Interpret Remainders

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Interpret Remainders · Grade 4 · Worksheet 1

1. A farmer has 187 eggs to pack into cartons that hold 12 eggs each. How many full cartons can be packed, and how many eggs will be left over? Answer: 15 R7 Solution: Divide the total number of eggs by the carton capacity: 187 ÷ 12 Calculate how many full cartons: 12 × 15 = 180 eggs Find the remainder: 187 - 180 = 7 eggs left over This means 15 full cartons can be packed, with 7 eggs remaining unpackaged Check: (12 × 15) + 7 = 180 + 7 = 187 The answer is 15 R7.
   Full step-by-step solution

   Step 1: Divide the total number of eggs by the carton capacity: 187 ÷ 12 Step 2: Calculate how many full cartons: 12 × 15 = 180 eggs Step 3: Find the remainder: 187 - 180 = 7 eggs left over Step 4: This means 15 full cartons can be packed, with 7 eggs remaining unpackaged Step 5: Check: (12 × 15) + 7 = 180 + 7 = 187 The answer is 15 R7.

2. A teacher has 187 stickers to give equally to 9 students. How many stickers will each student get, and how many stickers will be left over? Answer: 20 R7 Solution: Divide the total number of stickers by the number of students: 187 ÷ 9 Calculate how many times 9 goes into 187: 9 × 20 = 180 Subtract: 187 - 180 = 7 stickers left over Each student gets 20 stickers, with 7 stickers remaining Check: (9 × 20) + 7 = 180 + 7 = 187 The answer is 20 R7, meaning each…
   Full step-by-step solution

   Step 1: Divide the total number of stickers by the number of students: 187 ÷ 9 Step 2: Calculate how many times 9 goes into 187: 9 × 20 = 180 Step 3: Subtract: 187 - 180 = 7 stickers left over Step 4: Each student gets 20 stickers, with 7 stickers remaining Step 5: Check: (9 × 20) + 7 = 180 + 7 = 187 The answer is 20 R7, meaning each student gets 20 stickers and 7 stickers will be left over.

3. Emma is making fruit baskets for her class party. She has 187 strawberries to share equally among 24 students. How many strawberries will each student receive? Answer: 7 Solution: Divide 187 by 24 to find how many strawberries each student gets. 24 × 7 = 168 187 - 168 = 19 Since we're sharing whole strawberries equally, we only consider the whole number part of the division (7).
   Full step-by-step solution

   Step 1: Divide 187 by 24 to find how many strawberries each student gets. Step 2: 24 × 7 = 168 Step 3: 187 - 168 = 19 Step 4: Since we're sharing whole strawberries equally, we only consider the whole number part of the division (7). Step 5: The 19 remaining strawberries cannot be divided evenly among all students, so each student gets 7 strawberries. The answer is 7.

4. The school is organizing a field trip for 128 students. Each school bus can carry 45 students. How many buses are needed to transport all the students to the field trip? Answer: 3 Solution: Identify the total number of students and the bus capacity. Total students = 128 Bus capacity = 45 students per bus Divide the total students by the bus capacity to find how many buses are needed.
   Full step-by-step solution

   Step 1: Identify the total number of students and the bus capacity. Total students = 128 Bus capacity = 45 students per bus Step 2: Divide the total students by the bus capacity to find how many buses are needed. 128 ÷ 45 = 2 remainder 38 This means 2 full buses carry 90 students (since 2 × 45 = 90), but there are 128 − 90 = 38 students left. Step 3: Consider the remaining students. Since each bus can carry 45 students and 38 students still need a ride, they need an extra bus for these 38 students. Step 4: Total buses needed = 2 full buses + 1 more bus for the remaining 38 students. So total buses = 3. Step 5: Check: 3 buses × 45 students = 135 seats, which is enough for 128 students. 2 buses would only hold 90 students, which is not enough. Final answer: 3 buses are needed.

5. 256 ÷ 6 = ? Answer: 42 R4 Solution: Set up the division. We are dividing 256 by 6. Look at the first digit of 256, which is 2.
   Full step-by-step solution

   Let's solve 256 ÷ 6 step-by-step using long division. Step 1: Set up the division. We are dividing 256 by 6. Step 2: Look at the first digit of 256, which is 2. 6 is larger than 2, so we cannot divide 6 into 2. We take the first two digits instead: 25. Step 3: Divide 25 by 6. We ask: How many times does 6 go into 25? 6 × 4 = 24, which is less than 25. 6 × 5 = 30, which is too big. So, 6 goes into 25 four times. Write 4 above the division bar, above the 5. Step 4: Multiply and subtract. Multiply: 4 × 6 = 24. Write 24 below 25. Subtract: 25 − 24 = 1. Step 5: Bring down the next digit. Bring down the 6 from 256. This makes the new number 16. Step 6: Divide 16 by 6. We ask: How many times does 6 go into 16? 6 × 2 = 12, which is less than 16. 6 × 3 = 18, which is too big. So, 6 goes into 16 two times. Write 2 above the division bar, above the 6. Step 7: Multiply and subtract again. Multiply: 2 × 6 = 12. Write 12 below 16. Subtract: 16 − 12 = 4. Step 8: Interpret the result. We have no more digits to bring down. The number on top (42) is the quotient. The number at the bottom (4) is the remainder. Therefore, 256 ÷ 6 = 42 with a remainder of 4, written as 42 R4. Final check: (6 × 42) + 4 = 252 + 4 = 256. This confirms the answer is correct.

6. 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

7. A factory packages 178 cookies into boxes that hold 12 cookies each. How many full boxes can be made, and how many cookies will be left unpackaged? Answer: 14 R10 Solution: Divide the total number of cookies by the number of cookies per box: 178 ÷ 12 Calculate how many full boxes: 12 × 14 = 168 cookies Subtract to find the remainder: 178 - 168 = 10 cookies left This means 14 full boxes can be made, with 10 cookies remaining unpackaged Check: (12 × 14) + 10 = 168 +…
   Full step-by-step solution

   Step 1: Divide the total number of cookies by the number of cookies per box: 178 ÷ 12 Step 2: Calculate how many full boxes: 12 × 14 = 168 cookies Step 3: Subtract to find the remainder: 178 - 168 = 10 cookies left Step 4: This means 14 full boxes can be made, with 10 cookies remaining unpackaged Step 5: Check: (12 × 14) + 10 = 168 + 10 = 178 The answer is 14 R10.

8. Liam has 235 stickers. He wants to put them into albums that hold 15 stickers per page. How many full pages can he fill, and how many stickers will be left over? Answer: 15 R10 Solution: Divide 235 by 15. 15 × 15 = 225, which is less than 235. 15 × 16 = 240, which is too high.
   Full step-by-step solution

   Step 1: Divide 235 by 15. 15 × 15 = 225, which is less than 235. 15 × 16 = 240, which is too high. So the quotient is 15. Step 2: Multiply: 15 × 15 = 225 stickers used. Step 3: Subtract: 235 − 225 = 10 stickers left over. Step 4: So Liam can fill 15 full pages, and 10 stickers will be left over. The answer is 15 R10.

9. The fourth-grade class is planning a pizza party. They have 148 students and each large pizza is cut into 12 slices. How many pizzas do they need to order so that every student can have at least one slice of pizza? Answer: 13 Solution: Identify the total number of students: 148 Identify how many slices each pizza provides: 12 Divide the total students by slices per pizza: 148 ÷ 12 Calculate the division: 12 × 12 = 144, so 148 - 144 = 4 This means 12 full pizzas would only cover 144 students, leaving 4 students without a slice.
   Full step-by-step solution

   Step 1: Identify the total number of students: 148 Step 2: Identify how many slices each pizza provides: 12 Step 3: Divide the total students by slices per pizza: 148 ÷ 12 Step 4: Calculate the division: 12 × 12 = 144, so 148 - 144 = 4 Step 5: This means 12 full pizzas would only cover 144 students, leaving 4 students without a slice. Step 6: Since every student needs a slice, you must order one more pizza to cover the remaining 4 students. Step 7: Total pizzas needed = 12 + 1 = 13 The answer is 13.