Fraction × Fraction

lessonbunny.com

Answer Key & Explanations

Fraction × Fraction · Grade 5 · Worksheet 1

1. 5/7 × 3/11 = ? Answer: 15/77 Solution: Multiply the numerators: 5 × 3 = 15 Multiply the denominators: 7 × 11 = 77 Combine the results to form the product fraction: 15/77 Check if the fraction can be simplified.
   Full step-by-step solution

   Step 1: Multiply the numerators: 5 × 3 = 15 Step 2: Multiply the denominators: 7 × 11 = 77 Step 3: Combine the results to form the product fraction: 15/77 Step 4: Check if the fraction can be simplified. The greatest common factor of 15 and 77 is 1, so 15/77 is already in simplest form. The answer is 15/77.

2. A rectangular garden is divided into a grid with 8 equal rows and 6 equal columns. If each grid square represents a planting area for flowers, and 3/4 of the total squares are planted with roses, how many squares contain roses? Answer: 36 Solution: Find the total number of grid squares. The garden has 8 rows and 6 columns. Total squares = rows × columns = 8 × 6 = 48.
   Full step-by-step solution

   Step 1: Find the total number of grid squares. The garden has 8 rows and 6 columns. Total squares = rows × columns = 8 × 6 = 48. Step 2: Determine how many squares contain roses. We are told 3/4 of the total squares are planted with roses. So, number of rose squares = (3/4) × total squares. Step 3: Calculate the number of rose squares. (3/4) × 48 = (3 × 48) / 4. First, 3 × 48 = 144. Then, 144 ÷ 4 = 36. Step 4: Conclusion. Therefore, 36 squares contain roses.

3. 7/12 × 2/7 = ? Answer: 1/6 Solution: Multiply the numerators: 7 × 2 = 14 Multiply the denominators: 12 × 7 = 84 Combine the results to form the product fraction: 14/84 Simplify the fraction by finding the greatest common factor of 14 and 84, which is 14 Divide both numerator and denominator by 14: 14 ÷ 14 = 1, 84 ÷ 14 = 6 The…
   Full step-by-step solution

   Step 1: Multiply the numerators: 7 × 2 = 14 Step 2: Multiply the denominators: 12 × 7 = 84 Step 3: Combine the results to form the product fraction: 14/84 Step 4: Simplify the fraction by finding the greatest common factor of 14 and 84, which is 14 Step 5: Divide both numerator and denominator by 14: 14 ÷ 14 = 1, 84 ÷ 14 = 6 Step 6: The simplified fraction is 1/6 The answer is 1/6.

4. 8/9 × 5/11 = ? Answer: 40/99 Solution: Multiply the numerators: 8 × 5 = 40 Multiply the denominators: 9 × 11 = 99 Combine the results to form the product fraction: 40/99 Check if the fraction can be simplified.
   Full step-by-step solution

   Step 1: Multiply the numerators: 8 × 5 = 40 Step 2: Multiply the denominators: 9 × 11 = 99 Step 3: Combine the results to form the product fraction: 40/99 Step 4: Check if the fraction can be simplified. The greatest common factor of 40 and 99 is 1, so 40/99 is already in simplest form. The answer is 40/99.

5. A rectangular bulletin board is divided into a grid with 12 equal rows and 8 equal columns. The art teacher covers 3/4 of the rows with blue paper and 2/3 of the columns with red paper. What fraction of the entire bulletin board is covered by both blue and red paper where they overlap? Answer: 1/2 Solution: Identify the fraction of rows covered with blue paper: 3/4 Identify the fraction of columns covered with red paper: 2/3 To find the fraction of the entire board where blue and red overlap, multiply the two fractions: (3/4) × (2/3) Multiply the numerators: 3 × 2 = 6 Multiply the denominators: 4 ×…
   Full step-by-step solution

   Step 1: Identify the fraction of rows covered with blue paper: 3/4 Step 2: Identify the fraction of columns covered with red paper: 2/3 Step 3: To find the fraction of the entire board where blue and red overlap, multiply the two fractions: (3/4) × (2/3) Step 4: Multiply the numerators: 3 × 2 = 6 Step 5: Multiply the denominators: 4 × 3 = 12 Step 6: Simplify the fraction: 6/12 = 1/2 The answer is 1/2.

6. 3/5 × 7/9 = ? Answer: 7/15 Solution: Multiply the numerators: 3 × 7 = 21 Multiply the denominators: 5 × 9 = 45 Combine the results to form the product fraction: 21/45 Simplify the fraction by finding the greatest common factor of 21 and 45, which is 3 Divide both numerator and denominator by 3: 21 ÷ 3 = 7, 45 ÷ 3 = 15 The…
   Full step-by-step solution

   Step 1: Multiply the numerators: 3 × 7 = 21 Step 2: Multiply the denominators: 5 × 9 = 45 Step 3: Combine the results to form the product fraction: 21/45 Step 4: Simplify the fraction by finding the greatest common factor of 21 and 45, which is 3 Step 5: Divide both numerator and denominator by 3: 21 ÷ 3 = 7, 45 ÷ 3 = 15 Step 6: The simplified fraction is 7/15 The answer is 7/15.

7. 1/6 × 6/11 = ? Answer: 1/11 Solution: Multiply the numerators: 1 × 6 = 6 Multiply the denominators: 6 × 11 = 66 Combine the results to form the product fraction: 6/66 Simplify the fraction by finding the greatest common factor of 6 and 66, which is 6 Divide both numerator and denominator by 6: 6 ÷ 6 = 1, 66 ÷ 6 = 11 The simplified…
   Full step-by-step solution

   Step 1: Multiply the numerators: 1 × 6 = 6 Step 2: Multiply the denominators: 6 × 11 = 66 Step 3: Combine the results to form the product fraction: 6/66 Step 4: Simplify the fraction by finding the greatest common factor of 6 and 66, which is 6 Step 5: Divide both numerator and denominator by 6: 6 ÷ 6 = 1, 66 ÷ 6 = 11 Step 6: The simplified fraction is 1/11 The answer is 1/11.

8. 11/14 × 13/16 = ? Answer: 143/224 Solution: Multiply the numerators: 11 × 13 = 143 Multiply the denominators: 14 × 16 = 224 Combine the results to form the product fraction: 143/224 Check if the fraction can be simplified.
   Full step-by-step solution

   Step 1: Multiply the numerators: 11 × 13 = 143 Step 2: Multiply the denominators: 14 × 16 = 224 Step 3: Combine the results to form the product fraction: 143/224 Step 4: Check if the fraction can be simplified. The greatest common factor of 143 and 224 is 1, so 143/224 is already in simplest form. The answer is 143/224.

9. Liam is baking cookies and needs 3/4 cup of chocolate chips for one batch. He decides to make 2/3 of a batch. How many cups of chocolate chips does Liam need for his smaller batch of cookies? Answer: 1/2 Solution: Liam needs 3/4 cup of chocolate chips for a full batch. He is making 2/3 of a batch. To find the amount needed for the smaller batch, we multiply the amount for a full batch by the fraction of the batch he is making.
   Full step-by-step solution

   Liam needs 3/4 cup of chocolate chips for a full batch. He is making 2/3 of a batch. To find the amount needed for the smaller batch, we multiply the amount for a full batch by the fraction of the batch he is making. Step 1: Write the multiplication. Amount needed = (3/4) × (2/3) Step 2: Multiply the numerators. Numerator: 3 × 2 = 6 Step 3: Multiply the denominators. Denominator: 4 × 3 = 12 Step 4: Write the result as a fraction. 6/12 Step 5: Simplify the fraction. Both 6 and 12 can be divided by 6. 6 ÷ 6 = 1 12 ÷ 6 = 2 So, 6/12 = 1/2 Therefore, Liam needs 1/2 cup of chocolate chips for his smaller batch.