Fraction Multiplication

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Answer Key & Explanations

Fraction Multiplication · Grade 5 · Worksheet 2

1. Noah draws a rectangle that is 8 units long and 5 units wide. He then shades a smaller rectangle inside it that is 3/4 the length and 2/5 the width of the original. What is the area of the shaded rectangle? Explain what 3/4 × 8 and 2/5 × 5 mean in terms of scaling the original rectangle. Answer: 12 square units Solution: Interpret the scaling. 3/4 × 8 means '3/4 of 8', which is the scaled length. 2/5 × 5 means '2/5 of 5', which is the scaled width.
   Full step-by-step solution

   Step 1: Interpret the scaling. 3/4 × 8 means '3/4 of 8', which is the scaled length. 2/5 × 5 means '2/5 of 5', which is the scaled width. Step 2: Calculate the scaled length: 3/4 × 8 = (3 × 8) / 4 = 24/4 = 6 units. Step 3: Calculate the scaled width: 2/5 × 5 = (2 × 5) / 5 = 10/5 = 2 units. Step 4: Find the area of the shaded rectangle: area = length × width = 6 × 2 = 12 square units. The answer is 12 square units.

2. Liam is building a rectangular garden bed that is 3.5 meters long and 2.25 meters wide. He wants to put a fence around the entire garden. How many meters of fencing does Liam need? Answer: 11.5 Solution: To find how much fencing Liam needs, we need to calculate the perimeter of the rectangular garden bed. Recall the formula for the perimeter of a rectangle. The perimeter P is given by P = 2 * (length + width).
   Full step-by-step solution

   To find how much fencing Liam needs, we need to calculate the perimeter of the rectangular garden bed. Step 1: Recall the formula for the perimeter of a rectangle. The perimeter P is given by P = 2 * (length + width). Step 2: Identify the given measurements. The length of the garden is 3.5 meters. The width of the garden is 2.25 meters. Step 3: Substitute the values into the formula. P = 2 * (3.5 + 2.25) Step 4: Perform the addition inside the parentheses. 3.5 + 2.25 = 5.75 Step 5: Multiply the result by 2. 2 * 5.75 = 11.5 Step 6: State the final answer. Therefore, Liam needs 11.5 meters of fencing.

3. Emma is painting a mural on a rectangular wall. The wall is 9 feet long. She has finished painting 2/3 of the length of the wall. Draw a mental picture of the wall divided into equal parts. What length of the wall, in feet, has Emma painted? Answer: 6 Solution: We need to find 2/3 of 9 feet. This means we take the whole length (9) and split it into 3 equal parts, then take 2 of those parts. Divide the whole length by the denominator (3): 9 divided by 3 equals 3.
   Full step-by-step solution

   Step 1: Understand the problem. We need to find 2/3 of 9 feet. This means we take the whole length (9) and split it into 3 equal parts, then take 2 of those parts. Step 2: Divide the whole length by the denominator (3): 9 divided by 3 equals 3. Each part is 3 feet long. Step 3: Multiply the size of one part by the numerator (2): 3 times 2 equals 6. Step 4: So, 2/3 of 9 feet is 6 feet. Emma has painted 6 feet of the wall.

4. A rectangular prism is drawn with dimensions: length = 8 1/3 cm, width = 6 cm, and height = 5 1/2 cm. What is the volume of this rectangular prism in cubic centimeters? Answer: 275 Solution: Length: 8 1/3 = 25/3 cm Height: 5 1/2 = 11/2 cm Width: 6 = 6/1 cm Volume = length × width × height Volume = (25/3) × (6/1) × (11/2) Multiply the numerators: 25 × 6 × 11 = 1650 Multiply the denominators: 3 × 1 × 2 = 6 Simplify the fraction: 1650/6 = 275 The volume is 275 cubic centimeters.
   Full step-by-step solution

   Step 1: Convert the mixed numbers to improper fractions Length: 8 1/3 = 25/3 cm Height: 5 1/2 = 11/2 cm Width: 6 = 6/1 cm Step 2: Write the volume formula Volume = length × width × height Step 3: Substitute the values Volume = (25/3) × (6/1) × (11/2) Step 4: Multiply the numerators: 25 × 6 × 11 = 1650 Step 5: Multiply the denominators: 3 × 1 × 2 = 6 Step 6: Simplify the fraction: 1650/6 = 275 Step 7: The volume is 275 cubic centimeters.

5. Matiu is making a traditional woven flax kete (basket). He has a piece of flax that is 600 centimeters long. He needs to use 2/3 of the flax for the body of the kete. What length of flax will Matiu use for the body of the kete? Explain what 2/3 × 600 means in this context. Answer: 400 Solution: 2/3 × 600 means finding 2/3 of 600. This is a scaling problem where we find a fractional part of a whole length. First, find 1/3 of 600.
   Full step-by-step solution

   Step 1: Understand the meaning. 2/3 × 600 means finding 2/3 of 600. This is a scaling problem where we find a fractional part of a whole length. Step 2: First, find 1/3 of 600. To do this, divide 600 by 3: 600 ÷ 3 = 200. So, 1/3 of 600 is 200 centimeters. Step 3: Since Matiu needs 2/3 of the flax, we take two of those thirds: 2 × 200 = 400 centimeters. Alternatively, multiply directly: 2/3 × 600 = (2 × 600) / 3 = 1200 / 3 = 400. The answer is 400 centimeters.