← Back to the Ratios worksheet
Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Every problem has a full worked solution with the final answer in bold. Compare each step with your own work, not only the result, and redo any problem where the method differed.
Standards: 6.RP.A.1, 6.RP.A.3a · Level: Grade 6
Problem 1 Writing a Ratio
Flutes come first, so the ratio is 14 to 9.
Answer: 14 : 9, 14 to 9, and 149.
Problem 2 Order Matters
Clarinets are named first, so the ratio is 9 : 14. The terms are swapped, so it compares clarinets with flutes, a different relationship.
Answer: 9 : 14.
Problem 3 Reading a Tape Diagram
(a) Count 4 muffin blocks and 7 scone blocks: 4 : 7.
(b) The whole is 4 + 7 = 11 blocks, so scones to all pastries is 7 : 11.
Answer: (a) 4 : 7; (b) 7 : 11.
Problem 4 Part-to-Part and Part-to-Whole
Walkers: 27 − 12 = 15.
(a) 12 : 15 (b) 12 : 27 (c) 15 : 27
Answer: (a) 12 : 15; (b) 12 : 27; (c) 15 : 27.
Problem 5 Making Equivalent Ratios
Multiply both terms by 2, 3 and 4: 4 × 2 = 8 and 7 × 2 = 14; 4 × 3 = 12 and 7 × 3 = 21; 4 × 4 = 16 and 7 × 4 = 28.
Answer: 8 : 14, 12 : 21, 16 : 28 (other correct answers are possible).
Problem 6 Completing a Ratio Table
Each column is 3 : 2. Flour 6 is 3 × 2, so sugar is 2 × 2 = 4. Flour 9 is 3 × 3, so sugar is 6. Sugar 10 is 2 × 5, so flour is 3 × 5 = 15. Flour 30 is 3 × 10, so sugar is 20.
Answer: sugar 4, 6, 20 and flour 15.
Problem 7 Simplest Form
(a) The greatest common factor of 36 and 48 is 12: 36 ÷ 12 = 3 and 48 ÷ 12 = 4.
(b) The greatest common factor of 45 and 30 is 15: 45 ÷ 15 = 3 and 30 ÷ 15 = 2.
Answer: (a) 3 : 4; (b) 3 : 2.
Problem 8 Equivalent or Not?
(a) 5 × 7 = 35 and 8 × 7 = 56, so they match.
(b) 9 : 12 simplifies to 3 : 4; 15 : 21 simplifies to 5 : 7. They differ.
(c) 16 : 10 simplifies to 8 : 5; 24 : 15 simplifies to 8 : 5. They match.
Answer: (a) yes; (b) no; (c) yes.
Problem 9 Finding the Missing Term
(a) 28 ÷ 7 = 4, and 3 × 4 = 12.
(b) 63 ÷ 9 = 7, and 5 × 7 = 35.
Answer: (a) 12; (b) 35.
Problem 10 Double Number Line
(a) Each step is 2 scoops and 5 quarts. After 10 quarts the next values are 15 and 20.
(b) 14 ÷ 2 = 7 steps, so 7 × 5 = 35 quarts.
Answer: (a) 15 and 20; (b) 35 quarts.
Problem 11 Finding a Whole from a Part
30 ÷ 5 = 6, so multiply 6 by 6: 36 sopranos.
Total: 30 + 36 = 66.
Answer: 36 sopranos and 66 singers.
Problem 12 Comparing Two Recipes
Use 35 cups of water for both. A: 3 : 5 = 21 : 35. B: 4 : 7 = 20 : 35.
With the same water, A has 21 cups of juice and B only 20.
Answer: Punch A.
Problem 13 Sharing a Total
The tape has 5 + 3 = 8 equal blocks. Each block is 40 ÷ 8 = 5 plants.
Tomatoes: 5 × 5 = 25. Peppers: 3 × 5 = 15. Check: 25 + 15 = 40.
Answer: 25 tomato plants and 15 pepper plants.
Problem 14 Camp Staffing
The ratio 2 : 14 simplifies to 1 : 7.
(a) 98 ÷ 7 = 14 counselors.
(b) 11 × 7 = 77 campers.
Answer: (a) 14 counselors; (b) 77 campers.
Problem 15 Mixing Green Paint
Parts: 4 + 9 = 13. One part: 52 ÷ 13 = 4 quarts.
Blue: 4 × 4 = 16. Yellow: 9 × 4 = 36. Check: 16 + 36 = 52.
Answer: 16 quarts of blue and 36 quarts of yellow.
Problem 16 Season Record
9 : 6 simplifies to 3 : 2, so each group has 5 games. 45 ÷ 5 = 9 groups.
Wins: 3 × 9 = 27. Losses: 2 × 9 = 18.
Answer: 27 wins and 18 losses.
Problem 17 Pet Store Difference
Fish have 8 blocks and hamsters 3 blocks, so the difference is 5 blocks. 5 blocks = 20, so 1 block = 4.
Fish: 8 × 4 = 32. Hamsters: 3 × 4 = 12. Check: 32 − 12 = 20.
Answer: 32 fish and 12 hamsters.
Problem 18 Science Fair Entries
7 + 5 = 12 parts, and 168 ÷ 12 = 14 students per part.
Sixth: 7 × 14 = 98. Seventh: 5 × 14 = 70. Difference: 98 − 70 = 28.
Answer: 28 more sixth graders.
Problem 19 Spot the Error
Adding the same number to both terms does not keep the relationship. To keep the ratio, multiply both terms by the same number. Here 3 × 2 = 6, so 5 × 2 = 10.
Answer: 10.
Problem 20 Fundraiser Revenue
3 + 2 = 5 items per group, and 135 ÷ 5 = 27 groups.
T-shirts: 3 × 27 = 81, so 81 × 12 = $972. Hoodies: 2 × 27 = 54, so 54 × 25 = $1,350.
Total: 972 + 1,350 = 2,322.
Answer: $2,322.