Fraction Multiplication

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Answer Key & Explanations

Fraction Multiplication · Grade 5 · Worksheet 1

1. Olivia is making a fruit smoothie. She has 10 cups of orange juice. The recipe calls for 2/5 of that amount. What does 2/5 × 10 mean in this situation, and how many cups of orange juice does Olivia need for the smoothie? Answer: 4 cups Solution: Understand what 2/5 × 10 means. It means finding 2/5 of the total 10 cups of orange juice. This is a scaling or resizing operation.
   Full step-by-step solution

   Step 1: Understand what 2/5 × 10 means. It means finding 2/5 of the total 10 cups of orange juice. This is a scaling or resizing operation. Step 2: First, find 1/5 of 10 by dividing 10 by 5: 10 ÷ 5 = 2 cups. Step 3: Since we need 2/5, multiply the 1/5 amount by 2: 2 × 2 = 4 cups. Step 4: Therefore, 2/5 × 10 = 4, meaning Olivia needs 4 cups of orange juice for the smoothie. The answer is 4 cups.

2. Sophia is planning a hiking trip and wants to know how far she can hike. Her usual hiking speed is 3 miles per hour. She plans to hike for 2/3 of an hour. What does 2/3 × 3 mean in this context, and how many miles will she hike? Answer: 2 miles Solution: The problem asks for the meaning of 2/3 × 3. This means finding 2/3 of 3 miles. Multiply the whole number by the numerator: 3 × 2 = 6.
   Full step-by-step solution

   Step 1: The problem asks for the meaning of 2/3 × 3. This means finding 2/3 of 3 miles. Step 2: Multiply the whole number by the numerator: 3 × 2 = 6. Step 3: Divide the result by the denominator: 6 ÷ 3 = 2. Step 4: So, 2/3 × 3 = 2, meaning Sophia hikes 2 miles in 2/3 of an hour. The answer is 2 miles.

3. 2/3 × 600 = ? Answer: 400 Solution: Understand that 2/3 × 600 means finding two-thirds of 600 First find one-third of 600 by dividing: 600 ÷ 3 = 200 Since we need two-thirds, multiply the result by 2: 200 × 2 = 400 Therefore, 2/3 × 600 = 400 The answer is 400.
   Full step-by-step solution

   Step 1: Understand that 2/3 × 600 means finding two-thirds of 600 Step 2: First find one-third of 600 by dividing: 600 ÷ 3 = 200 Step 3: Since we need two-thirds, multiply the result by 2: 200 × 2 = 400 Step 4: Therefore, 2/3 × 600 = 400 The answer is 400.

4. 4/5 × 750 = ? Answer: 600 Solution: Understand that 4/5 × 750 means finding four-fifths of 750 First find one-fifth of 750 by dividing: 750 ÷ 5 = 150 Since we need four-fifths, multiply the result by 4: 150 × 4 = 600 Therefore, 4/5 × 750 = 600 The answer is 600.
   Full step-by-step solution

   Step 1: Understand that 4/5 × 750 means finding four-fifths of 750 Step 2: First find one-fifth of 750 by dividing: 750 ÷ 5 = 150 Step 3: Since we need four-fifths, multiply the result by 4: 150 × 4 = 600 Step 4: Therefore, 4/5 × 750 = 600 The answer is 600.

5. A rectangular prism is drawn with a length of 6 cm, width of 4 cm, and height of 5 cm. What is the volume of this prism in cubic centimeters? Answer: 120 Solution: The formula for volume of a rectangular prism is length × width × height Substitute the given measurements: 6 cm × 4 cm × 5 cm First multiply 6 × 4 = 24 Then multiply 24 × 5 = 120 The volume is 120 cubic centimeters The answer is 120.
   Full step-by-step solution

   Step 1: The formula for volume of a rectangular prism is length × width × height Step 2: Substitute the given measurements: 6 cm × 4 cm × 5 cm Step 3: First multiply 6 × 4 = 24 Step 4: Then multiply 24 × 5 = 120 Step 5: The volume is 120 cubic centimeters The answer is 120.

6. Sophia is designing a rectangular mural on a large wall. The mural is 720 centimeters long. She plans to use 5/8 of the length for a landscape scene. Imagine the mural divided into 8 equal parts along its length. What does the multiplication 5/8 × 720 mean in this situation, and how many centimeters long is the landscape section? Answer: 450 Solution: The expression 5/8 × 720 means 'five-eighths of 720'. Step 2: First, find one-eighth of 720 by dividing 720 by 8: 720 ÷ 8 = 90 centimeters.
   Full step-by-step solution

   Step 1: The expression 5/8 × 720 means 'five-eighths of 720'. Step 2: First, find one-eighth of 720 by dividing 720 by 8: 720 ÷ 8 = 90 centimeters. Step 3: Five-eighths means five of those one-eighth parts: 5 × 90 = 450 centimeters. Step 4: So, 5/8 × 720 = 450. The landscape section is 450 centimeters long.

7. Emma is planning a 600-kilometer road trip. She wants to drive only 3/5 of the total distance on the first day to avoid getting too tired. What does 3/5 × 600 mean in this situation, and how many kilometers will Emma drive on the first day? Answer: 360 kilometers Solution: 3/5 × 600 means finding 3/5 of 600, or scaling the total distance of 600 km down to 3/5 of its size. This is like dividing the trip into 5 equal segments and then taking 3 of those segments. First, find 1/5 of 600.
   Full step-by-step solution

   Step 1: Understand the meaning. 3/5 × 600 means finding 3/5 of 600, or scaling the total distance of 600 km down to 3/5 of its size. This is like dividing the trip into 5 equal segments and then taking 3 of those segments. Step 2: First, find 1/5 of 600. Divide 600 by 5: 600 ÷ 5 = 120. So 1/5 of 600 is 120 kilometers. Step 3: Now, 3/5 of 600 means 3 groups of 1/5, so multiply 120 by 3: 120 × 3 = 360. Step 4: Therefore, 3/5 × 600 = 360. Emma will drive 360 kilometers on the first day. The answer is 360 kilometers.