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Equivalent Ratio Tables

Grade 6 · Ratios · Worksheet 1

  1. If 4:9 = 16:x, then x = ? Answer: ______________
  2. Complete the table of equivalent ratios: | Hana's score | 12 | 18 | 30 | 42 | x | |--------------|----|----|----|----|----| | Matiu's score| 15 | 22.5 | 37.5 | 52.5 | 75 | Find x. Answer: ______________
  3. If 12:18 = x:27, then x = ? Answer: ______________
  4. A recipe for lemonade requires mixing 5 cups of water with 2 cups of lemon juice. If Liam wants to make a large batch using 15 cups of water, how many cups of lemon juice should he use to maintain the same flavor? Answer: ______________
  5. Isabella is organizing a school fundraiser and is making batches of homemade lemonade. The recipe calls for 7 cups of water for every 2 cups of lemon juice. She needs to make enough lemonade for the entire school, so she uses a large container and fills in a ratio table to scale up the recipe. Complete the table below with the missing equivalent ratios. | Water (cups) | Lemon Juice (cups) | |--------------|-------------------| | 7 | 2 | | 14 | 4 | | 21 | ? | | 28 | 8 | | ? | 10 | | 49 | ? | Answer: ______________
  6. Complete the table of equivalent ratios: | Hana's score | 8 | 16 | 24 | 32 | 40 | |--------------|---|---|---|---|---| | Matiu's score| 12 | 24 | 36 | x | 60 | Find x. Answer: ______________
  7. If 3:8 = x:56, then x = ? Answer: ______________
  8. A rectangular garden is drawn on a coordinate plane with corners at (1, 2), (13, 2), (13, 8), and (1, 8). The gardener plants flowers in a pattern where for every 4 square units of garden area, she plants 3 flower beds. How many flower beds will she need for the entire garden? Answer: ______________
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Answer Key & Explanations

Equivalent Ratio Tables · Grade 6 · Worksheet 1

  1. If 4:9 = 16:x, then x = ? Answer: 36 Solution: We are given the proportion: 4:9 = 16:x. Write the proportion as fractions. 4:9 means 4/9, and 16:x means 16/x.
    Full step-by-step solution

    We are given the proportion: 4:9 = 16:x. Step 1: Write the proportion as fractions. 4:9 means 4/9, and 16:x means 16/x. So we have: 4/9 = 16/x Step 2: Cross-multiply to eliminate the fractions. 4 * x = 9 * 16 Step 3: Perform the multiplication on the right side. 4 * x = 144 Step 4: Solve for x by dividing both sides by 4. x = 144 / 4 Step 5: Calculate the division. x = 36 So the value of x is 36. We can check: 4/9 = 16/36, because 16/36 simplifies to 4/9. Correct.

  2. Complete the table of equivalent ratios: | Hana's score | 12 | 18 | 30 | 42 | x | |--------------|----|----|----|----|----| | Matiu's score| 15 | 22.5 | 37.5 | 52.5 | 75 | Find x. Answer: 60 Solution: Identify the ratio from the first column: Hana : Matiu = 12 : 15. Simplify by dividing both by 3: 4 : 5. For the last column, Matiu's score is 75.
    Full step-by-step solution

    Step 1: Identify the ratio from the first column: Hana : Matiu = 12 : 15. Simplify by dividing both by 3: 4 : 5. So the ratio is 4:5. Step 2: For the last column, Matiu's score is 75. Let Hana's score be x. The ratio must be equivalent: 4/5 = x/75. Step 3: Cross-multiply: 4 * 75 = 5 * x. Step 4: Calculate 4 * 75 = 300. Step 5: So 300 = 5x. Step 6: Divide both sides by 5: x = 300 ÷ 5 = 60. Step 7: Check: 12/15 = 60/75 simplifies to 4/5 = 4/5. Correct. The answer is 60.

  3. If 12:18 = x:27, then x = ? Answer: 18 Solution: We are given the proportion: 12:18 = x:27. Write the proportion in fraction form. 12:18 means 12/18, and x:27 means x/27.
    Full step-by-step solution

    We are given the proportion: 12:18 = x:27. Step 1: Write the proportion in fraction form. 12:18 means 12/18, and x:27 means x/27. So we have: 12/18 = x/27 Step 2: Simplify 12/18 if possible. 12/18 = (12 ÷ 6)/(18 ÷ 6) = 2/3. So the equation becomes: 2/3 = x/27 Step 3: Solve for x by cross-multiplying. 2/3 = x/27 Multiply both sides by 27: 27 * (2/3) = x Step 4: Perform the multiplication. 27 * 2 = 54 54 / 3 = 18 So x = 18. Step 5: Check the answer. 12/18 = 2/3, and 18/27 = 2/3. Both ratios are equal, so the answer is correct. Final answer: x = 18

  4. A recipe for lemonade requires mixing 5 cups of water with 2 cups of lemon juice. If Liam wants to make a large batch using 15 cups of water, how many cups of lemon juice should he use to maintain the same flavor? Answer: 6 Solution: The recipe says 5 cups of water to 2 cups of lemon juice. Identify the new amount of water. Liam is using 15 cups of water.
    Full step-by-step solution

    Step 1: Understand the original ratio. The recipe says 5 cups of water to 2 cups of lemon juice. So the ratio of water to lemon juice is 5 : 2. Step 2: Identify the new amount of water. Liam is using 15 cups of water. Step 3: Find the scaling factor. We see that 15 cups of water is 3 times the original 5 cups because: 15 ÷ 5 = 3. Step 4: Apply the scaling factor to the lemon juice. Original lemon juice = 2 cups. Multiply by the same scaling factor: 2 × 3 = 6 cups. Step 5: Conclusion. To keep the same flavor, Liam should use 6 cups of lemon juice. Final answer: 6

  5. Isabella is organizing a school fundraiser and is making batches of homemade lemonade. The recipe calls for 7 cups of water for every 2 cups of lemon juice. She needs to make enough lemonade for the entire school, so she uses a large container and fills in a ratio table to scale up the recipe. Complete the table below with the missing equivalent ratios. | Water (cups) | Lemon Juice (cups) | |--------------|-------------------| | 7 | 2 | | 14 | 4 | | 21 | ? | | 28 | 8 | | ? | 10 | | 49 | ? | Answer: 6, 35, 14 Solution: The ratio is 7 cups water to 2 cups lemon juice, or 7:2. This means for every 7 cups of water, you need 2 cups of juice. For the third row, water is 21 cups.
    Full step-by-step solution

    Step 1: The ratio is 7 cups water to 2 cups lemon juice, or 7:2. This means for every 7 cups of water, you need 2 cups of juice. Step 2: For the third row, water is 21 cups. To find the lemon juice, determine how many times 7 goes into 21: 21 / 7 = 3. Then multiply the juice amount by 3: 2 * 3 = 6 cups. So the first missing value is 6. Step 3: For the fifth row, lemon juice is 10 cups. To find the water, determine how many times 2 goes into 10: 10 / 2 = 5. Then multiply the water amount by 5: 7 * 5 = 35 cups. So the second missing value is 35. Step 4: For the sixth row, water is 49 cups. To find the lemon juice, determine how many times 7 goes into 49: 49 / 7 = 7. Then multiply the juice amount by 7: 2 * 7 = 14 cups. So the third missing value is 14. Step 5: The completed table is: | Water (cups) | Lemon Juice (cups) | |--------------|-------------------| | 7 | 2 | | 14 | 4 | | 21 | 6 | | 28 | 8 | | 35 | 10 | | 49 | 14 | The missing values are 6, 35, and 14.

  6. Complete the table of equivalent ratios: | Hana's score | 8 | 16 | 24 | 32 | 40 | |--------------|---|---|---|---|---| | Matiu's score| 12 | 24 | 36 | x | 60 | Find x. Answer: 48 Solution: Identify the ratio from the first column: Hana : Matiu = 8 : 12. This simplifies to 2 : 3 (divide both by 4). So for every 2 points Hana scores, Matiu scores 3 points.
    Full step-by-step solution

    Step 1: Identify the ratio from the first column: Hana : Matiu = 8 : 12. This simplifies to 2 : 3 (divide both by 4). So for every 2 points Hana scores, Matiu scores 3 points. Step 2: For the fourth column, Hana's score is 32. Let Matiu's score be x. The ratio must be equivalent: 8/12 = 32/x. Step 3: Cross-multiply: 8 * x = 12 * 32. Step 4: Calculate 12 * 32 = 384. Step 5: So 8x = 384. Step 6: Divide both sides by 8: x = 384 ÷ 8 = 48. Step 7: Check: 8/12 = 32/48 simplifies to 2/3 = 2/3. Correct. The answer is 48.

  7. If 3:8 = x:56, then x = ? Answer: 21 Solution: Write the proportion: 3/8 = x/56 Cross-multiply: 3 * 56 = 8 * x Calculate the left side: 3 * 56 = 168 Write the equation: 168 = 8x Divide both sides by 8: 168 ÷ 8 = x Calculate: 168 ÷ 8 = 21 Therefore, x = 21
    Full step-by-step solution

    Step 1: Write the proportion: 3/8 = x/56 Step 2: Cross-multiply: 3 * 56 = 8 * x Step 3: Calculate the left side: 3 * 56 = 168 Step 4: Write the equation: 168 = 8x Step 5: Divide both sides by 8: 168 ÷ 8 = x Step 6: Calculate: 168 ÷ 8 = 21 Step 7: Therefore, x = 21

  8. A rectangular garden is drawn on a coordinate plane with corners at (1, 2), (13, 2), (13, 8), and (1, 8). The gardener plants flowers in a pattern where for every 4 square units of garden area, she plants 3 flower beds. How many flower beds will she need for the entire garden? Answer: 54 Solution: Find the length of the rectangle using the x-coordinates: 13 - 1 = 12 units Find the width of the rectangle using the y-coordinates: 8 - 2 = 6 units Calculate the total area: 12 × 6 = 72 square units Set up the ratio: 3 flower beds for every 4 square units Calculate how many flower beds are…
    Full step-by-step solution

    Step 1: Find the length of the rectangle using the x-coordinates: 13 - 1 = 12 units Step 2: Find the width of the rectangle using the y-coordinates: 8 - 2 = 6 units Step 3: Calculate the total area: 12 × 6 = 72 square units Step 4: Set up the ratio: 3 flower beds for every 4 square units Step 5: Calculate how many flower beds are needed: (72 ÷ 4) × 3 = 18 × 3 = 54 Step 6: The gardener needs 54 flower beds for the entire garden.