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Ratio Concepts

Grade 6 · Ratios · Worksheet 1

  1. Aisha is making a special fruit punch for a school event. The recipe requires mixing mango juice and orange juice in a 4:7 ratio. If Aisha uses 1,260 milliliters of mango juice, how many milliliters of orange juice does she need to maintain the correct ratio? Answer: ______________
  2. A rectangular swimming pool is drawn on a coordinate plane with corners at (0, 0), (12, 0), (12, 8), and (0, 8). A diving area is marked as a smaller rectangle inside the pool with corners at (2, 2), (10, 2), (10, 6), and (2, 6). What is the ratio of the area of the diving area to the area of the entire swimming pool? Express your answer in simplest form. Answer: ______________
  3. Noah is mixing a cleaning solution. The ratio of water to vinegar in the mixture is 7:2. If Noah uses 56 cups of water, how many cups of vinegar does he need? Answer: ______________
  4. A rectangular garden is drawn on a coordinate plane with vertices at (2, 1), (8, 1), (8, 5), and (2, 5). A path runs diagonally from the vertex at (2, 1) to (8, 5), splitting the garden into two triangular flower beds. What is the ratio of the area of the smaller triangular flower bed to the area of the entire rectangular garden? Answer: ______________
  5. A rectangular garden is drawn on a coordinate plane with corners at (2, 1), (8, 1), (8, 5), and (2, 5). If the gardener plants flowers at a density of 15 flowers per square unit, how many flowers will be needed to fill the entire garden? Answer: ______________
  6. If 2/3 = x/15, then x = ? Answer: ______________
  7. 3:5 = 18:? Answer: ______________
  8. (2/3) ÷ (4/9) = ? Answer: ______________
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Answer Key & Explanations

Ratio Concepts · Grade 6 · Worksheet 1

  1. Aisha is making a special fruit punch for a school event. The recipe requires mixing mango juice and orange juice in a 4:7 ratio. If Aisha uses 1,260 milliliters of mango juice, how many milliliters of orange juice does she need to maintain the correct ratio? Answer: 2205 Solution: The ratio of mango juice to orange juice is 4:7. This means for every 4 parts of mango juice, there are 7 parts of orange juice. Aisha uses 1,260 ml of mango juice, which represents 4 parts of the ratio.
    Full step-by-step solution

    Step 1: The ratio of mango juice to orange juice is 4:7. This means for every 4 parts of mango juice, there are 7 parts of orange juice. Step 2: Aisha uses 1,260 ml of mango juice, which represents 4 parts of the ratio. Step 3: Find the value of one part by dividing the total mango juice by 4: 1260 / 4 = 315 ml per part. Step 4: Since orange juice is 7 parts, multiply the value per part by 7: 315 * 7 = 2205 ml. Step 5: Therefore, Aisha needs 2205 milliliters of orange juice. The answer is 2205.

  2. A rectangular swimming pool is drawn on a coordinate plane with corners at (0, 0), (12, 0), (12, 8), and (0, 8). A diving area is marked as a smaller rectangle inside the pool with corners at (2, 2), (10, 2), (10, 6), and (2, 6). What is the ratio of the area of the diving area to the area of the entire swimming pool? Express your answer in simplest form. Answer: 1/3 Solution: Find the dimensions of the entire swimming pool. The pool goes from x=0 to x=12, so length = 12 - 0 = 12 units. The pool goes from y=0 to y=8, so width = 8 - 0 = 8 units.
    Full step-by-step solution

    Step 1: Find the dimensions of the entire swimming pool. The pool goes from x=0 to x=12, so length = 12 - 0 = 12 units. The pool goes from y=0 to y=8, so width = 8 - 0 = 8 units. Area of entire pool = length × width = 12 × 8 = 96 square units. Step 2: Find the dimensions of the diving area. The diving area goes from x=2 to x=10, so length = 10 - 2 = 8 units. The diving area goes from y=2 to y=6, so width = 6 - 2 = 4 units. Area of diving area = length × width = 8 × 4 = 32 square units. Step 3: Find the ratio of diving area to entire pool. Ratio = area of diving area / area of entire pool = 32/96 Step 4: Simplify the ratio. Both 32 and 96 can be divided by 32: 32÷32 = 1, 96÷32 = 3 So the simplified ratio is 1/3. The answer is 1/3.

  3. Noah is mixing a cleaning solution. The ratio of water to vinegar in the mixture is 7:2. If Noah uses 56 cups of water, how many cups of vinegar does he need? Answer: 16 Solution: The ratio of water to vinegar is 7:2. This means for every 7 cups of water, there are 2 cups of vinegar. Noah uses 56 cups of water.
    Full step-by-step solution

    Step 1: The ratio of water to vinegar is 7:2. This means for every 7 cups of water, there are 2 cups of vinegar. Step 2: Noah uses 56 cups of water. Find how many groups of 7 are in 56: 56 ÷ 7 = 8 groups. Step 3: Each group has 2 cups of vinegar, so multiply: 8 × 2 = 16 cups of vinegar. The answer is 16.

  4. A rectangular garden is drawn on a coordinate plane with vertices at (2, 1), (8, 1), (8, 5), and (2, 5). A path runs diagonally from the vertex at (2, 1) to (8, 5), splitting the garden into two triangular flower beds. What is the ratio of the area of the smaller triangular flower bed to the area of the entire rectangular garden? Answer: 1:4 Solution: In any rectangle, a diagonal splits it into two congruent triangles, meaning they have the exact same shape and size. A ratio compares two quantities, and simplifying that relationship gives the final answer.
    Full step-by-step solution

    In any rectangle, a diagonal splits it into two congruent triangles, meaning they have the exact same shape and size. Therefore, the area of each triangle is exactly half the area of the entire rectangle. A ratio compares two quantities, and simplifying that relationship gives the final answer.

  5. A rectangular garden is drawn on a coordinate plane with corners at (2, 1), (8, 1), (8, 5), and (2, 5). If the gardener plants flowers at a density of 15 flowers per square unit, how many flowers will be needed to fill the entire garden? Answer: 360 Solution: Identify the coordinates of the garden. The corners are at (2, 1), (8, 1), (8, 5), and (2, 5). Determine the length and width of the rectangle.
    Full step-by-step solution

    Step 1: Identify the coordinates of the garden. The corners are at (2, 1), (8, 1), (8, 5), and (2, 5). Step 2: Determine the length and width of the rectangle. The points (2, 1) and (8, 1) have the same y-coordinate, so the horizontal distance between them is the length. Length = 8 - 2 = 6 units. The points (2, 1) and (2, 5) have the same x-coordinate, so the vertical distance between them is the width. Width = 5 - 1 = 4 units. Step 3: Calculate the area of the garden. Area of a rectangle = length × width. Area = 6 × 4 = 24 square units. Step 4: Calculate the number of flowers needed. Flower density = 15 flowers per square unit. Total flowers = Area × Density = 24 × 15. Step 5: Perform the multiplication. 24 × 15 = 24 × (10 + 5) = (24 × 10) + (24 × 5) = 240 + 120 = 360. Step 6: State the final answer. The gardener will need 360 flowers to fill the entire garden.

  6. If 2/3 = x/15, then x = ? Answer: 10 Solution: 2/3 = x/15 The equation means that the two fractions are equal. To solve for x, we can cross-multiply.
    Full step-by-step solution

    We start with the equation: 2/3 = x/15 Step 1: The equation means that the two fractions are equal. To solve for x, we can cross-multiply. That means: 2 * 15 = 3 * x Step 2: Perform the multiplication on the left side: 2 * 15 = 30 So we have: 30 = 3 * x Step 3: Divide both sides by 3 to solve for x: 30 / 3 = x Step 4: Calculate the division: 30 ÷ 3 = 10 So x = 10 Step 5: Check the answer: 2/3 = 10/15 Simplify 10/15 by dividing numerator and denominator by 5: 10 ÷ 5 = 2, 15 ÷ 5 = 3, so 10/15 = 2/3. This matches the original equation. Final answer: x = 10

  7. 3:5 = 18:? Answer: 30 Solution: We are given the proportion: 3:5 = 18:? Write the proportion as fractions. 3:5 means 3/5, and 18:?
    Full step-by-step solution

    We are given the proportion: 3:5 = 18:? Step 1: Write the proportion as fractions. 3:5 means 3/5, and 18:? means 18/x, where x is the unknown number. So we have: 3/5 = 18/x Step 2: Cross-multiply to solve for x. 3 * x = 18 * 5 Step 3: Perform the multiplication. 3x = 90 Step 4: Divide both sides by 3 to isolate x. x = 90 / 3 x = 30 Step 5: Check the answer. 3:5 = 18:30 3/5 = 0.6, 18/30 = 0.6, so it matches. Final answer: 30

  8. (2/3) ÷ (4/9) = ? Answer: 3/2 Solution: Write the division of fractions as multiplication by the reciprocal: (2/3) ÷ (4/9) = (2/3) × (9/4) Multiply the numerators: 2 × 9 = 18 Multiply the denominators: 3 × 4 = 12 Write the resulting fraction: 18/12 Simplify the fraction by dividing numerator and denominator by their greatest common…
    Full step-by-step solution

    Step 1: Write the division of fractions as multiplication by the reciprocal: (2/3) ÷ (4/9) = (2/3) × (9/4) Step 2: Multiply the numerators: 2 × 9 = 18 Step 3: Multiply the denominators: 3 × 4 = 12 Step 4: Write the resulting fraction: 18/12 Step 5: Simplify the fraction by dividing numerator and denominator by their greatest common factor (6): 18 ÷ 6 = 3, 12 ÷ 6 = 2 Step 6: The simplified fraction is 3/2 The answer is 3/2.