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Fraction × Fraction

Grade 5 · Fractions · Worksheet 3

  1. A rectangular quilt is designed with a pattern that repeats across its surface. The quilt is divided into a grid of 12 equal rows and 15 equal columns. If 2/3 of the rows use blue fabric and 3/5 of the columns use yellow fabric, what fraction of the entire quilt area shows squares where both blue rows and yellow columns overlap? Answer: ______________
  2. 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: ______________
  3. A rectangular garden is divided into a grid with 8 equal rows and 6 equal columns. Each grid square is planted with flowers. If 3/4 of the rows and 2/3 of the columns are filled with roses, what fraction of the entire garden is planted with roses? Answer: ______________
  4. 1/6 × 6/11 = ? Answer: ______________
  5. 7/8 × 9/10 = ? Answer: ______________
  6. 3/5 × 4/10 = ? Answer: ______________
  7. 7/9 × 8/11 = ? Answer: ______________
  8. 9/11 × 10/13 = ? Answer: ______________
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Answer Key & Explanations

Fraction × Fraction · Grade 5 · Worksheet 3

  1. A rectangular quilt is designed with a pattern that repeats across its surface. The quilt is divided into a grid of 12 equal rows and 15 equal columns. If 2/3 of the rows use blue fabric and 3/5 of the columns use yellow fabric, what fraction of the entire quilt area shows squares where both blue rows and yellow columns overlap? Answer: 2/5 Solution: Identify the fractions representing the overlapping sections - Blue rows fraction: 2/3 of all rows - Yellow columns fraction: 3/5 of all columns Multiply the fractions to find the overlapping area - Overlap fraction = (2/3) × (3/5) Multiply the numerators: 2 × 3 = 6 Multiply the denominators: 3…
    Full step-by-step solution

    Step 1: Identify the fractions representing the overlapping sections - Blue rows fraction: 2/3 of all rows - Yellow columns fraction: 3/5 of all columns Step 2: Multiply the fractions to find the overlapping area - Overlap fraction = (2/3) × (3/5) Step 3: Multiply the numerators: 2 × 3 = 6 Step 4: Multiply the denominators: 3 × 5 = 15 Step 5: Simplify the fraction: 6/15 = 2/5 The answer is 2/5 of the entire quilt area shows both blue and yellow.

  2. 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.

  3. A rectangular garden is divided into a grid with 8 equal rows and 6 equal columns. Each grid square is planted with flowers. If 3/4 of the rows and 2/3 of the columns are filled with roses, what fraction of the entire garden is planted with roses? Answer: 1/2 Solution: The garden has 8 rows and 6 columns. Total number of grid squares = 8 × 6 = 48. - 3/4 of the rows are filled with roses.
    Full step-by-step solution

    Let's go step by step. --- **Step 1: Understand the garden grid** The garden has 8 rows and 6 columns. Total number of grid squares = 8 × 6 = 48. --- **Step 2: Interpret the rose coverage** - 3/4 of the rows are filled with roses. Number of rose rows = 3/4 × 8 = 6 rows. - 2/3 of the columns are filled with roses. Number of rose columns = 2/3 × 6 = 4 columns. --- **Step 3: Determine the rose squares** If we think of the garden as a grid: Only the squares that are in both a rose row AND a rose column will be planted with roses. Why? Because the problem says: "3/4 of the rows and 2/3 of the columns are filled with roses" — this means entire rows and entire columns, not individual squares randomly. But if a row is a "rose row", it means every square in that row is rose? No — careful: It says "3/4 of the rows" and "2/3 of the columns" are filled with roses. This means: We mark 6 entire rows as rose rows, and 4 entire columns as rose columns. But a square is planted with roses only if it lies in the intersection of a rose row and a rose column. --- **Step 4: Visualize the intersection** Rose rows: 6 rows Rose columns: 4 columns Each rose row has 6 columns total, but only the 4 rose columns in that row will be rose squares. So each rose row contributes 4 rose squares. Number of rose squares = (number of rose rows) × (number of rose columns) = 6 × 4 = 24. --- **Step 5: Fraction of garden with roses** Total squares = 48 Rose squares = 24 Fraction = 24 / 48 = 1/2. --- **Step 6: Conclusion** The fraction of the entire garden planted with roses is 1/2. --- **Final answer:** 1/2

  4. 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.

  5. 7/8 × 9/10 = ? Answer: 63/80 Solution: Multiply the numerators: 7 × 9 = 63 Multiply the denominators: 8 × 10 = 80 Combine the results to form the product fraction: 63/80 Check if the fraction can be simplified.
    Full step-by-step solution

    Step 1: Multiply the numerators: 7 × 9 = 63 Step 2: Multiply the denominators: 8 × 10 = 80 Step 3: Combine the results to form the product fraction: 63/80 Step 4: Check if the fraction can be simplified. The greatest common factor of 63 and 80 is 1, so 63/80 is already in simplest form. The answer is 63/80.

  6. 3/5 × 4/10 = ? Answer: 6/25 Solution: Multiply the numerators: 3 × 4 = 12 Multiply the denominators: 5 × 10 = 50 Combine the results to form the product fraction: 12/50 Simplify the fraction by finding the greatest common factor of 12 and 50, which is 2 Divide both numerator and denominator by 2: 12 ÷ 2 = 6, 50 ÷ 2 = 25 The…
    Full step-by-step solution

    Step 1: Multiply the numerators: 3 × 4 = 12 Step 2: Multiply the denominators: 5 × 10 = 50 Step 3: Combine the results to form the product fraction: 12/50 Step 4: Simplify the fraction by finding the greatest common factor of 12 and 50, which is 2 Step 5: Divide both numerator and denominator by 2: 12 ÷ 2 = 6, 50 ÷ 2 = 25 Step 6: The simplified fraction is 6/25 The answer is 6/25.

  7. 7/9 × 8/11 = ? Answer: 56/99 Solution: Multiply the numerators: 7 × 8 = 56 Multiply the denominators: 9 × 11 = 99 Combine the results to form the product fraction: 56/99 Check if the fraction can be simplified.
    Full step-by-step solution

    Step 1: Multiply the numerators: 7 × 8 = 56 Step 2: Multiply the denominators: 9 × 11 = 99 Step 3: Combine the results to form the product fraction: 56/99 Step 4: Check if the fraction can be simplified. The greatest common factor of 56 and 99 is 1, so 56/99 is already in simplest form. The answer is 56/99.

  8. 9/11 × 10/13 = ? Answer: 90/143 Solution: Multiply the numerators: 9 × 10 = 90 Multiply the denominators: 11 × 13 = 143 Combine the results to form the product fraction: 90/143 Check if the fraction can be simplified.
    Full step-by-step solution

    Step 1: Multiply the numerators: 9 × 10 = 90 Step 2: Multiply the denominators: 11 × 13 = 143 Step 3: Combine the results to form the product fraction: 90/143 Step 4: Check if the fraction can be simplified. The greatest common factor of 90 and 143 is 1, so 90/143 is already in simplest form. The answer is 90/143.