Q1: What is the first step in solving 156 ÷ 12 using partial quotients? (a) Subtract 12 from 156 repeatedly (b) Estimate how many groups of 12 fit into 156 (c) Multiply 12 by 10 (d) Divide 156 by 2
Solution:
Ans: (b) Explanation: In the partial quotients method, we start by estimating how many groups of the divisor fit into the dividend. This helps us subtract convenient multiples rather than subtracting one at a time.
Q2: Using partial quotients, if you subtract 10 groups of 8 from 240, what is left? (a) 80 (b) 160 (c) 240 (d) 0
Solution:
Ans: (b) Explanation: 10 groups of 8 equals \(10 \times 8 = 80\). Subtracting from 240: \(240 - 80 = 160\). We still have 160 remaining to continue dividing.
Q3: When dividing 345 ÷ 15 using partial quotients, you subtract 10 groups of 15, then 10 more groups of 15. How many more groups of 15 can you subtract? (a) 3 (b) 5 (c) 10 (d) 20
Solution:
Ans: (b) Explanation: First: \(10 \times 15 = 150\), so \(345 - 150 = 195\). Second: \(10 \times 15 = 150\), so \(195 - 150 = 45\). Now: \(45 \div 15 = 3\) groups, but the question asks how many more groups can be subtracted from 45, which is 3 groups. Wait, let me recalculate: We have 45 left, and \(45 \div 15 = 3\). Actually, after 20 groups (10+10), we have 45 left, which is exactly 3 more groups of 15, but option (b) is 5. Let me reconsider the problem setup. Actually: After subtracting 20 groups total, we removed \(20 \times 15 = 300\) from 345, leaving \(345 - 300 = 45\). Then \(45 \div 15 = 3\) more groups. But option (a) is 3, not (b). There's an error in my answer key. Let me correct this.
Q3: When dividing 345 ÷ 15 using partial quotients, you subtract 10 groups of 15, then 10 more groups of 15. How many more groups of 15 can you subtract? (a) 3 (b) 5 (c) 10 (d) 1
Solution:
Ans: (a) Explanation: First: \(10 \times 15 = 150\), so \(345 - 150 = 195\). Second: \(10 \times 15 = 150\), so \(195 - 150 = 45\). Now: \(45 \div 15 = 3\) groups. After subtracting 20 groups total, we have 45 remaining, which equals exactly 3 more groups of 15.
Q4: What is 168 ÷ 14 using partial quotients? (a) 10 (b) 11 (c) 12 (d) 13
Q5: In the division problem 432 ÷ 18, if you use 20 as your first partial quotient, what would you subtract from 432? (a) 180 (b) 360 (c) 400 (d) 20
Solution:
Ans: (b) Explanation: A partial quotient of 20 means we take 20 groups of 18. Calculate: \(20 \times 18 = 360\). We subtract 360 from 432.
Q6: When solving 525 ÷ 25 using partial quotients, which multiplication fact is most helpful? (a) 10 × 25 = 250 (b) 5 × 25 = 125 (c) 2 × 25 = 50 (d) 1 × 25 = 25
Solution:
Ans: (a) Explanation: The most helpful fact is \(10 \times 25 = 250\) because we can use it twice: \(250 + 250 = 500\), leaving only 25. This uses larger chunks and makes division faster with fewer steps.
Q7: What is the remainder when 275 is divided by 13 using partial quotients? (a) 0 (b) 2 (c) 3 (d) 1
Solution:
Ans: (b) Explanation: Using partial quotients: \(20 \times 13 = 260\), so \(275 - 260 = 15\) \(1 \times 13 = 13\), so \(15 - 13 = 2\) The remainder is 2, and the quotient is 21.
Q8: Which statement about partial quotients is true? (a) You must always subtract groups of 10 first (b) You can subtract any convenient multiple of the divisor (c) The method only works for even numbers (d) You cannot have a remainder with this method
Solution:
Ans: (b) Explanation: The partial quotients method is flexible. You can subtract any convenient multiple of the divisor (like 5 groups, 10 groups, or even 1 group). This makes the method adaptable to different problems and student comfort levels.
Section B: Fill in the Blanks
Q9: In partial quotients division, we subtract __________ of the divisor from the dividend until we reach zero or a remainder.
Solution:
Ans: multiples Explanation: The partial quotients method works by subtracting multiples (or groups) of the divisor repeatedly. These multiples can be convenient numbers like 10, 5, or any number that makes calculation easier.
Q10: When dividing 396 by 12 using partial quotients, if you subtract 30 groups of 12, you have subtracted __________ from 396.
Solution:
Ans: 360 Explanation: Calculate \(30 \times 12 = 360\). When using 30 as a partial quotient, we subtract 360 from the dividend 396, leaving 36 remaining.
Q11: The answer to a division problem is called the __________.
Solution:
Ans: quotient Explanation: In division, the result or answer is called the quotient. In partial quotients method, we add up all the partial quotients to find the final quotient.
Q12: To find 644 ÷ 23 using partial quotients, a good first step is to subtract __________ groups of 23, which equals 230.
Solution:
Ans: 10 Explanation: Since \(10 \times 23 = 230\), subtracting 10 groups is a convenient first step. This is a friendly multiple that's easy to calculate and leaves 414 remaining from 644.
Q13: In the problem 567 ÷ 21, after subtracting 20 groups of 21 (which is 420), you have __________ left.
Solution:
Ans: 147 Explanation: Calculate: \(20 \times 21 = 420\). Then subtract: \(567 - 420 = 147\). After this partial quotient of 20, we have 147 remaining to continue dividing.
Q14: The partial quotients method is also called the __________ method because we subtract chunks at a time.
Solution:
Ans: chunking Explanation: The partial quotients method is often called the chunking method because we subtract large "chunks" or multiples of the divisor rather than dividing all at once.
Section C: Word Problems
Q15: A bakery has 336 cookies to pack into boxes. Each box holds 16 cookies. Using partial quotients, how many boxes can the bakery fill?
Solution:
Ans: Step-by-step solution: We need to divide 336 ÷ 16 using partial quotients. First partial quotient: \(10 \times 16 = 160\) \(336 - 160 = 176\) Second partial quotient: \(10 \times 16 = 160\) \(176 - 160 = 16\) Third partial quotient: \(1 \times 16 = 16\) \(16 - 16 = 0\) Total quotient: \(10 + 10 + 1 = 21\) Final Answer: 21 boxes
Q16: A school has 468 students going on a field trip. Each bus can hold 26 students. Using the partial quotients method, how many buses are needed? Will there be any students left over?
Solution:
Ans: Step-by-step solution: We need to divide 468 ÷ 26 using partial quotients. First partial quotient: \(10 \times 26 = 260\) \(468 - 260 = 208\) Second partial quotient: \(5 \times 26 = 130\) \(208 - 130 = 78\) Third partial quotient: \(3 \times 26 = 78\) \(78 - 78 = 0\) Total quotient: \(10 + 5 + 3 = 18\) Remainder: 0 Final Answer: 18 buses are needed with no students left over
Q17: A farmer collected 735 eggs and wants to pack them in cartons of 15 eggs each. Use partial quotients to find how many cartons the farmer can fill completely.
Q18: A toy store has 504 action figures to display equally on 24 shelves. Using partial quotients, how many action figures will be on each shelf?
Solution:
Ans: Step-by-step solution: We need to divide 504 ÷ 24 using partial quotients. First partial quotient: \(10 \times 24 = 240\) \(504 - 240 = 264\) Second partial quotient: \(10 \times 24 = 240\) \(264 - 240 = 24\) Third partial quotient: \(1 \times 24 = 24\) \(24 - 24 = 0\) Total quotient: \(10 + 10 + 1 = 21\) Final Answer: 21 action figures per shelf
Q19: A library has 858 books to arrange on shelves. Each shelf can hold 33 books. Use the partial quotients method to find how many shelves will be completely filled and how many books will be left over.
Solution:
Ans: Step-by-step solution: We need to divide 858 ÷ 33 using partial quotients. First partial quotient: \(10 \times 33 = 330\) \(858 - 330 = 528\) Second partial quotient: \(10 \times 33 = 330\) \(528 - 330 = 198\) Third partial quotient: \(5 \times 33 = 165\) \(198 - 165 = 33\) Fourth partial quotient: \(1 \times 33 = 33\) \(33 - 33 = 0\) Total quotient: \(10 + 10 + 5 + 1 = 26\) Remainder: 0 Final Answer: 26 shelves will be completely filled with 0 books left over
Q20: A sports team is selling 672 raffle tickets. If each team member sells 32 tickets, how many team members are there? Solve using partial quotients.
Solution:
Ans: Step-by-step solution: We need to divide 672 ÷ 32 using partial quotients. First partial quotient: \(10 \times 32 = 320\) \(672 - 320 = 352\) Second partial quotient: \(10 \times 32 = 320\) \(352 - 320 = 32\) Third partial quotient: \(1 \times 32 = 32\) \(32 - 32 = 0\) Total quotient: \(10 + 10 + 1 = 21\) Final Answer: 21 team members
The document Worksheet (with Solutions): Multi-Digit Division With Partial Quotients is a part of the Grade 4 Course Math Grade 4.
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