Interpret Remainders

lessonbunny.com

Answer Key & Explanations

Interpret Remainders · Grade 4 · Worksheet 1

1. Emma is baking cookies for her class party. She has 185 chocolate chips to divide equally among 24 cookies. How many chocolate chips will be left over after she puts the same number on each cookie? Answer: 17 Solution: Emma has 185 chocolate chips to divide equally among 24 cookies. Divide 185 by 24 to find how many chips go on each cookie and how many are left over.
   Full step-by-step solution

   Step 1: Emma has 185 chocolate chips to divide equally among 24 cookies. Step 2: Divide 185 by 24 to find how many chips go on each cookie and how many are left over. Step 3: 24 × 7 = 168 (this is how many chips would be used if 7 went on each cookie) Step 4: 185 - 168 = 17 (these are the chips left over after putting 7 on each cookie) Step 5: Since 17 is less than 24, we cannot put another whole chip on each cookie. The answer is 17 chocolate chips left over.

2. Emma is organizing a school bake sale and needs to package cookies into boxes. She has 187 cookies to package, and each box can hold exactly 12 cookies. How many complete boxes of cookies can Emma fill? Answer: 15 Solution: Identify the total number of cookies and how many fit in one box. Emma has 187 cookies, and each box holds 12 cookies. Divide the total cookies by the number per box to find out how many full boxes can be made.
   Full step-by-step solution

   Step 1: Identify the total number of cookies and how many fit in one box. Emma has 187 cookies, and each box holds 12 cookies. Step 2: Divide the total cookies by the number per box to find out how many full boxes can be made. 187 ÷ 12. Step 3: Perform the division: 12 × 15 = 180. Since 12 × 16 = 192, which is more than 187, 15 is the largest whole number of boxes we can fill completely. Step 4: Check the remainder: 187 - 180 = 7. There are 7 cookies left over, but the question asks for complete boxes, so we only count the 15 full boxes. The answer is 15 complete boxes.

3. Mason has 274 baseball cards. He wants to put them into albums that hold 18 cards per page. How many full pages can he fill, and how many cards will be left over? Answer: 15 R4 Solution: Divide the total cards by the page capacity: 274 ÷ 18. 18 × 15 = 270, which is the largest multiple of 18 less than 274. Subtract to find the remainder: 274 - 270 = 4.
   Full step-by-step solution

   Step 1: Divide the total cards by the page capacity: 274 ÷ 18. Step 2: 18 × 15 = 270, which is the largest multiple of 18 less than 274. Step 3: Subtract to find the remainder: 274 - 270 = 4. Step 4: So Mason can fill 15 full pages, and 4 cards will be left over. Step 5: Check: (18 × 15) + 4 = 270 + 4 = 274. The answer is 15 R4.

4. Matiu is helping to organize books in the school library. He has 162 books to place on shelves. Each shelf can hold exactly 8 books. How many shelves will Matiu need to hold all the books? Answer: 21 Solution: Total books = 162. Books per shelf = 8. Divide: 162 ÷ 8 = 20 with a remainder.
   Full step-by-step solution

   Step 1: Total books = 162. Books per shelf = 8. Step 2: Divide: 162 ÷ 8 = 20 with a remainder. Step 3: 8 × 20 = 160, and 162 - 160 = 2. Step 4: The quotient 20 means 20 shelves can hold 160 books, but 2 books are left over. Step 5: Since those 2 books still need a shelf, we must add one more shelf: 20 + 1 = 21. Step 6: Matiu needs 21 shelves to hold all 162 books.

5. Tane is packing 263 apples into crates that hold 18 apples each. How many full crates can he pack, and how many apples will be left over? Answer: 14 R11 Solution: Divide 263 by 18. 18 × 14 = 252, and 263 - 252 = 11. So 263 ÷ 18 = 14 remainder 11.
   Full step-by-step solution

   Step 1: Divide 263 by 18. 18 × 14 = 252, and 263 - 252 = 11. So 263 ÷ 18 = 14 remainder 11. Step 2: The quotient 14 means Tane can pack 14 full crates. Step 3: The remainder 11 means 11 apples are left over and cannot fill another crate. Step 4: Check: 18 × 14 = 252, plus 11 leftover = 263 total apples. The answer is 14 R11.

6. Olivia is organizing a book drive. She has 215 books to pack into boxes that hold 9 books each. How many full boxes can she pack, and how many books will be left over? Answer: 23 R8 Solution: Divide 215 by 9. 9 × 23 = 207, which is less than 215. 9 × 24 = 216, which is too many.
   Full step-by-step solution

   Step 1: Divide 215 by 9. 9 × 23 = 207, which is less than 215. 9 × 24 = 216, which is too many. So the quotient is 23. Step 2: Subtract to find the remainder: 215 - 207 = 8. Step 3: This means Olivia can pack 23 full boxes, and 8 books will be left over. Step 4: Check: (9 × 23) + 8 = 207 + 8 = 215. The answer is 23 R8.

7. 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.

8. Charlotte is organizing a book fair at her school. She has 234 books to display on shelves. Each shelf can hold exactly 15 books. How many shelves will Charlotte need to display all of the books? Answer: 16 Solution: Identify the total number of books: 234. Identify how many books fit on one shelf: 15. Divide 234 by 15 to find how many full shelves and any leftover books.
   Full step-by-step solution

   Step 1: Identify the total number of books: 234. Step 2: Identify how many books fit on one shelf: 15. Step 3: Divide 234 by 15 to find how many full shelves and any leftover books. Step 4: 15 × 15 = 225, and 234 - 225 = 9. So 234 ÷ 15 = 15 remainder 9. Step 5: The remainder of 9 means there are 9 books left over that still need a shelf. Step 6: Since every book must be displayed, Charlotte needs one more shelf for the leftover 9 books. Step 7: Total shelves needed = 15 full shelves + 1 extra shelf = 16 shelves. The answer is 16 shelves.

9. Emma is making gift bags for her birthday party. She has 143 pieces of candy to share equally among 8 gift bags. How many pieces of candy will be in each gift bag? Answer: 17 Solution: We need to divide 143 pieces of candy equally among 8 gift bags.
   Full step-by-step solution

   Step 1: We need to divide 143 pieces of candy equally among 8 gift bags. Step 2: Set up the division problem: 143 ÷ 8 Step 3: Calculate 8 × 17 = 136 Step 4: Subtract 143 - 136 = 7 Step 5: Since we're dividing candy equally among bags, we use the quotient (17) as our answer, not the remainder. Step 6: Each gift bag will get 17 pieces of candy, with 7 pieces left over. The answer is 17.