Multiply 2-Digit by 2-Digit

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Answer Key & Explanations

Multiply 2-Digit by 2-Digit · Grade 4 · Worksheet 3

1. Ava is helping her teacher organize the classroom library. She has 36 bookshelves, and each bookshelf can hold 25 books. How many books can the classroom library hold in total? Answer: 900 Solution: Identify the numbers to multiply: 36 bookshelves × 25 books per shelf Multiply 36 by 25 First multiply 36 × 20 = 720 Then multiply 36 × 5 = 180 Add the partial products: 720 + 180 = 900 The classroom library can hold 900 books in total.
   Full step-by-step solution

   Step 1: Identify the numbers to multiply: 36 bookshelves × 25 books per shelf Step 2: Multiply 36 by 25 Step 3: First multiply 36 × 20 = 720 Step 4: Then multiply 36 × 5 = 180 Step 5: Add the partial products: 720 + 180 = 900 Step 6: The classroom library can hold 900 books in total.

2. Ava is helping her teacher set up for the school science fair. She needs to arrange 36 tables in the gymnasium. Each table will display 24 science projects. How many science projects will be displayed at the fair in total? Answer: 864 Solution: Identify the numbers to multiply. There are 36 tables and 24 projects per table. Set up the multiplication problem: 36 × 24.
   Full step-by-step solution

   Step 1: Identify the numbers to multiply. There are 36 tables and 24 projects per table. Step 2: Set up the multiplication problem: 36 × 24. Step 3: Break it down. First, multiply 36 by 20: 36 × 20 = 720. Step 4: Then, multiply 36 by 4: 36 × 4 = 144. Step 5: Add the two products together: 720 + 144 = 864. The total number of science projects is 864.

3. Jordan is planting a rectangular garden. The garden is 98 feet long and 30 feet wide. What is the area of the garden in square feet? Answer: 2940 Solution: The length is 98 feet and the width is 30 feet. Area = length × width = 98 × 30 = 2940.
   Full step-by-step solution

   Step 1: The length is 98 feet and the width is 30 feet. Step 2: Area = length × width = 98 × 30 = 2940. The answer is 2940 square feet.

4. 84 × 57 = ? Answer: 4788 Solution: Multiply 84 by 7 (the ones digit of 57) 84 × 7 = 588 Multiply 84 by 50 (the tens digit of 57) 84 × 50 = 4200 588 + 4200 = 4788 The answer is 4788.
   Full step-by-step solution

   Step 1: Multiply 84 by 7 (the ones digit of 57) 84 × 7 = 588 Step 2: Multiply 84 by 50 (the tens digit of 57) 84 × 50 = 4200 Step 3: Add the two partial products together 588 + 4200 = 4788 The answer is 4788.

5. Matiu is designing a rectangular garden on a grid. The longer side of the rectangle is 38 units and the shorter side is 22 units. Each grid square represents 1 square meter. What is the total area of the garden in square meters? Answer: 836 Solution: The area of a rectangle is length × width. Here, length = 38 units and width = 22 units. Break 22 into 20 + 2 to use partial products.
   Full step-by-step solution

   Step 1: The area of a rectangle is length × width. Here, length = 38 units and width = 22 units. Step 2: Break 22 into 20 + 2 to use partial products. Step 3: Multiply 38 × 20 = 760. Step 4: Multiply 38 × 2 = 76. Step 5: Add the partial products: 760 + 76 = 836. Step 6: The area is 836 square meters. The answer is 836.

6. 42 × 36 = ? Answer: 1512 Solution: Multiply 42 by 6 (the ones digit of 36). 42 × 6 = 252. Multiply 42 by 30 (the tens digit of 36).
   Full step-by-step solution

   Step 1: Multiply 42 by 6 (the ones digit of 36). 42 × 6 = 252. Step 2: Multiply 42 by 30 (the tens digit of 36). 42 × 30 = 1260. Step 3: Add the two partial products together. 252 + 1260 = 1512. The answer is 1512.

7. A rectangular swimming pool is drawn on a grid. The longer side measures 28 units and the shorter side measures 15 units. If each grid unit represents 2 feet, what is the actual area of the pool in square feet? Answer: 1680 Solution: Area on grid = length × width = 28 × 15 28 × 15 = 28 × (10 + 5) = (28 × 10) + (28 × 5) = 280 + 140 = 420 square units Each grid unit represents 2 feet, so each square unit represents (2 × 2) = 4 square feet Actual area = grid area × scale factor = 420 × 4 420 × 4 = (400 × 4) + (20 × 4) = 1600 +…
   Full step-by-step solution

   Step 1: Find the area of the pool on the grid Area on grid = length × width = 28 × 15 28 × 15 = 28 × (10 + 5) = (28 × 10) + (28 × 5) = 280 + 140 = 420 square units Step 2: Apply the scale factor Each grid unit represents 2 feet, so each square unit represents (2 × 2) = 4 square feet Step 3: Calculate the actual area Actual area = grid area × scale factor = 420 × 4 420 × 4 = (400 × 4) + (20 × 4) = 1600 + 80 = 1680 square feet The answer is 1680.

8. Kai runs a small bakery. Each tray holds 52 cupcakes, and Kai bakes 33 trays for a party. How many cupcakes does Kai bake in total? Answer: 1716 Solution: Each tray has 52 cupcakes, and there are 33 trays. Multiply: 52 × 33 = 1716.
   Full step-by-step solution

   Step 1: Each tray has 52 cupcakes, and there are 33 trays. Step 2: Multiply: 52 × 33 = 1716. The answer is 1716 cupcakes.