Q1: When 17 is divided by 5, what is the remainder? (a) 2 (b) 3 (c) 4 (d) 5
Solution:
Ans: (a) Explanation: When we divide 17 by 5, we get \(17 \div 5 = 3\) R 2. This is because \(5 \times 3 = 15\), and \(17 - 15 = 2\). The remainder is 2.
Q2: Sarah has 23 cookies and wants to pack them equally into boxes of 4. How many cookies will be left over? (a) 1 (b) 2 (c) 3 (d) 4
Solution:
Ans: (c) Explanation: \(23 \div 4 = 5\) R 3. Sarah can fill 5 boxes completely using \(5 \times 4 = 20\) cookies. The number of cookies left over is \(23 - 20 = 3\). The remainder is 3.
Q3: Which division problem has a remainder of 0? (a) \(29 \div 6\) (b) \(35 \div 7\) (c) \(41 \div 8\) (d) \(19 \div 3\)
Solution:
Ans: (b) Explanation: When a number divides evenly with no leftover, the remainder is 0. \(35 \div 7 = 5\) with no remainder because \(7 \times 5 = 35\) exactly. The other options: (a) gives R 5, (c) gives R 1, and (d) gives R 1.
Q4: What is the largest possible remainder when dividing by 6? (a) 4 (b) 5 (c) 6 (d) 7
Solution:
Ans: (b) Explanation: The largest possible remainder when dividing by any number is always one less than the divisor. When dividing by 6, the largest remainder can be 5. The remainder must always be less than the divisor.
Q5: If \(46 \div 9 = 5\) R \(n\), what is the value of \(n\)? (a) 0 (b) 1 (c) 2 (d) 3
Solution:
Ans: (b) Explanation: To find the remainder, we calculate: \(9 \times 5 = 45\), then \(46 - 45 = 1\). The remainder \(n = 1\).
Q6: Tom has 50 pencils to share equally among 8 students. How many pencils will each student get, and how many will be left over? (a) 6 pencils each, 2 left over (b) 5 pencils each, 10 left over (c) 6 pencils each, 1 left over (d) 7 pencils each, 6 left over
Solution:
Ans: (a) Explanation: \(50 \div 8 = 6\) R 2. Each student gets 6 pencils because \(8 \times 6 = 48\). The number left over is \(50 - 48 = 2\). The quotient is 6 and the remainder is 2.
Q7: Which statement about remainders is always true? (a) The remainder is always larger than the divisor (b) The remainder is always smaller than the divisor (c) The remainder is always equal to the divisor (d) The remainder can be any number
Solution:
Ans: (b) Explanation: The remainder must always be smaller than the divisor. If the remainder were equal to or larger than the divisor, you could divide at least one more time. This is a fundamental rule of division with remainders.
Q8: What is \(72 \div 8\)? (a) 8 R 8 (b) 9 R 0 (c) 8 R 0 (d) 7 R 16
Solution:
Ans: (b) Explanation: \(72 \div 8 = 9\) with no remainder because \(8 \times 9 = 72\) exactly. The quotient is 9 and the remainder is 0.
Section B: Fill in the Blanks
Q9:When you divide a number and there is an amount left over that cannot be divided evenly, that amount is called the __________.
Solution:
Ans: remainder Explanation: The remainder is the amount left over after division when the dividend cannot be divided evenly by the divisor.
Q10:In the division problem \(37 \div 4 = 9\) R 1, the number 9 is called the __________ and 1 is the remainder.
Solution:
Ans: quotient Explanation: The quotient is the answer to a division problem, representing how many times the divisor fits into the dividend.
Q11:The remainder when dividing 25 by 3 is __________.
Solution:
Ans: 1 Explanation: \(25 \div 3 = 8\) R 1 because \(3 \times 8 = 24\), and \(25 - 24 = 1\). The remainder is 1.
Q12:If you divide 42 by 7, the remainder is __________ because 42 is evenly divisible by 7.
Solution:
Ans: 0 Explanation: When a number is evenly divisible, there is no remainder. \(42 \div 7 = 6\) with a remainder of 0.
Q13:When dividing by 9, the possible remainders are 0, 1, 2, 3, 4, 5, 6, 7, and __________.
Solution:
Ans: 8 Explanation: The possible remainders when dividing by 9 are all whole numbers from 0 to 8. The largest possible remainder is always one less than the divisor.
Q14:In the expression \(53 = (7 \times 7) + n\), the value of \(n\) is the remainder, which equals __________.
Solution:
Ans: 4 Explanation: \(7 \times 7 = 49\), so \(53 - 49 = 4\). This shows that \(53 \div 7 = 7\) R 4. The remainder \(n = 4\).
Section C: Word Problems
Q15:A baker has 67 cupcakes. She wants to pack them into boxes that hold 8 cupcakes each. How many full boxes can she make, and how many cupcakes will be left over?
Solution:
Ans: \(67 \div 8 = 8\) R 3 \(8 \times 8 = 64\) \(67 - 64 = 3\) Final Answer: The baker can make 8 full boxes with 3 cupcakes left over.
Q16:A teacher has 85 stickers to distribute equally among 9 students. How many stickers will each student receive, and how many stickers will the teacher have remaining?
Solution:
Ans: \(85 \div 9 = 9\) R 4 \(9 \times 9 = 81\) \(85 - 81 = 4\) Final Answer: Each student will receive 9 stickers, and the teacher will have 4 stickers remaining.
Q17:A rope is 58 feet long. If you cut it into pieces that are each 6 feet long, how many pieces will you have, and how much rope will be left over?
Solution:
Ans: \(58 \div 6 = 9\) R 4 \(6 \times 9 = 54\) \(58 - 54 = 4\) Final Answer: You will have 9 pieces of rope with 4 feet left over.
Q18:Marcus is arranging 74 books on shelves. Each shelf can hold 10 books. How many shelves will be completely filled, and how many books will be on the partially filled shelf?
Solution:
Ans: \(74 \div 10 = 7\) R 4 \(10 \times 7 = 70\) \(74 - 70 = 4\) Final Answer: 7 shelves will be completely filled, and 4 books will be on the partially filled shelf.
Q19:A group of 95 children are going on a field trip. Each van can hold 12 children. How many vans are needed to transport all the children?
Solution:
Ans: \(95 \div 12 = 7\) R 11 \(12 \times 7 = 84\) \(95 - 84 = 11\) Since there are 11 children remaining, we need one more van. \(7 + 1 = 8\) Final Answer: 8 vans are needed to transport all the children.
Q20:A farmer collected 131 eggs. He wants to pack them into cartons that hold 12 eggs each. After filling as many cartons as possible, how many eggs will not fit into a complete carton?
Solution:
Ans: \(131 \div 12 = 10\) R 11 \(12 \times 10 = 120\) \(131 - 120 = 11\) Final Answer: 11 eggs will not fit into a complete carton.
The document Worksheet (with Solutions): Remainders is a part of the Grade 4 Course Math Grade 4.
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