Interpret Remainders

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Interpret Remainders · Grade 4 · Worksheet 3

1. 156 ÷ 12 = ? Answer: 13 Solution: We need to divide 156 into 12 equal parts. That means we want to find how many times 12 fits into 156. Break down 156 into parts that are easier to divide by 12.
   Full step-by-step solution

   Let's solve 156 ÷ 12 step-by-step. Step 1: Understand the problem. We need to divide 156 into 12 equal parts. That means we want to find how many times 12 fits into 156. Step 2: Break down 156 into parts that are easier to divide by 12. We know 12 × 10 = 120. So 156 = 120 + 36. Step 3: Divide each part by 12. First part: 120 ÷ 12 = 10. Second part: 36 ÷ 12 = 3. Step 4: Add the results. 10 + 3 = 13. Step 5: Check the answer. 12 × 13 = (12 × 10) + (12 × 3) = 120 + 36 = 156. This matches the original number, so the division is correct. ANSWER: 13

2. Liam has 157 marbles. He wants to put them into bags that hold 9 marbles each. How many full bags can he make, and how many marbles will be left over? Answer: 17 R4 Solution: Divide 157 by 9. 9 × 17 = 153, which is less than 157. 9 × 18 = 162, which is too many.
   Full step-by-step solution

   Step 1: Divide 157 by 9. 9 × 17 = 153, which is less than 157. 9 × 18 = 162, which is too many. So the quotient is 17. Step 2: Subtract to find the remainder: 157 - 153 = 4. Step 3: This means Liam can make 17 full bags, with 4 marbles left over. Step 4: Check: (9 × 17) + 4 = 153 + 4 = 157. The answer is 17 R4.

3. The school is organizing a field trip and needs to transport 148 students. Each school bus can carry 36 students. How many buses are needed to transport all the students? Answer: 5 Solution: We have 148 students in total. Each bus can carry 36 students. We need to find how many buses are needed to transport everyone.
   Full step-by-step solution

   Step 1: Understand the problem. We have 148 students in total. Each bus can carry 36 students. We need to find how many buses are needed to transport everyone. Step 2: Divide the total students by the bus capacity. 148 ÷ 36 = ? Step 3: Perform the division. 36 × 4 = 144 148 − 144 = 4 So, 148 ÷ 36 = 4 remainder 4. Step 4: Interpret the result. 4 full buses will carry 36 × 4 = 144 students. But there are 148 students, so 4 students remain. These 4 students also need a bus, even though that bus won’t be full. Step 5: Determine the total number of buses. 4 buses (full) + 1 bus (for the remaining 4 students) = 5 buses. Step 6: Conclusion. 5 buses are needed to transport all 148 students.

4. Sophia is organizing a book fair. She has 214 books to display on tables that can hold 16 books each. How many full tables can she set up, and how many books will be left over? Answer: 13 R6 Solution: Divide the total books by the table capacity: 214 ÷ 16. 16 × 13 = 208, so 13 full tables can be set up. Subtract to find the remainder: 214 - 208 = 6 books left over.
   Full step-by-step solution

   Step 1: Divide the total books by the table capacity: 214 ÷ 16. Step 2: 16 × 13 = 208, so 13 full tables can be set up. Step 3: Subtract to find the remainder: 214 - 208 = 6 books left over. Step 4: Check: (16 × 13) + 6 = 208 + 6 = 214. The answer is 13 R6.

5. Emma is organizing a school bake sale and needs to package cookies into boxes. Each box can hold exactly 12 cookies. If she has 158 cookies to package, how many complete boxes can she fill? Answer: 13 Solution: Identify the total number of cookies: 158 Identify how many cookies fit in one box: 12 Divide the total cookies by the number per box to find how many full boxes can be made: 158 ÷ 12 Perform the division: 12 × 13 = 156 Subtract to find the remainder: 158 - 156 = 2 The question asks for complete…
   Full step-by-step solution

   Step 1: Identify the total number of cookies: 158 Step 2: Identify how many cookies fit in one box: 12 Step 3: Divide the total cookies by the number per box to find how many full boxes can be made: 158 ÷ 12 Step 4: Perform the division: 12 × 13 = 156 Step 5: Subtract to find the remainder: 158 - 156 = 2 Step 6: The question asks for complete boxes, so we only count the whole number from the division, which is 13. The 2 leftover cookies do not make a full box. The answer is 13 complete boxes.

6. Emma has 173 stickers. She wants to put them in albums that hold 15 stickers per page. How many full pages can she fill, and how many stickers will be left over? Answer: 11 R8 Solution: Divide the total stickers by the page capacity: 173 ÷ 15. 15 × 11 = 165, which is the largest multiple of 15 less than 173. Subtract to find the remainder: 173 - 165 = 8.
   Full step-by-step solution

   Step 1: Divide the total stickers by the page capacity: 173 ÷ 15. Step 2: 15 × 11 = 165, which is the largest multiple of 15 less than 173. Step 3: Subtract to find the remainder: 173 - 165 = 8. Step 4: So Emma can fill 11 full pages, and 8 stickers will be left over. Step 5: Check: (15 × 11) + 8 = 165 + 8 = 173. The answer is 11 R8.

7. 156 ÷ 7 = ? Answer: 22 R2 Solution: We start with 7 into 15 (the first two digits of 156). 7 × 2 = 14, which is less than or equal to 15. Write 2 above the division bar (over the 5 of 15).
   Full step-by-step solution

   Let's divide 156 by 7 using long division step-by-step. Step 1: We start with 7 into 15 (the first two digits of 156). 7 × 2 = 14, which is less than or equal to 15. Write 2 above the division bar (over the 5 of 15). 15 − 14 = 1. Step 2: Bring down the next digit, which is 6. Now we have 16. Step 3: Divide 7 into 16. 7 × 2 = 14, which is less than or equal to 16. Write 2 above the division bar (over the 6 of 156). 16 − 14 = 2. Step 4: We have no more digits to bring down. The quotient is 22, and the remainder is 2. Thus, 156 ÷ 7 = 22 R2. Check: 7 × 22 = 154, 154 + 2 = 156. Correct.

8. Liam is organizing his trading card collection into albums. Each album page holds exactly 8 cards. If Liam has 127 cards, how many complete pages can he fill? Answer: 15 Solution: We are told each album page holds exactly 8 cards. Liam has 127 cards. To find how many complete pages he can fill, we divide the total number of cards by the number of cards per page.
   Full step-by-step solution

   We are told each album page holds exactly 8 cards. Liam has 127 cards. Step 1: To find how many complete pages he can fill, we divide the total number of cards by the number of cards per page. 127 ÷ 8 Step 2: Perform the division. 8 × 15 = 120 127 − 120 = 7 So, 127 ÷ 8 = 15 remainder 7. Step 3: Interpret the result. The quotient (15) is the number of full pages that can be completely filled with 8 cards each. The remainder (7) means there are 7 cards left over, which do not make a complete page. Step 4: Conclusion. Liam can fill 15 complete pages.

9. A factory packages cookies into boxes that hold 24 cookies each. If they have 587 cookies to package, how many cookies will be left over after filling as many complete boxes as possible? Answer: 11 Solution: Divide the total number of cookies by the number that fits in each box: 587 ÷ 24 Calculate how many complete boxes can be filled: 24 × 24 = 576 cookies (24 full boxes) Subtract to find how many cookies are used in complete boxes: 587 - 576 = 11 cookies Since we're looking for cookies left over…
   Full step-by-step solution

   Step 1: Divide the total number of cookies by the number that fits in each box: 587 ÷ 24 Step 2: Calculate how many complete boxes can be filled: 24 × 24 = 576 cookies (24 full boxes) Step 3: Subtract to find how many cookies are used in complete boxes: 587 - 576 = 11 cookies Step 4: Since we're looking for cookies left over after filling complete boxes, the answer is the remainder: 11 cookies The answer is 11.