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Ratio Concepts

Grade 6 · Ratios · Worksheet 3

  1. If 4/7 = x/35, then x = ? Answer: ______________
  2. Ava is making a fruit punch. The recipe calls for 6 cups of orange juice for every 1 cup of pineapple juice. If Ava uses 36 cups of orange juice, how many cups of pineapple juice does she need? Answer: ______________
  3. Aroha is making a fruit salad. The ratio of apples to oranges is 7:5. If there are 35 apples, how many oranges are there? Answer: ______________
  4. If the ratio of boys to girls in a class is 5:3 and there are 40 students total, how many boys are there? Answer: ______________
  5. Aisha is making a special fruit punch for a school event. The recipe requires mixing cranberry juice and orange juice in a 4:7 ratio. If Aisha uses 1.2 liters of cranberry juice, how many liters of orange juice does she need to maintain the correct ratio? Answer: ______________
  6. Ava is making a fruit punch for a school party. The recipe requires mixing orange juice and pineapple juice in a 4:7 ratio. If Ava uses 2.8 liters of orange juice, how many liters of pineapple juice does she need to maintain the correct ratio? Answer: ______________
  7. 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 Liam uses 450 milliliters of blue paint, how many milliliters of red paint should he use to maintain the correct ratio? Answer: ______________
  8. A school is organizing a field trip to a science museum. The total cost for transportation and admission is $1,275. If 34 students are going on the trip, what is the cost per student? Answer: ______________
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Answer Key & Explanations

Ratio Concepts · Grade 6 · Worksheet 3

  1. If 4/7 = x/35, then x = ? Answer: 20 Solution: Step 1: Set up the proportion: 4/7 = x/35 Step 2: Find what number you multiply 7 by to get 35: 35 ÷ 7 = 5 Step 3: Multiply the numerator by the same number: 4 × 5 = 20 Step 4: Therefore, x = 20 Step 5: Verify: 4/7 = 20/35 (both simplify to the same fraction) The answer is 20.
    Full step-by-step solution

    Step 1: Set up the proportion: 4/7 = x/35 Step 2: Find what number you multiply 7 by to get 35: 35 ÷ 7 = 5 Step 3: Multiply the numerator by the same number: 4 × 5 = 20 Step 4: Therefore, x = 20 Step 5: Verify: 4/7 = 20/35 (both simplify to the same fraction) The answer is 20.

  2. Ava is making a fruit punch. The recipe calls for 6 cups of orange juice for every 1 cup of pineapple juice. If Ava uses 36 cups of orange juice, how many cups of pineapple juice does she need? Answer: 6 Solution: The ratio of orange juice to pineapple juice is 6:1, meaning for every 6 cups of orange juice, there is 1 cup of pineapple juice. Ava uses 36 cups of orange juice.
    Full step-by-step solution

    Step 1: The ratio of orange juice to pineapple juice is 6:1, meaning for every 6 cups of orange juice, there is 1 cup of pineapple juice. Step 2: Ava uses 36 cups of orange juice. To find how many cups of pineapple juice are needed, divide the amount of orange juice by 6: 36 ÷ 6 = 6. Step 3: So, Ava needs 6 cups of pineapple juice. The answer is 6.

  3. Aroha is making a fruit salad. The ratio of apples to oranges is 7:5. If there are 35 apples, how many oranges are there? Answer: 25 Solution: The ratio of apples to oranges is 7:5. This means for every 7 apples, there are 5 oranges. There are 35 apples.
    Full step-by-step solution

    Step 1: The ratio of apples to oranges is 7:5. This means for every 7 apples, there are 5 oranges. Step 2: There are 35 apples. Find how many groups of 7 apples there are: 35 ÷ 7 = 5 groups. Step 3: Each group has 5 oranges, so multiply: 5 groups × 5 oranges per group = 25 oranges. Step 4: Therefore, there are 25 oranges. The answer is 25.

  4. If the ratio of boys to girls in a class is 5:3 and there are 40 students total, how many boys are there? Answer: 25 Solution: The ratio of boys to girls is 5:3, so the total number of parts is 5 + 3 = 8 parts. The total number of students is 40, so each part represents 40 ÷ 8 = 5 students.
    Full step-by-step solution

    Step 1: The ratio of boys to girls is 5:3, so the total number of parts is 5 + 3 = 8 parts. Step 2: The total number of students is 40, so each part represents 40 ÷ 8 = 5 students. Step 3: The number of boys is 5 parts × 5 students per part = 25 students. The answer is 25.

  5. Aisha is making a special fruit punch for a school event. The recipe requires mixing cranberry juice and orange juice in a 4:7 ratio. If Aisha uses 1.2 liters of cranberry juice, how many liters of orange juice does she need to maintain the correct ratio? Answer: 2.1 Solution: The ratio of cranberry juice to orange juice is 4:7. This means for every 4 parts of cranberry juice, we need 7 parts of orange juice. Aisha uses 1.2 liters of cranberry juice.
    Full step-by-step solution

    Step 1: The ratio of cranberry juice to orange juice is 4:7. This means for every 4 parts of cranberry juice, we need 7 parts of orange juice. Step 2: Aisha uses 1.2 liters of cranberry juice. We need to find out how many liters correspond to 1 part in the ratio. Step 3: Divide the amount of cranberry juice by its ratio part: 1.2 liters / 4 = 0.3 liters. So, 1 part is equal to 0.3 liters. Step 4: Multiply the value of 1 part by the orange juice ratio part: 0.3 liters/part * 7 parts = 2.1 liters. Step 5: Therefore, Aisha needs 2.1 liters of orange juice. The answer is 2.1.

  6. Ava is making a fruit punch for a school party. The recipe requires mixing orange juice and pineapple juice in a 4:7 ratio. If Ava uses 2.8 liters of orange juice, how many liters of pineapple juice does she need to maintain the correct ratio? Answer: 4.9 Solution: The ratio of orange juice to pineapple juice is 4:7. This means for every 4 parts of orange juice, we need 7 parts of pineapple juice. Ava uses 2.8 liters of orange juice.
    Full step-by-step solution

    Step 1: The ratio of orange juice to pineapple juice is 4:7. This means for every 4 parts of orange juice, we need 7 parts of pineapple juice. Step 2: Ava uses 2.8 liters of orange juice. This represents the 4 parts in the ratio. Step 3: Find the value of one part by dividing the orange juice quantity by 4: 2.8 / 4 = 0.7 liters per part. Step 4: Multiply the value of one part by 7 to find the pineapple juice needed: 0.7 * 7 = 4.9 liters. The answer is 4.9 liters of pineapple juice.

  7. 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 Liam uses 450 milliliters of blue paint, how many milliliters of red paint should he use to maintain the correct ratio? Answer: 270 Solution: We are told the ratio of red to blue paint is 3:5. That means for every 5 milliliters of blue paint, we need 3 milliliters of red paint. Red / Blue = 3 / 5.
    Full step-by-step solution

    We are told the ratio of red to blue paint is 3:5. That means for every 5 milliliters of blue paint, we need 3 milliliters of red paint. Step 1: Understand the ratio as a fraction. Red / Blue = 3 / 5. Step 2: We know the amount of blue paint used is 450 milliliters. Let R be the milliliters of red paint needed. From the ratio: R / 450 = 3 / 5. Step 3: Solve for R. Multiply both sides by 450: R = (3 / 5) * 450. Step 4: Perform the multiplication. First, 450 divided by 5 is 90. Then, 90 multiplied by 3 is 270. So, R = 270 milliliters. Step 5: Check the ratio. Red : Blue = 270 : 450. Divide both sides by 90: 270/90 = 3, 450/90 = 5. Ratio is 3:5, which matches. ANSWER: 270

  8. A school is organizing a field trip to a science museum. The total cost for transportation and admission is $1,275. If 34 students are going on the trip, what is the cost per student? Answer: 37.5 Solution: Identify the total cost: $1,275 Identify the number of students: 34 Divide the total cost by the number of students to find the cost per student: 1275 ÷ 34 Calculate 34 × 37 = 1258 Calculate 1275 - 1258 = 17 Add a decimal point and continue dividing: 17 ÷ 34 = 0.5 Combine the results: 37 + 0.5 =…
    Full step-by-step solution

    Step 1: Identify the total cost: $1,275 Step 2: Identify the number of students: 34 Step 3: Divide the total cost by the number of students to find the cost per student: 1275 ÷ 34 Step 4: Calculate 34 × 37 = 1258 Step 5: Calculate 1275 - 1258 = 17 Step 6: Add a decimal point and continue dividing: 17 ÷ 34 = 0.5 Step 7: Combine the results: 37 + 0.5 = 37.5 Therefore, the cost per student is $37.50.