Interpret Remainders

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Interpret Remainders · Grade 4 · Worksheet 3

1. Kaia is helping her family pack oranges into crates for the farmer's market. Each crate can hold exactly 9 oranges. If they have 263 oranges to pack, how many complete crates can they fill? Answer: 29 Solution: Total oranges = 263. Oranges per crate = 9. Divide 263 by 9: 9 × 29 = 261, and 263 - 261 = 2.
   Full step-by-step solution

   Step 1: Total oranges = 263. Oranges per crate = 9. Step 2: Divide 263 by 9: 9 × 29 = 261, and 263 - 261 = 2. Step 3: The quotient is 29, with a remainder of 2. Step 4: The question asks for complete crates, so we only count the full groups of 9. The 2 leftover oranges are not enough to fill another crate. Answer: 29 complete crates.

2. The school is organizing a field trip for 125 students. Each school bus can carry 36 students. How many buses are needed to transport all the students? Answer: 4 Solution: We have 125 students, and each bus can carry 36 students. We need to find how many buses are needed to fit everyone. Divide the total students by the bus capacity.
   Full step-by-step solution

   Step 1: Understand the problem. We have 125 students, and each bus can carry 36 students. We need to find how many buses are needed to fit everyone. Step 2: Divide the total students by the bus capacity. 125 ÷ 36 = ? Step 3: Perform the division. 36 × 3 = 108 125 − 108 = 17 So, 125 ÷ 36 = 3 remainder 17. Step 4: Interpret the result. 3 full buses will carry 108 students, but 17 students will be left without a seat. Since we cannot leave any student behind, we need one more bus for the remaining 17 students. Step 5: Determine the total number of buses. 3 buses + 1 bus = 4 buses. Step 6: Check the answer. 4 buses × 36 students = 144 seats, which is more than enough for 125 students. Final answer: 4 buses are needed.

3. A factory packages 275 cookies into boxes that hold 12 cookies each. After filling as many complete boxes as possible, how many cookies will be left over that cannot fill another complete box? Answer: 11 Solution: Divide the total number of cookies by the number that fits in each box: 275 ÷ 12 Calculate how many complete boxes can be filled: 12 × 22 = 264 cookies Subtract to find how many cookies are left: 275 - 264 = 11 cookies Since 11 cookies is less than a full box of 12, these are the leftover…
   Full step-by-step solution

   Step 1: Divide the total number of cookies by the number that fits in each box: 275 ÷ 12 Step 2: Calculate how many complete boxes can be filled: 12 × 22 = 264 cookies Step 3: Subtract to find how many cookies are left: 275 - 264 = 11 cookies Step 4: Since 11 cookies is less than a full box of 12, these are the leftover cookies The answer is 11.

4. Sophia has 193 beads. She wants to make necklaces that each use 12 beads. How many complete necklaces can she make, and how many beads will be left over? Answer: 16 R1 Solution: Divide 193 by 12. Step 2: 12 × 16 = 192, which is the largest multiple of 12 less than 193. Step 3: Subtract to find the remainder: 193 - 192 = 1.
   Full step-by-step solution

   Step 1: Divide 193 by 12. Step 2: 12 × 16 = 192, which is the largest multiple of 12 less than 193. Step 3: Subtract to find the remainder: 193 - 192 = 1. Step 4: So Sophia can make 16 complete necklaces, and 1 bead will be left over. Step 5: Check: (12 × 16) + 1 = 192 + 1 = 193. The answer is 16 R1.

5. Mere has 246 lollipops to pack into bags that hold 14 lollipops each. How many full bags can she pack, and how many lollipops will be left over? Answer: 17 R8 Solution: Divide 246 by 14. Step 2: 14 × 17 = 238, which is the largest multiple of 14 less than 246. Step 3: Subtract to find the remainder: 246 - 238 = 8.
   Full step-by-step solution

   Step 1: Divide 246 by 14. Step 2: 14 × 17 = 238, which is the largest multiple of 14 less than 246. Step 3: Subtract to find the remainder: 246 - 238 = 8. Step 4: So Mere can pack 17 full bags, and 8 lollipops will be left over. Step 5: Check: (14 × 17) + 8 = 238 + 8 = 246. The answer is 17 R8.

6. The school is organizing a field trip for 148 students. Each school bus can carry 36 students. How many buses are needed to transport all the students to the field trip? Answer: 5 Solution: Identify the total number of students and the bus capacity. Total students = 148 Bus capacity = 36 students per bus Divide the total students by the bus capacity to find how many full buses are needed.
   Full step-by-step solution

   Step 1: Identify the total number of students and the bus capacity. Total students = 148 Bus capacity = 36 students per bus Step 2: Divide the total students by the bus capacity to find how many full buses are needed. 148 ÷ 36 = 4 remainder 4 This means 4 full buses carry 36 × 4 = 144 students. Step 3: Check if there are remaining students. 148 − 144 = 4 students left. Step 4: Since each bus can carry 36 students and there are 4 students left, they need an extra bus for those 4 students. So total buses = 4 + 1 = 5. Step 5: Verify: 5 buses × 36 students = 180 seats, which is enough for 148 students. Final answer: 5 buses are needed.

7. 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.

8. 156 ÷ 8 = ? Answer: 19.5 Solution: Set up the division. We are dividing 156 by 8. First, check how many times 8 goes into the first digit of 156.
   Full step-by-step solution

   Let's solve 156 ÷ 8 step-by-step. Step 1: Set up the division. We are dividing 156 by 8. Step 2: First, check how many times 8 goes into the first digit of 156. The first digit is 1. Since 8 is larger than 1, 8 does not go into 1. So we take the first two digits, 15. Step 3: Divide 15 by 8. 8 × 1 = 8 8 × 2 = 16 (too big, since 16 > 15) So 8 goes into 15 one time. Write 1 above the division bar over the 5. Step 4: Multiply and subtract. 1 × 8 = 8 Subtract 8 from 15: 15 − 8 = 7 Step 5: Bring down the next digit. Bring down the 6 from 156, making the new number 76. Step 6: Divide 76 by 8. 8 × 9 = 72 8 × 10 = 80 (too big, since 80 > 76) So 8 goes into 76 nine times. Write 9 above the division bar over the 6. Step 7: Multiply and subtract again. 9 × 8 = 72 Subtract 72 from 76: 76 − 72 = 4 Step 8: Interpret the remainder. We have no more digits to bring down. The remainder is 4. Since we are allowing decimals, we can continue by adding a decimal point and zeros. Step 9: Add a decimal point and a zero. Write a decimal point after the 19 in the quotient, and bring down a zero after the remainder 4, making it 40. Step 10: Divide 40 by 8. 8 × 5 = 40 exactly. Write 5 after the decimal point in the quotient. Step 11: Final result. The quotient is 19.5. So, 156 ÷ 8 = 19.5

9. Mere has 198 beads. She wants to make necklaces that each use 16 beads. How many complete necklaces can she make, and how many beads will be left over? Answer: 12 R6 Solution: Divide 198 by 16. Step 2: 16 × 12 = 192, which is the largest multiple of 16 less than 198. Step 3: Subtract to find the remainder: 198 - 192 = 6.
   Full step-by-step solution

   Step 1: Divide 198 by 16. Step 2: 16 × 12 = 192, which is the largest multiple of 16 less than 198. Step 3: Subtract to find the remainder: 198 - 192 = 6. Step 4: So Mere can make 12 complete necklaces, and 6 beads will be left over. Step 5: Check: (16 × 12) + 6 = 192 + 6 = 198. The answer is 12 R6.