Equivalent Ratio Tables

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Equivalent Ratio Tables · Grade 6 · Worksheet 3

1. A fruit punch recipe calls for mixing orange juice and pineapple juice in a ratio of 5:3. If Emma wants to make 32 cups of punch for her party, how many cups of orange juice should she use? Answer: 20 Solution: The ratio of orange juice to pineapple juice is 5:3. This means for every 5 cups of orange juice, we use 3 cups of pineapple juice. Find the total number of parts.
   Full step-by-step solution

   Let's solve this step-by-step. Step 1: Understand the ratio. The ratio of orange juice to pineapple juice is 5:3. This means for every 5 cups of orange juice, we use 3 cups of pineapple juice. Step 2: Find the total number of parts. Total parts = 5 + 3 = 8 parts. Step 3: Relate parts to total punch. We know 8 parts = 32 cups of punch. So 1 part = 32 / 8 = 4 cups. Step 4: Find cups of orange juice. Orange juice is 5 parts. So orange juice = 5 × 4 = 20 cups. Step 5: Conclusion. Emma should use 20 cups of orange juice.

2. Liam is mixing paint for an art project. He needs to create a specific shade of purple by mixing red and blue paint in a 3:5 ratio. If he uses 450 milliliters of red paint, how many milliliters of blue paint should he add to maintain the correct ratio? Answer: 750 Solution: We are told the ratio of red to blue paint is 3:5. That means for every 3 parts of red paint, we need 5 parts of blue paint.
   Full step-by-step solution

   We are told the ratio of red to blue paint is 3:5. That means for every 3 parts of red paint, we need 5 parts of blue paint. Step 1: Understand the ratio meaning. Red : Blue = 3 : 5 If Liam uses 450 ml of red paint, we can set up a proportion: 3 parts red → 5 parts blue 450 ml red → ? ml blue Step 2: Set up the proportion equation. Let B = milliliters of blue paint needed. From the ratio: 3 / 5 = 450 / B Step 3: Solve for B. Cross-multiply: 3 × B = 5 × 450 3B = 2250 Step 4: Divide both sides by 3. B = 2250 / 3 B = 750 Step 5: Conclusion. Liam needs 750 milliliters of blue paint to maintain the 3:5 ratio with 450 ml of red paint. ANSWER: 750

3. Complete the table of equivalent ratios: | Kaia's steps | 9 | 18 | 27 | 36 | x | |--------------|---|---|---|---|---| | Tane's steps | 14 | 28 | 42 | 56 | 84 | Find x. Answer: 54 Solution: Identify the ratio from the first column: Kaia : Tane = 9 : 14. For the last column, Tane's steps are 84. Let Kaia's steps be x.
   Full step-by-step solution

   Step 1: Identify the ratio from the first column: Kaia : Tane = 9 : 14. Step 2: For the last column, Tane's steps are 84. Let Kaia's steps be x. The ratio must be equivalent: 9/14 = x/84. Step 3: Cross-multiply: 9 * 84 = 14 * x. Step 4: Calculate 9 * 84 = 756. Step 5: So 756 = 14x. Step 6: Divide both sides by 14: x = 756 ÷ 14 = 54. Step 7: Check: 9/14 = 54/84 simplifies to 9/14 = 9/14. Correct. The answer is 54.

4. A rectangular garden is drawn on a coordinate plane with vertices at (2, 1), (8, 1), (8, 5), and (2, 5). If the gardener plants flowers in a pattern that creates 3 rows and 4 columns of flower beds within the garden, what is the ratio of the area of one flower bed to the total garden area? Answer: 1:12 Solution: Vertices: (2, 1), (8, 1), (8, 5), (2, 5) Length along x-axis: from x = 2 to x = 8 → length = 8 − 2 = 6 units Length along y-axis: from y = 1 to y = 5 → width = 5 − 1 = 4 units Area of garden = length × width = 6 × 4 = 24 square units.
   Full step-by-step solution

   Let's go step by step. --- **Step 1: Find the dimensions of the garden** Vertices: (2, 1), (8, 1), (8, 5), (2, 5) Length along x-axis: from x = 2 to x = 8 → length = 8 − 2 = 6 units Length along y-axis: from y = 1 to y = 5 → width = 5 − 1 = 4 units Area of garden = length × width = 6 × 4 = 24 square units. --- **Step 2: Understand the flower bed arrangement** The problem says: 3 rows and 4 columns of flower beds. That means the garden is divided into 3 equal parts along the vertical (y) direction and 4 equal parts along the horizontal (x) direction. --- **Step 3: Find the dimensions of one flower bed** Total length (x-direction) = 6 units Divided into 4 columns → width of one flower bed = 6 / 4 = 1.5 units Total width (y-direction) = 4 units Divided into 3 rows → height of one flower bed = 4 / 3 units Area of one flower bed = (1.5) × (4/3) = (3/2) × (4/3) = (3 × 4) / (2 × 3) = 12 / 6 = 2 square units --- **Step 4: Ratio of one flower bed area to total garden area** One flower bed area = 2 Total garden area = 24 Ratio = 2 : 24 Simplify: divide both by 2 → 1 : 12 --- **Final Answer:** 1:12

5. A wildlife sanctuary is tracking the population of deer and elk in their preserve. The current ratio of deer to elk is 7:4. If there are 1,540 deer in the sanctuary, how many elk are there? Answer: 880 Solution: The ratio of deer to elk is 7:4, which means for every 7 deer, there are 4 elk. We know there are 1,540 deer, which represents 7 parts of the ratio.
   Full step-by-step solution

   Step 1: The ratio of deer to elk is 7:4, which means for every 7 deer, there are 4 elk. Step 2: We know there are 1,540 deer, which represents 7 parts of the ratio. Step 3: Find the value of one ratio part by dividing the number of deer by 7: 1,540 ÷ 7 = 220 Step 4: Since there are 4 parts for elk, multiply the value of one part by 4: 220 × 4 = 880 Step 5: Therefore, there are 880 elk in the sanctuary.

6. A construction company mixes concrete using cement, sand, and gravel in a ratio of 2:3:5. If they need to prepare 1500 kilograms of concrete for a foundation project, how many kilograms of sand should they use? Answer: 450 Solution: Add all the ratio parts together: 2 + 3 + 5 = 10 total parts The sand represents 3 parts out of the total 10 parts Calculate the fraction for sand: 3/10 of the total mixture Multiply the total concrete amount by the sand fraction: 1500 × 3/10 Calculate: 1500 × 3 = 4500, then 4500 ÷ 10 = 450 The…
   Full step-by-step solution

   Step 1: Add all the ratio parts together: 2 + 3 + 5 = 10 total parts Step 2: The sand represents 3 parts out of the total 10 parts Step 3: Calculate the fraction for sand: 3/10 of the total mixture Step 4: Multiply the total concrete amount by the sand fraction: 1500 × 3/10 Step 5: Calculate: 1500 × 3 = 4500, then 4500 ÷ 10 = 450 Step 6: The company needs 450 kilograms of sand Final answer: 450

7. If 7:9 = 63:x, then x = ? Answer: 81 Solution: Write the proportion as equivalent fractions: 7/9 = 63/x Cross-multiply: 7 * x = 9 * 63 Calculate the right side: 9 * 63 = 567 So we have 7x = 567 Divide both sides by 7: x = 567 ÷ 7 Calculate: 567 ÷ 7 = 81 Therefore, x = 81
   Full step-by-step solution

   Step 1: Write the proportion as equivalent fractions: 7/9 = 63/x Step 2: Cross-multiply: 7 * x = 9 * 63 Step 3: Calculate the right side: 9 * 63 = 567 Step 4: So we have 7x = 567 Step 5: Divide both sides by 7: x = 567 ÷ 7 Step 6: Calculate: 567 ÷ 7 = 81 Therefore, x = 81

8. If 4:7 = 20:x, then x = ? Answer: 35 Solution: We are given the proportion: 4:7 = 20:x. Write the proportion as fractions. 4:7 means 4/7, and 20:x means 20/x.
   Full step-by-step solution

   We are given the proportion: 4:7 = 20:x. Step 1: Write the proportion as fractions. 4:7 means 4/7, and 20:x means 20/x. So we have: 4/7 = 20/x Step 2: Cross-multiply to eliminate the fractions. 4 * x = 7 * 20 Step 3: Perform the multiplication on the right side. 4 * x = 140 Step 4: Solve for x by dividing both sides by 4. x = 140 / 4 Step 5: Calculate the division. x = 35 Thus, the value of x is 35.

9. Complete the ratio table: 6:11 = 36:__ = __:121 Answer: 66 and 66 Solution: Start with the ratio 6:11. To find the missing number after 36, ask: 6 times what equals 36? 36 ÷ 6 = 6, so multiply by 6.
   Full step-by-step solution

   Step 1: Start with the ratio 6:11. To find the missing number after 36, ask: 6 times what equals 36? 36 ÷ 6 = 6, so multiply by 6. Then multiply 11 by 6: 11 × 6 = 66. So 36:66 is equivalent. Step 2: Now find the missing number before 121. Ask: 11 times what equals 121? 121 ÷ 11 = 11, so multiply by 11. Then multiply 6 by 11: 6 × 11 = 66. So 66:121 is equivalent. Step 3: Both missing numbers are 66. The completed table is 6:11 = 36:66 = 66:121. The answer is 66 and 66.