Fraction Multiplication

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Answer Key & Explanations

Fraction Multiplication · Grade 5 · Worksheet 2

1. 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.

2. 3/4 × 600 = ? Answer: 450 Solution: Understand that 3/4 × 600 means finding three-fourths of 600 First find one-fourth of 600 by dividing: 600 ÷ 4 = 150 Since we need three-fourths, multiply the result by 3: 150 × 3 = 450 Therefore, 3/4 × 600 = 450 The answer is 450.
   Full step-by-step solution

   Step 1: Understand that 3/4 × 600 means finding three-fourths of 600 Step 2: First find one-fourth of 600 by dividing: 600 ÷ 4 = 150 Step 3: Since we need three-fourths, multiply the result by 3: 150 × 3 = 450 Step 4: Therefore, 3/4 × 600 = 450 The answer is 450.

3. 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.

4. A farmer plants corn in a rectangular field that is 3/4 of a mile long and 5/8 of a mile wide. What fraction of a square mile is the area of the corn field? Answer: 15/32 Solution: The area of a rectangle is found by multiplying length × width Multiply the fractions: 3/4 × 5/8 Multiply the numerators: 3 × 5 = 15 Multiply the denominators: 4 × 8 = 32 The area is 15/32 of a square mile The answer is 15/32.
   Full step-by-step solution

   Step 1: The area of a rectangle is found by multiplying length × width Step 2: Multiply the fractions: 3/4 × 5/8 Step 3: Multiply the numerators: 3 × 5 = 15 Step 4: Multiply the denominators: 4 × 8 = 32 Step 5: The area is 15/32 of a square mile The answer is 15/32.

5. A rectangular garden measures 3/4 of a kilometer in length and 2/5 of a kilometer in width. What is the area of the garden in square kilometers? Answer: 3/10 Solution: To find the area of a rectangle, we multiply its length by its width. Write down the given dimensions. Length = 3/4 km Width = 2/5 km 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: Write down the given dimensions. Length = 3/4 km Width = 2/5 km Step 2: Write the area formula. Area = Length × Width Step 3: Substitute the given fractions into the formula. Area = (3/4) × (2/5) Step 4: 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 5: 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 6: State the final answer. The area of the garden is 3/10 square kilometers.

6. Tane is making a traditional Māori kite. The kite requires a piece of fabric that is 2/3 of a meter long. He has a long piece of fabric that is 12 meters in total. What length of fabric does 2/3 of 12 meters represent, and what does the multiplication 2/3 × 12 mean in this context? Answer: 8 meters Solution: Understand what 2/3 × 12 means. The multiplication 2/3 × 12 means finding 2/3 of 12. In other words, we are scaling down 12 by a factor of 2/3.
   Full step-by-step solution

   Step 1: Understand what 2/3 × 12 means. The multiplication 2/3 × 12 means finding 2/3 of 12. In other words, we are scaling down 12 by a factor of 2/3. Step 2: First, divide the whole amount (12) into 3 equal parts to find one-third: 12 ÷ 3 = 4 meters. Step 3: Since we want 2/3, we take two of those parts: 2 × 4 = 8 meters. Step 4: Alternatively, we can multiply directly: 2/3 × 12 = (2 × 12) / 3 = 24 / 3 = 8 meters. The answer is 8 meters.

7. 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.

8. 5/7 × 735 = ? Answer: 525 Solution: Understand that 5/7 × 735 means finding five-sevenths of 735 First find one-seventh of 735 by dividing: 735 ÷ 7 = 105 Since we need five-sevenths, multiply the result by 5: 105 × 5 = 525 Therefore, 5/7 × 735 = 525 The answer is 525.
   Full step-by-step solution

   Step 1: Understand that 5/7 × 735 means finding five-sevenths of 735 Step 2: First find one-seventh of 735 by dividing: 735 ÷ 7 = 105 Step 3: Since we need five-sevenths, multiply the result by 5: 105 × 5 = 525 Step 4: Therefore, 5/7 × 735 = 525 The answer is 525.

9. 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.