Interpret Remainders

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Answer Key & Explanations

Interpret Remainders · Grade 4 · Worksheet 2

1. A rectangular swimming pool is drawn with a length of 15 meters and a width of 8 meters. A tiled border of equal width is added around the entire pool, making the total length 19 meters and total width 12 meters. What is the width of the tiled border in meters? Answer: 2 Solution: The original pool length is 15 meters and the new total length is 19 meters. The difference in length is 19 - 15 = 4 meters.
   Full step-by-step solution

   Step 1: The original pool length is 15 meters and the new total length is 19 meters. Step 2: The difference in length is 19 - 15 = 4 meters. Step 3: Since the border is on both ends of the length, the border width is half of this difference: 4 ÷ 2 = 2 meters. Step 4: Verify with the width: Original width is 8 meters, new total width is 12 meters. Step 5: The difference in width is 12 - 8 = 4 meters. Step 6: Since the border is on both sides of the width, the border width is half of this difference: 4 ÷ 2 = 2 meters. Step 7: Both calculations give the same result of 2 meters. The width of the tiled border is 2 meters.

2. Emma is making fruit baskets for her class party. She has 132 pieces of fruit to distribute equally among 8 baskets. How many pieces of fruit will be in each basket? Answer: 16 Solution: Emma has 132 pieces of fruit and 8 baskets.
   Full step-by-step solution

   Step 1: Emma has 132 pieces of fruit and 8 baskets. Step 2: Divide 132 by 8 to find how many pieces go in each basket: 132 ÷ 8 Step 3: 8 × 16 = 128 Step 4: 132 - 128 = 4 pieces left over Step 5: Since we're putting equal amounts in each basket, we can only use the 128 pieces that divide evenly Step 6: 128 ÷ 8 = 16 pieces per basket The answer is 16 pieces of fruit in each basket.

3. 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.

4. A factory packages cookies into boxes that hold 24 cookies each. They have 1,350 cookies to package. After filling as many complete boxes as possible, how many cookies will be left over that cannot fill a complete box? Answer: 6 Solution: We need to find how many cookies are left after making complete boxes of 24 cookies each. Divide 1,350 by 24 to find the remainder.
   Full step-by-step solution

   Step 1: We need to find how many cookies are left after making complete boxes of 24 cookies each. Step 2: Divide 1,350 by 24 to find the remainder. Step 3: 24 × 56 = 1,344 (this is the number of cookies in complete boxes) Step 4: 1,350 - 1,344 = 6 cookies left over Step 5: Since 6 cookies is less than 24, they cannot make another complete box. The answer is 6.

5. Noah has 231 baseball cards. He wants to put them into albums that hold 16 cards per page. How many full pages can he fill, and how many cards will be left over? Answer: 14 R7 Solution: Divide 231 by 16. 16 × 14 = 224, which is less than 231. 16 × 15 = 240, which is too large.
   Full step-by-step solution

   Step 1: Divide 231 by 16. 16 × 14 = 224, which is less than 231. 16 × 15 = 240, which is too large. So the quotient is 14. Step 2: Subtract to find the remainder: 231 - 224 = 7. Step 3: This means Noah can fill 14 full pages, and 7 cards will be left over. Check: (16 × 14) + 7 = 224 + 7 = 231. The answer is 14 R7.

6. Isabella is packing 247 books into boxes that hold 18 books each. How many full boxes can she pack, and how many books will be left over? Answer: 13 R13 Solution: Divide 247 by 18. 18 × 13 = 234, which is less than 247. 18 × 14 = 252, which is too big.
   Full step-by-step solution

   Step 1: Divide 247 by 18. 18 × 13 = 234, which is less than 247. 18 × 14 = 252, which is too big. So the quotient is 13. Step 2: Multiply to find how many books are in full boxes: 18 × 13 = 234 books. Step 3: Subtract to find the remainder: 247 − 234 = 13 books left over. Step 4: This means Isabella can pack 13 full boxes, and 13 books will be left unpacked. Step 5: Check: (18 × 13) + 13 = 234 + 13 = 247. The answer is 13 R13.

7. 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.