow. How many cups of blue are in 72 cups of green paint?
Summary card
Part-part-whole
Whole = sum of parts; one part = total ÷ number of parts.
Watch out: a : b is part to part, not part to whole.