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🧩 6th grade math · Patterns & Algebra

Ratio tables and tapes

Equivalent ratios are the same comparison. Multiply both numbers by the same number to make one. 3 : 4 times 2 is 6 : 8. Adding the same number to both (5 : 6) breaks the ratio.

Worked example

The ratio of cups of juice to cups of soda is 4 : 3. How many cups of soda go with 16 cups of juice?
cups of juicecups of soda4316?
Answer: 12 cups of soda
The ratio 4 : 3 is already in lowest terms. 16 is 4 × 4, so multiply the other number by 4 too: 3 × 4 = 12.

For grown-ups: Ratio tables, tape diagrams, double number lines; plot ratio pairs. Below: three problems to try with the worked answers, and a free printable sheet. Children can practise the same skill as a game, with no sign-up and no ads.

  • CCSS 6.RP.A.3a
What this practises, for teachers

Practices ratio tables, tape diagrams, double number lines; plot ratio pairs (6.RP.A.3a). A printable sheet with its answer key, worked answers on the page, no accounts.

▶ Practise it

For your class

🖨️ Printable sheet and key

Try three

  1. Which ratio is equivalent to 7 : 6?
    Show the answer and how
    Answer: 28 : 24
    The right answer is 28 : 24. Multiply both numbers by the same amount: 7 × 4 = 28 and 6 × 4 = 24. Adding does not keep a ratio equal.
  2. The ratio of cups of juice to cups of soda is 5 : 2. How many cups of soda go with 15 cups of juice?
    cups of juicecups of soda5215?
    Show the answer and how
    Answer: 6 cups of soda
    The ratio 5 : 2 is already in lowest terms. 15 is 5 × 3, so multiply the other number by 3 too: 2 × 3 = 6.
  3. The ratio of red beads to white beads is 6 : 9. How many red beads go with 24 white beads?
    red beadswhite beads69?24
    Show the answer and how
    Answer: 16 red beads
    The ratio 6 : 9 is 2 : 3 in lowest terms (divide both by 3). 24 is 3 × 8, so multiply the other number by 8 too: 2 × 8 = 16.

Before and after

Learn first: How much for one? (6th)

Comes next: Best buy and speed (6th), Change units with ratios (6th)

Name: ____________________Date: ____________Score: ____ / 12

Ratio tables and tapes (6th grade)

  1. Which ratio is equivalent to 3 : 2?
  2. The ratio of cups of flour to cups of sugar is 1 : 6. How many cups of sugar go with 5 cups of flour?
    cups of flourcups of sugar165?
  3. The ratio of red beads to white beads is 3 : 5. How many white beads go with 6 red beads?
    red beadswhite beads356?
  4. The ratio of dogs to cats is 2 : 1. How many cats go with 10 dogs?
    dogscats2110?
  5. Which ratio is equivalent to 7 : 6?
  6. Which ratio is equivalent to 3 : 2?
  7. Which ratio is equivalent to 6 : 5?
  8. The ratio of bikes to scooters is 8 : 14. How many scooters go with 28 bikes?
    bikesscooters81428?
  9. Which ratio is equivalent to 7 : 5?
  10. Which ratio is equivalent to 3 : 7?
  11. The ratio of cups of flour to cups of sugar is 24 : 15. How many cups of sugar go with 16 cups of flour?
    cups of flourcups of sugar241516?
  12. The ratio of bikes to scooters is 27 : 24. How many bikes go with 32 scooters?
    bikesscooters2724?32

Answer key

  1. 9 : 6
  2. 30 cups of sugar
  3. 10 white beads
  4. 5 cats
  5. 28 : 24
  6. 9 : 6
  7. 12 : 10
  8. 49 scooters
  9. 21 : 15
  10. 6 : 14
  11. 10 cups of sugar
  12. 36 bikes

More 6th grade skills: all 6th grade math skills, or every grade at math skills.