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Fraction × Fraction

Grade 5 · Fractions · Worksheet 3

  1. A construction company is building a new playground. They need to cover an area that is 3/4 of a full basketball court with rubber tiles. If each tile covers 5/8 of the required area, what fraction of the full basketball court will be covered by one tile? Answer: ______________
  2. 1/6 × 4/1 = ? Answer: ______________
  3. 6/11 × 1/6 = ? Answer: ______________
  4. A construction crew is building a new playground. They need to cover a rectangular area with rubber tiles. Each tile covers 3/5 of a square meter. If they need to cover 4/7 of the total playground area today, what fraction of a square meter will they cover with tiles? Answer: ______________
  5. 3/4 × 5/7 = ? Answer: ______________
  6. 11/15 × 13/17 = ? Answer: ______________
  7. A rectangular swimming pool is divided into a grid pattern with 12 equal rows and 8 equal columns. Each grid square represents a section of the pool. If 2/3 of the rows are designated for swimming laps and 3/4 of the columns are designated for deep water, what fraction of the entire pool area is designated for both swimming laps AND deep water? Answer: ______________
  8. 9/11 × 10/13 = ? Answer: ______________
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Answer Key & Explanations

Fraction × Fraction · Grade 5 · Worksheet 3

  1. A construction company is building a new playground. They need to cover an area that is 3/4 of a full basketball court with rubber tiles. If each tile covers 5/8 of the required area, what fraction of the full basketball court will be covered by one tile? Answer: 15/32 Solution: The playground area is 3/4 of a full basketball court. Each tile covers 5/8 of the playground area (not the full court). We are asked: what fraction of the full basketball court does one tile cover?
    Full step-by-step solution

    Let's go step by step. --- **Step 1: Understand the problem** The playground area is 3/4 of a full basketball court. Each tile covers 5/8 of the playground area (not the full court). We are asked: what fraction of the **full basketball court** does one tile cover? --- **Step 2: Set up the relationship** Let the full court area = 1 (as a fraction). Playground area = 3/4 of full court. One tile covers 5/8 of the playground area. So, Fraction of full court covered by one tile = (Playground area) × (Fraction of playground covered by one tile) = (3/4) × (5/8) --- **Step 3: Multiply the fractions** Multiply numerators: 3 × 5 = 15 Multiply denominators: 4 × 8 = 32 So, (3/4) × (5/8) = 15/32 --- **Step 4: Interpret the result** One tile covers 15/32 of the full basketball court. --- **Final Answer:** 15/32

  2. 1/6 × 4/1 = ? Answer: 2/3 Solution: Multiply the numerators: 1 × 4 = 4 Multiply the denominators: 6 × 1 = 6 Combine the results to form the product fraction: 4/6 Simplify the fraction by finding the greatest common factor of 4 and 6, which is 2 Divide both numerator and denominator by 2: 4 ÷ 2 = 2, 6 ÷ 2 = 3 The simplified…
    Full step-by-step solution

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

  3. 6/11 × 1/6 = ? Answer: 1/11 Solution: Multiply the numerators: 6 × 1 = 6 Multiply the denominators: 11 × 6 = 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: 6 × 1 = 6 Step 2: Multiply the denominators: 11 × 6 = 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.

  4. A construction crew is building a new playground. They need to cover a rectangular area with rubber tiles. Each tile covers 3/5 of a square meter. If they need to cover 4/7 of the total playground area today, what fraction of a square meter will they cover with tiles? Answer: 12/35 Solution: Identify the two fractions to multiply: the area per tile (3/5) and the portion of the playground to cover (4/7).
    Full step-by-step solution

    Step 1: Identify the two fractions to multiply: the area per tile (3/5) and the portion of the playground to cover (4/7). Step 2: Multiply the fractions: (3/5) × (4/7) Step 3: Multiply the numerators: 3 × 4 = 12 Step 4: Multiply the denominators: 5 × 7 = 35 Step 5: The result is 12/35 Step 6: This fraction cannot be simplified further since 12 and 35 have no common factors. The answer is 12/35 of a square meter.

  5. 3/4 × 5/7 = ? Answer: 15/28 Solution: Multiply the numerators: 3 × 5 = 15 Multiply the denominators: 4 × 7 = 28 Combine the results to form the product fraction: 15/28 Check if the fraction can be simplified.
    Full step-by-step solution

    Step 1: Multiply the numerators: 3 × 5 = 15 Step 2: Multiply the denominators: 4 × 7 = 28 Step 3: Combine the results to form the product fraction: 15/28 Step 4: Check if the fraction can be simplified. The greatest common factor of 15 and 28 is 1, so 15/28 is already in simplest form. The answer is 15/28.

  6. 11/15 × 13/17 = ? Answer: 143/255 Solution: Multiply the numerators: 11 × 13 = 143 Multiply the denominators: 15 × 17 = 255 Combine the results to form the product fraction: 143/255 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: 15 × 17 = 255 Step 3: Combine the results to form the product fraction: 143/255 Step 4: Check if the fraction can be simplified. The greatest common factor of 143 and 255 is 1, so 143/255 is already in simplest form. The answer is 143/255.

  7. A rectangular swimming pool is divided into a grid pattern with 12 equal rows and 8 equal columns. Each grid square represents a section of the pool. If 2/3 of the rows are designated for swimming laps and 3/4 of the columns are designated for deep water, what fraction of the entire pool area is designated for both swimming laps AND deep water? Answer: 1/2 Solution: Identify the fractions that represent the overlapping area - 2/3 of the rows are for swimming laps - 3/4 of the columns are for deep water Multiply the fractions to find the overlapping area 2/3 × 3/4 = (2 × 3)/(3 × 4) = 6/12 6/12 = 1/2 This means half of the entire pool area is designated for…
    Full step-by-step solution

    Step 1: Identify the fractions that represent the overlapping area - 2/3 of the rows are for swimming laps - 3/4 of the columns are for deep water Step 2: Multiply the fractions to find the overlapping area 2/3 × 3/4 = (2 × 3)/(3 × 4) = 6/12 Step 3: Simplify the fraction 6/12 = 1/2 Step 4: Interpret the result This means half of the entire pool area is designated for both swimming laps AND deep water. The answer is 1/2.

  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.