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Grade 6
Ratios
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1. Ratios and equivalent ratios
Warm-up
Three quick questions from earlier lessons.
Discover
A purple paint uses 2 cups of red for 3 cups of blue. To make the same color with 6 cups of red, how much blue?
9 cups
7 cups
Key idea
Equivalent ratios multiply both quantities by the same number.
A ratioa:b compares two quantities in order. Equivalent ratios come from multiplying (or dividing) both parts by the same number: a:b=ka:kb. Tables and double number lines show them.
Worked example
4:5=?:20.
Multiply both by 4
5 × 4 = 20.
16:20
4 × 4.
Your turn, guided
Your turn: 3:7=12:?.
28
× 4.
Practice ★
A recipe uses 7 cups of flour for every 6 cups of sugar. How many cups of sugar go with 42 cups of flour?
A recipe uses 2 cups of flour for every 7 cups of sugar. How many cups of sugar go with 12 cups of flour?
Which ratio is equivalent to 4:6?
8:12
6:8
6:4
Watch out!
Practice ★★
Complete the equivalent ratio 8:6=?:18.
Complete the equivalent ratio 6:2=?:12.
Exit ticket
Three questions to check you have got it.
A recipe uses 7 cups of flour for every 6 cups of sugar. How many cups of sugar go with 42 cups of flour?
A recipe uses 2 cups of flour for every 7 cups of sugar. How many cups of sugar go with 12 cups of flour?
A recipe uses 9 cups of flour for every 2 cups of sugar. How many cups of sugar go with 27 cups of flour?
Summary card
Equivalent ratios
Multiply both parts by the same number.
Watch out: adding the same amount changes the ratio.
2. Part-part-whole ratio problems
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?
52
32
Key idea
Ratios compare parts; the whole is the sum of the parts.
In a ratio a:b of two parts, the whole has a+b parts. To share a total: total ÷ (a+b) gives one part; then multiply. The fraction of the whole for the first part is a+ba.
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.
6
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.
