Fraction Multiplication

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Answer Key & Explanations

Fraction Multiplication · Grade 5 · Worksheet 3

1. 4/7 × 840 = ? Answer: 480 Solution: Understand that 4/7 × 840 means finding four-sevenths of 840 First find one-seventh of 840 by dividing: 840 ÷ 7 = 120 Since we need four-sevenths, multiply the result by 4: 120 × 4 = 480 Therefore, 4/7 × 840 = 480 The answer is 480.
   Full step-by-step solution

   Step 1: Understand that 4/7 × 840 means finding four-sevenths of 840 Step 2: First find one-seventh of 840 by dividing: 840 ÷ 7 = 120 Step 3: Since we need four-sevenths, multiply the result by 4: 120 × 4 = 480 Step 4: Therefore, 4/7 × 840 = 480 The answer is 480.

2. Liam is building a rectangular garden bed that measures 3/4 meter in length and 2/5 meter in width. What is the area of his garden bed in square meters? Answer: 3/10 Solution: To find the area of a rectangle, we multiply the length by the width. Write down the given measurements. Length = 3/4 meter Width = 2/5 meter Set up the area formula.
   Full step-by-step solution

   To find the area of a rectangle, we multiply the length by the width. Step 1: Write down the given measurements. Length = 3/4 meter Width = 2/5 meter Step 2: Set up the area formula. Area = Length × Width Area = (3/4) × (2/5) Step 3: Multiply the fractions. To multiply fractions, multiply the numerators together and multiply the denominators together. Numerator: 3 × 2 = 6 Denominator: 4 × 5 = 20 So, Area = 6/20 Step 4: Simplify the fraction. Find the greatest common factor (GCF) of 6 and 20. The GCF is 2. Divide both the numerator and the denominator by 2. 6 ÷ 2 = 3 20 ÷ 2 = 10 So, 6/20 simplifies to 3/10. Step 5: State the final answer. The area of the garden bed is 3/10 square meters.

3. Liam is building a rectangular garden that measures 3/4 meter by 2/5 meter. He wants to cover the entire garden with soil. What is the total area of Liam's garden in square meters? Answer: 3/10 Solution: To find the area of a rectangle, we multiply its length by its width. Identify the length and width. Length = 3/4 meter Width = 2/5 meter Write the area formula.
   Full step-by-step solution

   To find the area of a rectangle, we multiply its length by its width. Step 1: Identify the length and width. Length = 3/4 meter Width = 2/5 meter Step 2: Write the area formula. Area = Length × Width Step 3: Substitute the values into the formula. Area = (3/4) × (2/5) Step 4: Multiply the fractions. To multiply fractions, multiply the numerators (top numbers) together and multiply the denominators (bottom numbers) together. Numerator: 3 × 2 = 6 Denominator: 4 × 5 = 20 So, Area = 6/20 Step 5: Simplify the fraction. We can simplify 6/20 by dividing both the numerator and the denominator by their greatest common factor, which is 2. 6 ÷ 2 = 3 20 ÷ 2 = 10 So, 6/20 simplifies to 3/10. Step 6: State the final answer. The total area of Liam's garden is 3/10 square meters.

4. Mason is making a batch of his famous chili. The recipe calls for 12 cups of water, but he wants to use only 2/3 of that amount to make a smaller batch. Explain what it means to find 2/3 of 12, and then calculate how many cups of water Mason should use. Answer: 8 Solution: Multiplying a whole number by a fraction means finding that fraction of the whole. Here, 2/3 × 12 means 'two-thirds of 12'. First, find 1/3 of 12.
   Full step-by-step solution

   Step 1: Understand the meaning of 2/3 of 12. Multiplying a whole number by a fraction means finding that fraction of the whole. Here, 2/3 × 12 means 'two-thirds of 12'. Step 2: First, find 1/3 of 12. To find 1/3, divide 12 by 3: 12 ÷ 3 = 4. So, one-third of 12 is 4 cups. Step 3: Since we want 2/3, we take 2 of those one-third parts: 2 × 4 = 8. Step 4: So, 2/3 × 12 = 8. Mason should use 8 cups of water. The answer is 8.

5. 3/4 × 1600 = ? Answer: 1200 Solution: Understand that 3/4 × 1600 means finding three-fourths of 1600 First find one-fourth of 1600 by dividing: 1600 ÷ 4 = 400 Since we need three-fourths, multiply the result by 3: 400 × 3 = 1200 Therefore, 3/4 × 1600 = 1200 The answer is 1200.
   Full step-by-step solution

   Step 1: Understand that 3/4 × 1600 means finding three-fourths of 1600 Step 2: First find one-fourth of 1600 by dividing: 1600 ÷ 4 = 400 Step 3: Since we need three-fourths, multiply the result by 3: 400 × 3 = 1200 Step 4: Therefore, 3/4 × 1600 = 1200 The answer is 1200.

6. Sophia is knitting a scarf that requires 720 centimeters of yarn. She has already knitted 5/8 of the scarf. What does 5/8 × 720 mean in this situation, and how many centimeters of yarn has Sophia used so far? Answer: 450 centimeters Solution: 5/8 × 720 means finding 5/8 of 720 centimeters. This is scaling the total yarn down to 5/8 of its original length. First, divide the total yarn (720 cm) into 8 equal parts to find 1/8.
   Full step-by-step solution

   Step 1: Understand the meaning. 5/8 × 720 means finding 5/8 of 720 centimeters. This is scaling the total yarn down to 5/8 of its original length. Step 2: First, divide the total yarn (720 cm) into 8 equal parts to find 1/8. 720 ÷ 8 = 90 centimeters per part. Step 3: Now, 5/8 means taking 5 of those parts. Multiply 90 by 5: 90 × 5 = 450 centimeters. Step 4: Therefore, 5/8 × 720 = 450. Sophia has used 450 centimeters of yarn so far. The answer is 450 centimeters.

7. Tane is baking a large batch of cookies for a school fundraiser. The recipe calls for 12 cups of flour, but he wants to make only 2/3 of the recipe. What does 2/3 × 12 mean in this situation, and how many cups of flour does Tane need? Answer: 8 cups Solution: This is a scaling problem where we take a fraction (2/3) of the whole number (12). Interpret 2/3 as dividing the whole into 3 equal parts and then taking 2 of those parts.
   Full step-by-step solution

   Step 1: Understand the multiplication: 2/3 × 12 means finding 2/3 of 12. This is a scaling problem where we take a fraction (2/3) of the whole number (12). Step 2: Interpret 2/3 as dividing the whole into 3 equal parts and then taking 2 of those parts. Step 3: First, find 1/3 of 12: Divide 12 by 3, which is 12 ÷ 3 = 4 cups. Step 4: Since we want 2/3, take 2 of those parts: 2 × 4 = 8 cups. Step 5: Alternatively, multiply directly: 2/3 × 12 = (2 × 12) / 3 = 24 / 3 = 8 cups. So, 2/3 × 12 means Tane uses 2 out of every 3 parts of the 12 cups of flour, which is 8 cups. The answer is 8 cups.

8. Emma is making a fruit salad for a party. She uses 3/4 of a pound of strawberries and 2/3 of a pound of blueberries. What is the total weight of the fruit she uses for the salad? Answer: 17/12 Solution: Identify the fractions to add: 3/4 and 2/3. Find a common denominator for 4 and 3. The least common denominator is 12.
   Full step-by-step solution

   Step 1: Identify the fractions to add: 3/4 and 2/3. Step 2: Find a common denominator for 4 and 3. The least common denominator is 12. Step 3: Convert 3/4 to an equivalent fraction with denominator 12: (3 × 3)/(4 × 3) = 9/12. Step 4: Convert 2/3 to an equivalent fraction with denominator 12: (2 × 4)/(3 × 4) = 8/12. Step 5: Add the fractions: 9/12 + 8/12 = 17/12. Step 6: The fraction 17/12 is the total weight in pounds. The answer is 17/12.

9. 5/9 × 693 = ? Answer: 385 Solution: Understand that 5/9 × 693 means finding five-ninths of 693 First find one-ninth of 693 by dividing: 693 ÷ 9 = 77 Since we need five-ninths, multiply the result by 5: 77 × 5 = 385 Therefore, 5/9 × 693 = 385 The answer is 385.
   Full step-by-step solution

   Step 1: Understand that 5/9 × 693 means finding five-ninths of 693 Step 2: First find one-ninth of 693 by dividing: 693 ÷ 9 = 77 Step 3: Since we need five-ninths, multiply the result by 5: 77 × 5 = 385 Step 4: Therefore, 5/9 × 693 = 385 The answer is 385.