Divide Multi-Digit Numbers - 4th Grade Math

A rectangle has area 936 square units and width 8 units. What is the length?
Answer: 117 This question tests 4th grade ability to find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, properties of operations, and/or the relationship between multiplication and division (CCSS.4.NBT.6). Division separates a total into equal groups—you can think of it as sharing (divide total among groups to find size of each) or grouping (divide total into groups of certain size to find how many groups). The standard algorithm divides place by place from left to right: divide, multiply, subtract, bring down next digit, repeat. When a number doesn't divide evenly, there is a remainder (the amount left over), which must always be less than the divisor. To find the length given area 936 and width 8, students use the relationship to multiplication: 8 times what equals 936?, finding quotient 117 with no remainder. Choice B is correct because using multiplication: 8 × 117 = 936, which demonstrates understanding of division process and place value. Choice A represents a basic division fact error, which happens when students make an error in one division step. To help students: Connect to multiplication: 936 ÷ 8 asks 'what times 8 equals 936?' Use place value: 936 ÷ 8 = (800 ÷ 8) + (136 ÷ 8) = 100 + 17 = 117. Check answers with multiplication: quotient × divisor + remainder should equal dividend (117 × 8 + 0 = 936 ✓), and emphasize remainder must be less than divisor.
There are $672$ tickets. If $6$ tickets are in each pack, how many packs can be made?
Answer: 112 Choice B is correct because 672 divided by 6 equals 112 packs. Choice A is incorrect because it is too small to match the division. Choice C is incorrect because it does not equal 672 divided by 6. Choice D is incorrect because it is close to the correct answer but not the actual quotient.
Keisha divides $457$ stickers equally among $3$ friends. What are the quotient and remainder?
Answer: 152 R1 152 R1 is correct because $457 \div 3 = 152$ with a remainder of $1$ . 152 R2 is incorrect because it has the wrong remainder. 153 R0 is incorrect because it rounds the quotient up instead of down. 151 R4 is incorrect because it rounds the quotient down too far and leaves too large a remainder.
Maria solves $4,596 \div 8$ by breaking it into easier parts: $(4,000 \div 8) + (596 \div 8)$ . She calculates $4,000 \div 8 = 500$ correctly. What should she get when she calculates $596 \div 8$ ?
Answer: 74 with remainder 4 596 ÷ 8 = 74 with a remainder of 4, since 8 × 74 = 592 and 596 − 592 = 4. Choice B rounds the quotient up by one, which doesn't match the actual division. Choice C keeps the correct quotient but drops the remainder. Choice D pairs an incorrect quotient with a remainder of 0.
Find the quotient: $936 \div 4$
Answer: 234 Dividing 936 by 4 gives 234. Choice B reflects a small error in the tens place during division. Choice C is missing a digit, as if a place value were dropped. Choice D reflects a minor error in carrying during the division process.
What is $3,276 \div 9$ ?
Answer: 364 This question tests 4th grade ability to find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, properties of operations, and/or the relationship between multiplication and division (CCSS.4.NBT.6). Division separates a total into equal groups—you can think of it as sharing (divide total among groups to find size of each) or grouping (divide total into groups of certain size to find how many groups). The standard algorithm divides place by place from left to right: divide, multiply, subtract, bring down next digit, repeat. When a number doesn't divide evenly, there is a remainder (the amount left over), which must always be less than the divisor. To divide 3,276 ÷ 9, students use place value to break into parts and divide each, finding quotient 364. Choice A is correct because using the standard algorithm gives quotient 364 with no remainder, and checking with multiplication confirms: 9 × 364 = 3,276. Choice C represents stopping too early or a place value error, which happens when students forget to divide all places. To help students: Use standard algorithm steps: (1) Divide—how many times does divisor go into current dividend? (2) Multiply—quotient digit times divisor, (3) Subtract—from current dividend, (4) Bring down next digit, (5) Repeat. Connect to multiplication: what times 9 equals 3,276? Check answers with multiplication. Use place value: 3,276 ÷ 9 = (2,700 ÷ 9) + (540 ÷ 9) + (36 ÷ 9) = 300 + 60 + 4 = 364. Watch for forgetting to bring down digits or weak facts.
What is $864 \div 6$ ?
Answer: 144 Choice D is correct because 864 divided by 6 equals 144. Choice A is incorrect because it is far too small for this division. Choice B is incorrect because it does not match the actual quotient. Choice C is incorrect because it is close to the correct answer but not the actual result of dividing 864 by 6.
Divide $2,345$ by $7$ . What is the quotient and remainder?
Answer: 335 R5 This question tests 4th grade ability to find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, properties of operations, and/or the relationship between multiplication and division (CCSS.4.NBT.6). Division separates a total into equal groups—you can think of it as sharing (divide total among groups to find size of each) or grouping (divide total into groups of certain size to find how many groups). The standard algorithm divides place by place from left to right: divide, multiply, subtract, bring down next digit, repeat. When a number doesn't divide evenly, there is a remainder (the amount left over), which must always be less than the divisor. To divide 2,345 ÷ 7, students use the standard algorithm: divide each place starting from left, finding quotient and remainder if applicable. Choice A is correct because using the standard algorithm, 7 goes into 23 three times (7×3=21, subtract to get 2), bring down 4 to make 24, 7 goes into 24 three times (7×3=21, subtract to get 3), bring down 5 to make 35, 7 goes into 35 five times (7×5=35, subtract to get 0), giving quotient 335 with remainder 0; checking with multiplication confirms 7×335=2,345. Choice B represents forgetting to bring down a digit or a remainder ≥ divisor (invalid), which happens when students don't divide enough times (remainder should be less than divisor). To help students: Use standard algorithm steps: (1) Divide—how many times does divisor go into current dividend? (2) Multiply—quotient digit times divisor, (3) Subtract—from current dividend, (4) Bring down next digit, (5) Repeat. Emphasize remainder must be LESS than divisor—if remainder equals or exceeds divisor, divide one more time, and check with multiplication: quotient × divisor + remainder = dividend.
Maya has 672 stickers to share equally among 7 friends. How many stickers does each friend get?
Answer: 96 This question tests 4th grade ability to find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, properties of operations, and/or the relationship between multiplication and division (CCSS.4.NBT.6). Division separates a total into equal groups—you can think of it as sharing (divide total among groups to find size of each) or grouping (divide total into groups of certain size to find how many groups). The standard algorithm divides place by place from left to right: divide, multiply, subtract, bring down next digit, repeat. When a number doesn't divide evenly, there is a remainder (the amount left over), which must always be less than the divisor. To divide $672 \div 7$ , students use place value to break into parts and divide each, finding quotient 96 with no remainder in this sharing context. Choice B is correct because using multiplication: $7 \times 96 = 672$ , which demonstrates understanding of division process and place value. Choice A represents forgetting to bring down a digit, which happens when students skip part of the algorithm. To help students: Use standard algorithm steps: (1) Divide—how many times does divisor go into current dividend? (2) Multiply—quotient digit times divisor, (3) Subtract—from current dividend, (4) Bring down next digit, (5) Repeat. For word problems with remainders, consider context—do you need another group (round up) or ignore leftovers (round down)? Check answers with multiplication: quotient × divisor + remainder should equal dividend ( $96 \times 7 + 0 = 672$ ✓).
If $7 \times \ ? = 1,176$ , what number goes in the blank?
Answer: 168 The correct answer is D, 168, because $7 \times 168 = 1{,}176$ . Choice A, 158, and Choice C, 148, are close but come from small multiplication slips in the tens digit. Choice B, 178, overshoots the product when multiplied by 7. Checking with division, $1{,}176 \div 7 = 168$ confirms the answer.
A rectangle has area $456$ square units and width $3$ units. What is the length?
Answer: 152 units Since area equals length times width, dividing the area of 456 square units by the width of 3 units gives a length of 152 units, making Choice D correct. Choice A, 15 units, could come from misplacing a decimal, as if 456 were divided by 30 instead of 3. Choice B, 153 units, is off by one from a small slip in the division. Choice C, 162 units, could result from a miscalculation that lands on a nearby but incorrect value.
What is $3,248 \div 4$ ?
Answer: 812 Dividing 3,248 by 4 gives 812 with no remainder, so Choice B is correct. Choice A, 821, has the last two digits swapped from the correct answer. Choice C, 82, is missing a digit, as if a placeholder step in the division were skipped. Choice D, 812 R4, adds a remainder that does not exist since 4 divides evenly into 3,248. Dividing carefully place by place confirms that 3,248 divided by 4 comes out to exactly 812.
Find the quotient: $936 \div 8$
Answer: 117 Dividing 936 by 8 gives 117, since 8 x 117 = 936. Choice A is far too small to be the correct quotient. Choice B is ten times too large, as if a decimal place were misplaced. Choice D reflects a small error in the division process.
Find the quotient: 504 ÷ 7
Answer: 72 Dividing 504 by 7 gives exactly 72, with no remainder. Choice D (71 R7) comes from stopping the division one step early and treating the leftover as a remainder. Choices B (70) and A (82) come from small errors in estimating the quotient's tens digit.
Find the quotient: $1,509 \div 5$ .
Answer: 301 R4 The correct answer is D, 301 R4, because $5 \times 301 = 1{,}505$ , and $1{,}509 - 1{,}505 = 4$ . Choice A has a remainder of 9, which is too large since 9 is bigger than the divisor 5. Choice B leaves out the remainder entirely. Choice C rounds the quotient up but leaves no remainder, which does not match the division.
A bakery packages 2,547 cookies into boxes that hold 8 cookies each. The baker needs to know how many full boxes can be made and how many cookies will be left over. Which equation correctly shows this division?
Answer: $2,547 ÷ 8 = 318 \text{ R } 3$ $2,547 ÷ 8 = 318 \text{ R } 3$ because $318 × 8 = 2,544$ and $2,547 - 2,544 = 3$ . Choice B has an incorrect quotient (308 instead of 318). Choice C has an impossible remainder (11 is greater than the divisor 8). Choice D has an incorrect quotient that's too large.
Roberto divides 6,147 by 3 and gets a quotient of 2,049. When he checks his work using multiplication, he finds that $2,049 × 3 = 6,147$ . What can Roberto conclude about his division?
Answer: His division is correct with quotient 2,049 and remainder 0 Since $2,049 × 3 = 6,147$ exactly matches the dividend, Roberto's division is completely correct with quotient 2,049 and remainder 0. Choice B incorrectly suggests a remainder when none exists. Choice C is redundant since remainder 0 is typically not written. Choice D provides an incorrect quotient.
Carlos puts $639$ marbles into bags of $5$ . How many full bags can he make, and how many marbles are left over?
Answer: 127 complete bags and 4 marbles left over The correct answer is B because $5 \times 127 = 635$ , and $639 - 635 = 4$ , so Carlos makes 127 complete bags with 4 marbles left over. Choice A is off by one bag. Choice C has the right number of bags but the wrong number of marbles left over. Choice D overshoots the number of bags entirely; $5 \times 129 = 645$ , which is more marbles than Carlos has.
Carlos has 945 beads. He puts them into groups of 9. How many groups can he make?
Answer: 105 This question tests 4th grade ability to find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, properties of operations, and/or the relationship between multiplication and division (CCSS.4.NBT.6). Division separates a total into equal groups—you can think of it as sharing (divide total among groups to find size of each) or grouping (divide total into groups of certain size to find how many groups). The standard algorithm divides place by place from left to right: divide, multiply, subtract, bring down next digit, repeat. When a number doesn't divide evenly, there is a remainder (the amount left over), which must always be less than the divisor. To divide $945 \div 9$ into groups of 9, students use place value to break into parts and divide each, finding quotient 105 with no remainder. Choice B is correct because using multiplication: $9 \times 105 = 945$ , which demonstrates understanding of division process and place value. Choice A represents a basic division fact error, which happens when students make an error in one division step. To help students: Use standard algorithm steps: (1) Divide—how many times does divisor go into current dividend? (2) Multiply—quotient digit times divisor, (3) Subtract—from current dividend, (4) Bring down next digit, (5) Repeat. For word problems with remainders, consider context—do you need another group (round up) or ignore leftovers (round down)? Check answers with multiplication: quotient × divisor + remainder should equal dividend ( $105 \times 9 + 0 = 945$ ✓).
Tyler is using rectangular arrays to solve 1,845 divided by 5. He arranges the objects into 5 equal rows. How many objects are in each row, including any objects left over?
Answer: 369 objects per row with no objects remaining Dividing 1,845 by 5 gives exactly 369, with no remainder, since 5 x 369 = 1,845. Choice C (369 objects with 5 remaining) pairs the correct quotient with an impossible remainder equal to the divisor. Choices B (368 with 5 remaining) and D (368 with 1 remaining) both use the wrong quotient.

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