Interpret Remainders

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Interpret Remainders · Grade 4 · Worksheet 2

1. A rectangular garden is divided into 4 equal sections. The garden has a total area of 156 square meters. If you walk along the entire perimeter of the garden, how many meters do you walk if the garden is 13 meters long? Answer: 50 Solution: We have a rectangular garden with total area 156 m² and length 13 m. It is divided into 4 equal sections. We need the perimeter of the whole garden.
   Full step-by-step solution

   Step 1: Understand the problem. We have a rectangular garden with total area 156 m² and length 13 m. It is divided into 4 equal sections. We need the perimeter of the whole garden. Step 2: Find the width of the garden. Area of rectangle = length × width 156 = 13 × width width = 156 ÷ 13 width = 12 m Step 3: Understand the division into 4 equal sections. Since the garden is rectangular, dividing it into 4 equal sections could be done in two ways: - 4 sections in a row (length divided by 4) - 2 by 2 grid (length divided by 2, width divided by 2) But the problem doesn't specify the arrangement, and the perimeter of the whole garden doesn't depend on the internal divisions. We only need the outer perimeter. Step 4: Calculate the perimeter. Perimeter of rectangle = 2 × (length + width) = 2 × (13 + 12) = 2 × 25 = 50 m Step 5: Conclusion. Walking along the entire perimeter means walking 50 meters. Final answer: 50

2. Emma is arranging 143 square tiles in a rectangular pattern for a mosaic. She wants each row to have the same number of tiles, and she wants to make as many full rows as possible. If she puts 9 tiles in each row, how many tiles will be left over that cannot form a full row? Answer: 8 tiles Solution: Divide the total number of tiles (143) by the number of tiles per row (9). 143 ÷ 9 = 15 remainder 8, because 9 × 15 = 135 and 143 − 135 = 8. Step 2: The remainder 8 represents the tiles that cannot form a full row of 9.
   Full step-by-step solution

   Step 1: Divide the total number of tiles (143) by the number of tiles per row (9). 143 ÷ 9 = 15 remainder 8, because 9 × 15 = 135 and 143 − 135 = 8. Step 2: The remainder 8 represents the tiles that cannot form a full row of 9. So, 8 tiles are left over. The answer is 8 tiles.

3. 156 ÷ 4 = ? Answer: 39 Solution: Set up the division. We want to divide 156 into 4 equal parts. Start with the largest place value, which is the hundreds place.
   Full step-by-step solution

   Let's solve 156 ÷ 4 step by step. Step 1: Set up the division. We want to divide 156 into 4 equal parts. Step 2: Start with the largest place value, which is the hundreds place. 156 has 1 hundred. Can we divide 1 by 4? No, because 4 is larger than 1. So we consider the next digit as well. Step 3: Look at the first two digits: 15 (from 156). How many times does 4 go into 15? 4 × 3 = 12, which is less than 15. 4 × 4 = 16, which is too big (more than 15). So, 4 goes into 15 three times. Step 4: Write 3 above the tens digit of 156 (since we used 15, the tens place). Now multiply: 3 × 4 = 12. Subtract 12 from 15: 15 − 12 = 3. Step 5: Bring down the next digit, which is 6. Now we have 36. Step 6: Divide 36 by 4. How many times does 4 go into 36? 4 × 9 = 36 exactly. So, write 9 above the ones digit of 156. Step 7: Multiply and subtract again: 9 × 4 = 36. 36 − 36 = 0. Step 8: There is no remainder. So, 156 ÷ 4 = 39. Final answer: 39

4. Emma is making gift bags for her birthday party. She has 143 pieces of candy to share equally among 6 gift bags. How many pieces of candy will be in each gift bag? Answer: 23 Solution: Divide the total number of candy pieces by the number of gift bags: 143 ÷ 6 Calculate the division: 6 × 23 = 138 Subtract to find the remainder: 143 - 138 = 5 Since we're dividing candy equally among gift bags, we can only use whole pieces in each bag.
   Full step-by-step solution

   Step 1: Divide the total number of candy pieces by the number of gift bags: 143 ÷ 6 Step 2: Calculate the division: 6 × 23 = 138 Step 3: Subtract to find the remainder: 143 - 138 = 5 Step 4: Since we're dividing candy equally among gift bags, we can only use whole pieces in each bag. The 5 leftover pieces cannot make another complete bag. Step 5: Therefore, each gift bag will get 23 pieces of candy. The answer is 23.

5. A rectangular garden is divided into square sections for different vegetables. The garden has 8 rows of squares, and each row contains 7 squares. If you want to plant exactly 3 tomato seeds in each square, how many tomato seeds do you need in total? Answer: 168 Solution: First, find the total number of squares in the garden. The garden has 8 rows, and each row has 7 squares. So, total squares = 8 × 7 = 56 squares.
   Full step-by-step solution

   First, find the total number of squares in the garden. The garden has 8 rows, and each row has 7 squares. So, total squares = 8 × 7 = 56 squares. Next, each square needs 3 tomato seeds. So, total seeds needed = total squares × seeds per square. That is: 56 × 3. Now calculate: 56 × 3 = 168. Therefore, the total number of tomato seeds needed is 168.

6. Charlotte is making gift bags for her classmates. She has 127 stickers to put into gift bags. Each gift bag must have exactly 7 stickers. How many complete gift bags can Charlotte make? Answer: 18 Solution: Total stickers = 127. Stickers per bag = 7. Divide 127 by 7: 7 × 18 = 126, and 127 - 126 = 1.
   Full step-by-step solution

   Step 1: Total stickers = 127. Stickers per bag = 7. Step 2: Divide 127 by 7: 7 × 18 = 126, and 127 - 126 = 1. Step 3: The quotient is 18, which is the number of complete bags. The remainder is 1, which means 1 sticker is left over and not enough for another full bag. Step 4: So, Charlotte can make 18 complete gift bags. The answer is 18.