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Fraction × Fraction

Grade 5 · Fractions · Worksheet 2

  1. 2/7 × 7/12 = ? Answer: ______________
  2. Emma is making a quilt and needs 3/5 of a yard of fabric for each square. If she wants to make 4/7 of a square to test her pattern, how many yards of fabric does she need for the test piece? Answer: ______________
  3. Emma is making a quilt and needs 3/5 of a yard of fabric for each square. If she wants to make 2/3 of a square as a test piece, how many yards of fabric does Emma need for her test piece? Answer: ______________
  4. Noah is building a model rocket and needs to paint the nose cone. The instructions say he needs 3/5 of a cup of paint for the entire rocket body. If he only needs to paint 2/3 of the nose cone section, what fraction of a cup of paint will Noah use for the nose cone? Answer: ______________
  5. 7/8 × 4/9 = ? Answer: ______________
  6. Noah is making a fruit salad for a class party. The recipe calls for 3/4 of a cup of strawberries for one serving. If Noah wants to make 2/3 of a serving, how many cups of strawberries should he use? Answer: ______________
  7. 3/5 × 7/9 = ? Answer: ______________
  8. 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: ______________
  9. 11/14 × 13/16 = ? Answer: ______________
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Answer Key & Explanations

Fraction × Fraction · Grade 5 · Worksheet 2

  1. 2/7 × 7/12 = ? Answer: 1/6 Solution: Write the multiplication: 2/7 × 7/12 Notice that 7 appears in both numerator and denominator, so we can simplify: 2/7 × 7/12 = 2/1 × 1/12 Multiply the numerators: 2 × 1 = 2 Multiply the denominators: 1 × 12 = 12 Write the product fraction: 2/12 Simplify by dividing numerator and denominator by…
    Full step-by-step solution

    Step 1: Write the multiplication: 2/7 × 7/12 Step 2: Notice that 7 appears in both numerator and denominator, so we can simplify: 2/7 × 7/12 = 2/1 × 1/12 Step 3: Multiply the numerators: 2 × 1 = 2 Step 4: Multiply the denominators: 1 × 12 = 12 Step 5: Write the product fraction: 2/12 Step 6: Simplify by dividing numerator and denominator by 2: 2 ÷ 2 = 1, 12 ÷ 2 = 6 Step 7: The simplified fraction is 1/6 The answer is 1/6.

  2. Emma is making a quilt and needs 3/5 of a yard of fabric for each square. If she wants to make 4/7 of a square to test her pattern, how many yards of fabric does she need for the test piece? Answer: 12/35 Solution: Emma needs 3/5 yard for a full square but only wants 4/7 of a square. To find the fabric needed for 4/7 of a square, multiply the fabric for one square (3/5) by the fraction of the square she's making (4/7).
    Full step-by-step solution

    Step 1: Emma needs 3/5 yard for a full square but only wants 4/7 of a square. Step 2: To find the fabric needed for 4/7 of a square, multiply the fabric for one square (3/5) by the fraction of the square she's making (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 yard of fabric. Step 6: The fraction 12/35 is already in simplest form since 12 and 35 have no common factors. The answer is 12/35.

  3. Emma is making a quilt and needs 3/5 of a yard of fabric for each square. If she wants to make 2/3 of a square as a test piece, how many yards of fabric does Emma need for her test piece? Answer: 2/5 Solution: Identify the fractions to multiply: 3/5 (fabric for full square) and 2/3 (fraction of square being made) Multiply the fractions: (3/5) × (2/3) Multiply numerators: 3 × 2 = 6 Multiply denominators: 5 × 3 = 15 Simplify the fraction: 6/15 = 2/5 The answer is 2/5 yard of fabric.
    Full step-by-step solution

    Step 1: Identify the fractions to multiply: 3/5 (fabric for full square) and 2/3 (fraction of square being made) Step 2: Multiply the fractions: (3/5) × (2/3) Step 3: Multiply numerators: 3 × 2 = 6 Step 4: Multiply denominators: 5 × 3 = 15 Step 5: Simplify the fraction: 6/15 = 2/5 Step 6: The answer is 2/5 yard of fabric.

  4. Noah is building a model rocket and needs to paint the nose cone. The instructions say he needs 3/5 of a cup of paint for the entire rocket body. If he only needs to paint 2/3 of the nose cone section, what fraction of a cup of paint will Noah use for the nose cone? Answer: 2/5 Solution: Identify the fractions to multiply: 3/5 (paint for entire rocket) and 2/3 (fraction of nose cone to paint) Multiply the fractions: (3/5) × (2/3) Multiply numerators: 3 × 2 = 6 Multiply denominators: 5 × 3 = 15 Simplify the fraction: 6/15 = 2/5 Noah will use 2/5 of a cup of paint for the nose cone.
    Full step-by-step solution

    Step 1: Identify the fractions to multiply: 3/5 (paint for entire rocket) and 2/3 (fraction of nose cone to paint) Step 2: Multiply the fractions: (3/5) × (2/3) Step 3: Multiply numerators: 3 × 2 = 6 Step 4: Multiply denominators: 5 × 3 = 15 Step 5: Simplify the fraction: 6/15 = 2/5 Noah will use 2/5 of a cup of paint for the nose cone.

  5. 7/8 × 4/9 = ? Answer: 7/18 Solution: Multiply the numerators: 7 × 4 = 28 Multiply the denominators: 8 × 9 = 72 Combine the results to form the product fraction: 28/72 Simplify the fraction by finding the greatest common factor of 28 and 72, which is 4 Divide both numerator and denominator by 4: 28 ÷ 4 = 7, 72 ÷ 4 = 18 The…
    Full step-by-step solution

    Step 1: Multiply the numerators: 7 × 4 = 28 Step 2: Multiply the denominators: 8 × 9 = 72 Step 3: Combine the results to form the product fraction: 28/72 Step 4: Simplify the fraction by finding the greatest common factor of 28 and 72, which is 4 Step 5: Divide both numerator and denominator by 4: 28 ÷ 4 = 7, 72 ÷ 4 = 18 Step 6: The simplified fraction is 7/18 The answer is 7/18.

  6. Noah is making a fruit salad for a class party. The recipe calls for 3/4 of a cup of strawberries for one serving. If Noah wants to make 2/3 of a serving, how many cups of strawberries should he use? Answer: 1/2 Solution: Identify the fractions to multiply. Noah needs 3/4 cup for a full serving but is making 2/3 of a serving. Multiply the fractions: (3/4) * (2/3).
    Full step-by-step solution

    Step 1: Identify the fractions to multiply. Noah needs 3/4 cup for a full serving but is making 2/3 of a serving. Step 2: Multiply the fractions: (3/4) * (2/3). Step 3: Multiply the numerators: 3 * 2 = 6. Step 4: Multiply the denominators: 4 * 3 = 12. Step 5: Write the resulting fraction: 6/12. Step 6: Simplify the fraction by dividing the numerator and denominator by their greatest common factor, which is 6: 6 ÷ 6 = 1, 12 ÷ 6 = 2. Step 7: The simplified fraction is 1/2. The answer is 1/2 cup.

  7. 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.

  8. 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.

  9. 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.