Multiply Fractions by Whole

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Answer Key & Explanations

Multiply Fractions by Whole · Grade 4 · Worksheet 1

1. A rectangular garden measures 12 feet long and 8 feet wide. The gardener plants tomato plants in a grid pattern, with 4 plants along the length and 3 plants along the width. How many tomato plants are in the garden? Answer: 12 Solution: 1. "4 plants along the length" means there are 4 plants in each row (along the 12-foot side). "3 plants along the width" means there are 3 plants in each column (along the 8-foot side).
   Full step-by-step solution

   Let's go step-by-step. 1. Understand the grid pattern: The garden is rectangular, and plants are arranged in rows and columns. "4 plants along the length" means there are 4 plants in each row (along the 12-foot side). "3 plants along the width" means there are 3 plants in each column (along the 8-foot side). 2. Interpret the arrangement: If there are 4 plants along the length, that means each row has 4 plants. If there are 3 plants along the width, that means there are 3 rows. 3. Calculate total number of plants: Total plants = (number of plants per row) × (number of rows) Total plants = 4 × 3 = 12. 4. Conclusion: The garden has 12 tomato plants in total. Answer: 12

2. A rectangular farm field measures 120 meters long and 80 meters wide. The farmer plants corn in a grid pattern with 15 rows along the length and 10 rows along the width. How many corn plants are in the entire field? Answer: 150 Solution: The farmer plants corn in a grid pattern with 15 rows along the length There are 10 rows along the width To find the total number of corn plants, multiply the number of rows along the length by the number of rows along the width 15 × 10 = 150 The total number of corn plants is 150
   Full step-by-step solution

   Step 1: The farmer plants corn in a grid pattern with 15 rows along the length Step 2: There are 10 rows along the width Step 3: To find the total number of corn plants, multiply the number of rows along the length by the number of rows along the width Step 4: 15 × 10 = 150 Step 5: The total number of corn plants is 150

3. Aroha is helping to pack gift bags for a school fundraiser. Each gift bag needs 2/3 of a meter of ribbon. If Aroha needs to decorate 120 gift bags, how many meters of ribbon does she need in total? Answer: 80 Solution: Each gift bag needs 2/3 of a meter of ribbon. There are 120 gift bags. Multiply the amount per bag by the number of bags: 2/3 × 120.
   Full step-by-step solution

   Step 1: Each gift bag needs 2/3 of a meter of ribbon. Step 2: There are 120 gift bags. Step 3: Multiply the amount per bag by the number of bags: 2/3 × 120. Step 4: Write 120 as a fraction: 120 = 120/1. Step 5: Multiply the numerators: 2 × 120 = 240. Step 6: Multiply the denominators: 3 × 1 = 3. Step 7: The fraction is 240/3. Step 8: Simplify by dividing: 240 ÷ 3 = 80. The answer is 80 meters of ribbon.

4. A rectangular classroom floor is covered with square tiles. There are 15 tiles along the length and 12 tiles along the width. If you look at the entire floor, how many tiles are there in total? Answer: 180 Solution: The classroom floor has tiles arranged in rows and columns There are 15 tiles along the length (rows) There are 12 tiles along the width (columns) To find the total number of tiles, multiply the number of rows by the number of columns 15 × 12 = 180 The total number of tiles is 180
   Full step-by-step solution

   Step 1: The classroom floor has tiles arranged in rows and columns Step 2: There are 15 tiles along the length (rows) Step 3: There are 12 tiles along the width (columns) Step 4: To find the total number of tiles, multiply the number of rows by the number of columns Step 5: 15 × 12 = 180 Step 6: The total number of tiles is 180

5. Liam is baking cookies for his class party. He needs to make 3/4 of a batch of cookies. If one batch requires 2 cups of flour, how many cups of flour does Liam need for 3/4 of a batch? Answer: 1.5 Solution: One full batch of cookies requires 2 cups of flour. Liam is making 3/4 of a batch, so we need to find 3/4 of 2 cups. Set up the calculation.
   Full step-by-step solution

   Step 1: Understand the problem. One full batch of cookies requires 2 cups of flour. Liam is making 3/4 of a batch, so we need to find 3/4 of 2 cups. Step 2: Set up the calculation. To find a fraction of a number, multiply the fraction by the number. So, we calculate: 3/4 × 2 Step 3: Multiply the fraction by the whole number. 3/4 × 2 = (3 × 2) / 4 Step 4: Perform the multiplication. 3 × 2 = 6 So, we have 6 / 4 Step 5: Simplify the fraction. 6/4 can be simplified by dividing numerator and denominator by 2: 6 ÷ 2 = 3 4 ÷ 2 = 2 So, 6/4 = 3/2 Step 6: Convert to decimal (if needed). 3/2 = 1.5 Step 7: State the answer. Liam needs 1.5 cups of flour for 3/4 of a batch.