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Fraction Multiplication

Grade 5 · Fractions · Worksheet 3

  1. Kaia has a rectangular vegetable garden that is 9 meters long and 7 meters wide. She wants to plant carrots in only 2/3 of the garden. What is the area of the garden that will be planted with carrots?
    Answer: ______________
  2. Ava draws a rectangle that is 12 units long and 8 units wide. She then draws a smaller rectangle whose length is 3/4 of the original length and whose width is 2/3 of the original width. What is the area of the smaller rectangle in square units?
    Answer: ______________
  3. Liam is building a rectangular garden bed that measures 3.5 meters long and 2.25 meters wide. He wants to know how much soil he needs to fill it to a depth of 0.4 meters. What is the volume of soil required in cubic meters?
    Answer: ______________
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Answer Key & Explanations

Fraction Multiplication · Grade 5 · Worksheet 3

  1. Kaia has a rectangular vegetable garden that is 9 meters long and 7 meters wide. She wants to plant carrots in only 2/3 of the garden. What is the area of the garden that will be planted with carrots? Answer: 42 Solution: Find the total area of the garden. Area = length × width = 9 m × 7 m = 63 square meters. Interpret 2/3 of the garden as scaling the total area by the fraction 2/3.
    Full step-by-step solution

    Step 1: Find the total area of the garden. Area = length × width = 9 m × 7 m = 63 square meters. Step 2: Interpret 2/3 of the garden as scaling the total area by the fraction 2/3. This means we take 2/3 of 63. Step 3: Multiply the total area by the fraction: 63 × (2/3) = (63 × 2) / 3 = 126 / 3. Step 4: Simplify: 126 ÷ 3 = 42. The area planted with carrots is 42 square meters.

  2. Ava draws a rectangle that is 12 units long and 8 units wide. She then draws a smaller rectangle whose length is 3/4 of the original length and whose width is 2/3 of the original width. What is the area of the smaller rectangle in square units? Answer: 48 Solution: Find the length of the smaller rectangle. The original length is 12 units. 3/4 of 12 means 12 multiplied by 3/4.
    Full step-by-step solution

    Step 1: Find the length of the smaller rectangle. The original length is 12 units. 3/4 of 12 means 12 multiplied by 3/4. 12 × 3/4 = (12 × 3)/4 = 36/4 = 9 units. Step 2: Find the width of the smaller rectangle. The original width is 8 units. 2/3 of 8 means 8 multiplied by 2/3. 8 × 2/3 = (8 × 2)/3 = 16/3 = 5 1/3 units. Step 3: Calculate the area of the smaller rectangle. Area = length × width = 9 × 16/3 = (9 × 16)/3 = 144/3 = 48 square units. The answer is 48.

  3. Liam is building a rectangular garden bed that measures 3.5 meters long and 2.25 meters wide. He wants to know how much soil he needs to fill it to a depth of 0.4 meters. What is the volume of soil required in cubic meters? Answer: 3.15 Solution: To find the volume of soil needed, we use the formula for the volume of a rectangular prism: Volume = length × width × height Length = 3.5 meters Width = 2.25 meters Height (depth) = 0.4 meters Multiply length and width.
    Full step-by-step solution

    To find the volume of soil needed, we use the formula for the volume of a rectangular prism: Volume = length × width × height Here: Length = 3.5 meters Width = 2.25 meters Height (depth) = 0.4 meters Step 1: Multiply length and width. 3.5 × 2.25 = ? First, 3 × 2.25 = 6.75 Then, 0.5 × 2.25 = 1.125 Add them: 6.75 + 1.125 = 7.875 So, length × width = 7.875 square meters. Step 2: Multiply the result by the depth (0.4 meters). 7.875 × 0.4 = ? 7.875 × 4 = 31.5 Now move the decimal one place to the left (since 0.4 = 4/10): 31.5 ÷ 10 = 3.15 So, the volume of soil required is 3.15 cubic meters.