Fraction × Fraction

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Fraction × Fraction · Grade 5 · Worksheet 1

1. A rectangular garden plot is divided into a grid of equal squares. The plot is 3/4 of a meter wide and 2/3 of a meter long. If you visualize this grid, what is the area of the entire garden plot in square meters? Answer: 1/2 Solution: We have a rectangular garden plot. Its width is 3/4 of a meter. Its length is 2/3 of a meter.
   Full step-by-step solution

   Step 1: Understand the problem We have a rectangular garden plot. Its width is 3/4 of a meter. Its length is 2/3 of a meter. We are told it is divided into a grid of equal squares, but the question asks for the total area in square meters. The grid detail is extra information — the area is simply length times width. Step 2: Write the area formula for a rectangle Area = length × width Step 3: Substitute the given values Length = 2/3 m Width = 3/4 m Area = (2/3) × (3/4) Step 4: Multiply the fractions Multiply the numerators: 2 × 3 = 6 Multiply the denominators: 3 × 4 = 12 So Area = 6/12 Step 5: Simplify the fraction 6/12 can be simplified by dividing numerator and denominator by 6: 6 ÷ 6 = 1 12 ÷ 6 = 2 So Area = 1/2 Step 6: State the final answer The area of the garden plot is 1/2 square meter.

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

   Liam needs 2/3 of a cup for one full batch. He is making 3/4 of a batch. To find the amount needed for 3/4 of a batch, multiply the amount for one batch by 3/4. So: (2/3) * (3/4) Multiply the numerators: 2 * 3 = 6 Multiply the denominators: 3 * 4 = 12 This gives 6/12. Simplify 6/12 by dividing numerator and denominator by 6: 6 ÷ 6 = 1 12 ÷ 6 = 2 So 6/12 = 1/2. Therefore, Liam needs 1/2 of a cup of chocolate chips.

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. Noah is building a model train set and needs to paint a section of track. He has 3/5 of a can of red paint. If he uses 2/3 of his red paint to paint the track, what fraction of a full can of paint does Noah use? Answer: 2/5 Solution: Identify the fractions to multiply. Noah has 3/5 of a can and uses 2/3 of that amount.
   Full step-by-step solution

   Step 1: Identify the fractions to multiply. Noah has 3/5 of a can and uses 2/3 of that amount. Step 2: Multiply the fractions: (3/5) × (2/3) Step 3: Multiply the numerators: 3 × 2 = 6 Step 4: Multiply the denominators: 5 × 3 = 15 Step 5: Simplify the fraction: 6/15 = 2/5 Noah uses 2/5 of a full can of paint.

5. Noah is building a model train set and needs to create a miniature forest. He calculates that each tree requires 2/5 of a square foot of space. If Noah's layout has 3/4 of a square foot available for trees, how many square feet will be occupied when he places trees in the available space? Answer: 3/10 Solution: Identify the operation. We need to find what fraction of the total available space will be used. Write the multiplication expression: (2/5) × (3/4) Multiply the numerators: 2 × 3 = 6 Multiply the denominators: 5 × 4 = 20 Write the resulting fraction: 6/20 Simplify the fraction by dividing the…
   Full step-by-step solution

   Step 1: Identify the operation. We need to find what fraction of the total available space will be used. This means multiplying the space per tree by the number of 'tree spaces' we are considering, which is essentially multiplying the two fractions. Step 2: Write the multiplication expression: (2/5) × (3/4) Step 3: Multiply the numerators: 2 × 3 = 6 Step 4: Multiply the denominators: 5 × 4 = 20 Step 5: Write the resulting fraction: 6/20 Step 6: Simplify the fraction by dividing the numerator and denominator by their greatest common factor, which is 2: 6 ÷ 2 = 3 and 20 ÷ 2 = 10 Step 7: The simplified fraction is 3/10. The answer is 3/10 of a square foot.

6. A rectangular mural is painted on a wall. The mural is divided into a grid of equal squares. It has 5 rows and 7 columns. The artist paints a sun in the squares where the top 3/5 of the rows and the left 4/7 of the columns overlap. What fraction of the entire mural shows the sun? Answer: 12/35 Solution: The mural has 5 rows. The sun is painted in the top 3/5 of the rows. The mural has 7 columns.
   Full step-by-step solution

   Step 1: The mural has 5 rows. The sun is painted in the top 3/5 of the rows. So, the fraction of rows with the sun is 3/5. Step 2: The mural has 7 columns. The sun is painted in the left 4/7 of the columns. So, the fraction of columns with the sun is 4/7. Step 3: The sun appears where these specific rows and columns overlap. To find the fraction of the total mural area showing the sun, multiply the fraction of rows by the fraction of columns: (3/5) × (4/7). Step 4: Multiply the numerators: 3 × 4 = 12. Step 5: Multiply the denominators: 5 × 7 = 35. Step 6: The fraction is 12/35. The answer is 12/35.

7. 8/9 × 7/10 = ? Answer: 28/45 Solution: Multiply the numerators: 8 × 7 = 56 Multiply the denominators: 9 × 10 = 90 Combine the results to form the product fraction: 56/90 Simplify the fraction by finding the greatest common factor of 56 and 90, which is 2 Divide both numerator and denominator by 2: 56 ÷ 2 = 28, 90 ÷ 2 = 45 The…
   Full step-by-step solution

   Step 1: Multiply the numerators: 8 × 7 = 56 Step 2: Multiply the denominators: 9 × 10 = 90 Step 3: Combine the results to form the product fraction: 56/90 Step 4: Simplify the fraction by finding the greatest common factor of 56 and 90, which is 2 Step 5: Divide both numerator and denominator by 2: 56 ÷ 2 = 28, 90 ÷ 2 = 45 Step 6: The simplified fraction is 28/45 The answer is 28/45.

8. A farmer is planting a rectangular field that measures 3/4 of a kilometer by 7/8 of a kilometer. What is the area of the field in square kilometers? Answer: 21/32 Solution: Write the multiplication problem for the area: (3/4) × (7/8) Multiply the numerators: 3 × 7 = 21 Multiply the denominators: 4 × 8 = 32 Write the resulting fraction: 21/32 Check if the fraction can be simplified - 21 and 32 have no common factors other than 1, so 21/32 is already in simplest form…
   Full step-by-step solution

   Step 1: Write the multiplication problem for the area: (3/4) × (7/8) Step 2: Multiply the numerators: 3 × 7 = 21 Step 3: Multiply the denominators: 4 × 8 = 32 Step 4: Write the resulting fraction: 21/32 Step 5: Check if the fraction can be simplified - 21 and 32 have no common factors other than 1, so 21/32 is already in simplest form The area of the field is 21/32 square kilometers.

9. 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.