Ratio reasoning means scaling a known ratio up or down to answer a question. That runs on multiplication, division, and equivalent fractions. Warm those up and you can reason through any recipe or rate.
Answer these 3, then press Show my path. No grade — this just points you to the right level.
1. What is 6 × 5?
2. What is 20 ÷ 4?
3. 3/4 = ?/8 — the missing top number is…?
Ratio reasoning means scaling a known ratio to fit a new amount. Multiply both numbers to grow it, or divide both to shrink it.
Your quick check picks one for you, but you can switch any time:
Level 0 Scale up one step at a time.
A. 1 pencil costs $2. Two pencils cost 2 × $2 = $___?
2 × 2 = 4.
B. Three pencils cost 3 × $2 = $___?
3 × 2 = 6.
C. So 4 pencils cost 4 × $2 = $___?
4 × 2 = 8.
Level 1 Scale down by dividing.
A. 12 stickers are shared into 3 equal bags. Each bag has 12 ÷ 3 = ___?
12 ÷ 3 = 4.
B. 15 marbles in 5 cups, equally. Each cup has 15 ÷ 5 = ___?
15 ÷ 5 = 3.
Level 2 Reason with a full ratio.
A. 2 cups of flour make 6 muffins. To make 12 muffins (double), you need ___ cups of flour?
Muffins doubled (6→12), so flour doubles: 2 × 2 = 4.
B. 3 pens cost $6. How much do 5 pens cost? (First find 1 pen.)
1 pen = $6 ÷ 3 = $2, so 5 pens = 5 × $2 = $10.
1. 1 box holds 4 toys. How many toys are in 5 boxes? 5 × 4 = ___?
5 × 4 = 20.
2. 4 apples cost $8. How much does 1 apple cost?
$8 ÷ 4 = $2 per apple.
You've practiced exactly what Lesson 3-6 uses. Time to dive in.
Start Lesson 3-6 →