Mixed Number Multiplication

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Mixed Number Multiplication · Grade 5 · Worksheet 2

1. Nikau is planting a vegetable garden. Nikau plants 4 rows of carrots. Each row has 8 carrot plants. How many carrot plants does Nikau have in total? Answer: 32 Solution: Number of rows of carrots: 4. Number of plants per row: 8. Multiply rows by plants per row: 4 × 8 = 32.
   Full step-by-step solution

   Step 1: Number of rows of carrots: 4. Step 2: Number of plants per row: 8. Step 3: Multiply rows by plants per row: 4 × 8 = 32. The answer is 32 carrot plants.

2. Emma is making a quilt for her grandmother. Each quilt block is a rectangle that measures 2 1/4 feet long and 1 3/4 feet wide. If she needs to make 12 identical blocks for the quilt, what is the total area of fabric she needs for all the blocks in square feet? Answer: 47.25 Solution: Area = length × width = 2 1/4 × 1 3/4 2 1/4 = 9/4 1 3/4 = 7/4 9/4 × 7/4 = 63/16 63 ÷ 16 = 3.9375 square feet per block 3.9375 × 12 = 47.25 square feet The total fabric needed is 47.25 square feet.
   Full step-by-step solution

   Step 1: Find the area of one quilt block Area = length × width = 2 1/4 × 1 3/4 Step 2: Convert mixed numbers to improper fractions 2 1/4 = 9/4 1 3/4 = 7/4 Step 3: Multiply the fractions 9/4 × 7/4 = 63/16 Step 4: Convert to decimal 63 ÷ 16 = 3.9375 square feet per block Step 5: Multiply by number of blocks 3.9375 × 12 = 47.25 square feet Step 6: The total fabric needed is 47.25 square feet.

3. Ava is baking cookies for a school bake sale. Each batch of cookie dough needs 3 cups of flour. Ava decides to make 4 batches of dough. How many cups of flour does Ava need in total? Answer: 12 Solution: Identify the amount of flour per batch: 3 cups. Identify the number of batches: 4. Multiply the amount per batch by the number of batches: 3 × 4 = 12.
   Full step-by-step solution

   Step 1: Identify the amount of flour per batch: 3 cups. Step 2: Identify the number of batches: 4. Step 3: Multiply the amount per batch by the number of batches: 3 × 4 = 12. The answer is 12 cups of flour.

4. A rectangular prism has a length of 8.5 cm, a width of 6.2 cm, and a height of 4.3 cm. What is the volume of this prism in cubic centimeters? Answer: 226.61 Solution: To find the volume of a rectangular prism, we use the formula: Volume = length × width × height Write down the given measurements. Length = 8.5 cm Width = 6.2 cm Height = 4.3 cm Multiply the length and the width first.
   Full step-by-step solution

   To find the volume of a rectangular prism, we use the formula: Volume = length × width × height Step 1: Write down the given measurements. Length = 8.5 cm Width = 6.2 cm Height = 4.3 cm Step 2: Multiply the length and the width first. 8.5 × 6.2 First, multiply 85 × 62 = 5270. Since 8.5 has one decimal place and 6.2 has one decimal place, the product must have two decimal places. So, 8.5 × 6.2 = 52.70 Step 3: Now multiply this result by the height. We have 52.70 × 4.3 First, multiply 5270 × 43 = 226610. Since 52.70 has two decimal places and 4.3 has one decimal place, the product must have three decimal places. So, 52.70 × 4.3 = 226.610 Step 4: Write the final answer. The volume is 226.61 cubic centimeters. (We drop the final zero as it is not needed after the decimal point). Final Answer: 226.61

5. Kaia is drawing a rectangular prism on a coordinate grid. The base of the prism has vertices at (1, 1), (9, 1), (9, 7), and (1, 7). The height of the prism is 3 3/5 units. What is the volume of Kaia's rectangular prism in cubic units? Answer: 172.8 Solution: Find the side lengths of the rectangular base. The distance from (1,1) to (9,1) is 9 - 1 = 8 units. The distance from (1,1) to (1,7) is 7 - 1 = 6 units.
   Full step-by-step solution

   Step 1: Find the side lengths of the rectangular base. The distance from (1,1) to (9,1) is 9 - 1 = 8 units. So the length is 8 units. The distance from (1,1) to (1,7) is 7 - 1 = 6 units. So the width is 6 units. Step 2: Find the area of the base. Area of base = length × width = 8 × 6 = 48 square units. Step 3: Find the volume. Volume = area of base × height. Height = 3 3/5. Convert the mixed number to an improper fraction: 3 3/5 = (3 × 5 + 3) / 5 = (15 + 3) / 5 = 18/5. Step 4: Multiply the area by the height. Volume = 48 × 18/5 = (48 × 18) / 5. Step 5: Multiply the numerator. 48 × 18 = 864. So Volume = 864 / 5. Step 6: Convert to a decimal or mixed number. 864 ÷ 5 = 172.8. The volume of Kaia's rectangular prism is 172.8 cubic units.

6. Emma is making a quilt for her grandmother. Each quilt block is a rectangle that measures 2 1/4 feet by 1 3/5 feet. If Emma makes 8 identical blocks, what is the total area of fabric she will need for all the blocks in square feet? Answer: 28.8 Solution: Find the area of one quilt block. Area = length × width Area = 2 1/4 × 1 3/5 Convert the mixed numbers to improper fractions.
   Full step-by-step solution

   Step 1: Find the area of one quilt block. Area = length × width Area = 2 1/4 × 1 3/5 Step 2: Convert the mixed numbers to improper fractions. 2 1/4 = (2 × 4 + 1)/4 = 9/4 1 3/5 = (1 × 5 + 3)/5 = 8/5 Step 3: Multiply the fractions to find the area of one block. Area = (9/4) × (8/5) = (9 × 8)/(4 × 5) = 72/20 Step 4: Simplify the fraction. 72/20 = 18/5 = 3.6 square feet Step 5: Multiply the area of one block by the number of blocks. Total area = 3.6 × 8 = 28.8 square feet The answer is 28.8.