Elementary School Math Quiz: Understand Division As Missing Factor
20 questions · exam conditions
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Understand Division As Missing FactorQuestion 1 of 20

Solve 24÷624 \div 6 using a missing factor: 6× ?=246 \times \ ? = 24.

18
3
6
4
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Elementary School Math Quiz

Elementary School Math Quiz: Understand Division As Missing Factor

Practice Understand Division As Missing Factor in Elementary School Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Understand Division As Missing Factor, giving you a quick way to practice the rules, question types, and explanations that matter most for Elementary School Math.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

Solve 24÷624 \div 6 using a missing factor: 6× ?=246 \times \ ? = 24.

  1. 18
  2. 3
  3. 6
  4. 4 (correct answer)
Explanation: Since 6×4=246 \times 4 = 24, the missing factor is 4, so 24÷6=424 \div 6 = 4. Choice A (18) comes from subtracting 6 from 24 instead of finding the missing factor. Choice B (3) is off by one from the correct answer. Choice C (6) repeats the known factor instead of solving for the missing one.

Question 2

What is 42÷642\div 6?

  1. 8
  2. 6
  3. 36
  4. 7 (correct answer)
Explanation: 42 divided by 6 equals 7, so D is correct. Choice A (8) is one more than the correct quotient. Choice B (6) repeats a number from the problem instead of solving for the quotient. Choice C (36) subtracts 6 from 42 instead of dividing.

Question 3

What is 56÷856\div 8? Think: what times 8 equals 56?

  1. 7 (correct answer)
  2. 64
  3. 8
  4. 5
Explanation: The correct answer is A) 7, since 7x8=56. Choice B (64) is the result of 8x8, not 56 divided by 8. Choice C (8) confuses the divisor with the quotient. Choice D (5) is too small; 5x8=40, not 56.

Question 4

Use the fact family with 6, 7, and 42 to find 42÷642 \div 6.

  1. 8
  2. 7 (correct answer)
  3. 6
  4. 36
Explanation: Since 6 times 7 equals 42, dividing 42 by 6 gives 7. Choice A, 8, is not part of this fact family. Choice C, 6, is the divisor itself, not the quotient. Choice D, 36, comes from subtracting 6 from 42 instead of dividing.

Question 5

Use fact family: 7×5=357\times 5=35 to find 35÷735\div 7.

  1. 12
  2. 5 (correct answer)
  3. 28
  4. 7
Explanation: Since 7 times 5 equals 35, dividing 35 by 7 gives 5. Choice A, 12, is not part of this fact family. Choice C, 28, comes from subtracting 7 from 35 instead of dividing. Choice D, 7, is the divisor itself, not the quotient.

Question 6

Carlos wants to find 56÷756 \div 7. He thinks: "What number times 7 gives me 56?" Which equation shows his thinking?

  1. 7×?=567 \times ? = 56 (correct answer)
  2. 56×7=?56 \times 7 = ?
  3. 56−7=?56 - 7 = ?
  4. 7+?=567 + ? = 56
Explanation: Carlos is using division as a missing factor problem. 56÷756 \div 7 means "what times 7 equals 56?" which is 7×?=567 \times ? = 56. Choice B multiplies instead of finding a missing factor, choice C subtracts, and choice D uses addition instead of multiplication.

Question 7

Ben solves 84÷1284 \div 12 by thinking "12 times what number equals 84?" After finding the answer, he wants to solve another division problem using the same three numbers. Which division problem could he solve?

  1. 96÷12=896 \div 12 = 8
  2. 84÷7=1284 \div 7 = 12 (correct answer)
  3. 84+12=9684 + 12 = 96
  4. 12×7=8412 \times 7 = 84
Explanation: Since 12 times 7 equals 84, the related division fact using the same three numbers is 84 divided by 7 equals 12, so B is correct. Choice A introduces a new number, 96, that is not part of the original three numbers. Choice C is an addition problem, not division. Choice D is a multiplication problem, not division.

Question 8

Sarah arranges 36 books into equal rows with 9 books in each row. She writes the equation 9×n=369 \times n = 36 to find the number of rows. What does nn represent in her equation?

  1. The number of rows of books she made (correct answer)
  2. The total number of books she started with
  3. The number of books in each row
  4. The number of books left over after making rows
Explanation: In the equation 9×n=369 \times n = 36, the 9 represents books per row, 36 is the total books, so nn must be the number of rows. Choice B is 36, choice C is 9, and choice D would be remainder in division with a remainder.

Question 9

Solve 63÷963\div 9 using the missing factor: 9×?=639\times ?=63.

  1. 7 (correct answer)
  2. 9
  3. 8
  4. 72
Explanation: Since 9 times 7 equals 63, dividing 63 by 9 gives 7. Choice B, 9, is the divisor itself, not the missing factor. Choice C, 8, is close to the answer but does not make the equation true. Choice D, 72, comes from multiplying 9 by 8 instead of finding the correct missing factor.

Question 10

Alex knows that 72÷8=972 \div 8 = 9. He wants to check his answer by writing a multiplication equation. Which equation should he write to verify his division is correct?

  1. 9×7=639 \times 7 = 63
  2. 72×8=57672 \times 8 = 576
  3. 8×9=728 \times 9 = 72 (correct answer)
  4. 8+9=178 + 9 = 17
Explanation: When you solve a division problem, you can always check your work using multiplication because division and multiplication are opposite operations. Think of division as asking "what number times the divisor gives me the dividend?" In Alex's problem, 72÷8=972 \div 8 = 9 means "72 divided by 8 equals 9." To verify this is correct, you need to check if 8 times 9 really does equal 72. If it does, then your division is right! Choice C gives us 8×9=728 \times 9 = 72, which is exactly what we need. When we multiply the divisor (8) by the quotient (9), we get back to our original dividend (72). This confirms that 72÷8=972 \div 8 = 9 is correct. Let's see why the other choices don't work. Choice A shows 9×7=639 \times 7 = 63, but this uses 7 instead of 8 and gives us 63 instead of our original number 72. Choice B gives us 72×8=57672 \times 8 = 576, which multiplies our dividend by the divisor instead of multiplying the divisor by the quotient - this creates a much larger number that doesn't help us check our work. Choice D shows 8+9=178 + 9 = 17, but addition won't help us verify division since these operations aren't related. Remember this checking strategy: to verify any division problem, multiply the divisor by the quotient. If you get back to your original dividend, your division is correct!

Question 11

What is 72÷972 \div 9?

  1. 81
  2. 7
  3. 9
  4. 8 (correct answer)
Explanation: 8 is correct because 9×8=729 \times 8 = 72, so 72÷9=872 \div 9 = 8. 81 is incorrect; it's the product of 9×99 \times 9, not related to dividing 72 by 9. 7 is incorrect because 9×7=639 \times 7 = 63, not 72. 9 is incorrect; it's the divisor itself, not the quotient.

Question 12

What is 35÷735 \div 7?

  1. 4
  2. 5 (correct answer)
  3. 42
  4. 7
Explanation: 5 is correct because 7 times 5 equals 35, so 35 divided by 7 is 5. 4 is incorrect because 7 times 4 equals 28, not 35. 42 is incorrect because 7 times 6 equals 42, not 35. 7 is incorrect because it repeats the divisor instead of the quotient.

Question 13

Emma has 42 stickers arranged into 6 equal groups. How many stickers are in each group?

  1. 8
  2. 6
  3. 36
  4. 7 (correct answer)
Explanation: 7 is correct because 42÷6=742 \div 6 = 7. 8 is incorrect; it doesn't match dividing 42 by 6. 6 is incorrect because it's the number of groups, not the number in each group. 36 is incorrect; it doesn't correspond to this division.

Question 14

What is 32÷832 \div 8?

  1. 5
  2. 4 (correct answer)
  3. 24
  4. 8
Explanation: 4 is correct because 4 times 8 equals 32, so 32 divided by 8 is 4. 5 is incorrect because it does not fit the fact family for 8 and 32. 24 is incorrect because it comes from subtracting instead of dividing. 8 is incorrect because it repeats the divisor instead of giving the quotient.

Question 15

Emma has 4242 stickers in 66 equal groups; solve 6×?=426 \times ?=42.

  1. 7 (correct answer)
  2. 8
  3. 36
  4. 6
Explanation: This question tests understanding division as an unknown-factor problem (CCSS.3.OA.6), specifically recognizing that division can be solved by finding the missing factor in a multiplication equation. Division and multiplication are inverse operations—they undo each other. When you see a division problem like 42÷642 \div 6 (stickers per group), you can think of it as a multiplication question: 'What number times 6 equals 42?' or '6 times what number equals 42?' This is the same as solving the equation ?×6=42? \times 6=42 or 6×?=426 \times ?=42. If you know your multiplication facts, you can use them to divide: Since 7×6=427 \times 6=42, then 42÷6=742 \div 6=7. The missing factor (7) is the quotient. Fact families show this relationship: 7×6=427 \times 6=42, 6×7=426 \times 7=42, 42÷7=642 \div 7=6, 42÷6=742 \div 6=7 are all related. In this problem, we need to find how many stickers per group with 42 stickers in 6 groups, solving 6×?=426 \times ?=42. Using the missing factor approach: We know 6×7=426 \times 7=42 from multiplication facts, so 42÷6=742 \div 6=7. Choice B is correct because 7×6=427 \times 6=42, so 7 is the missing factor that makes 42 when multiplied by 6, which means 42÷6=742 \div 6=7 stickers per group. This demonstrates understanding that division finds the unknown factor in multiplication. Choice C is incorrect because it provides 36, which might come from 6×6=366 \times 6=36 or using a wrong fact. This error occurs when students make calculation errors or confuse the numbers. To help students understand division as missing factor: Explicitly teach the connection—'42÷642 \div 6 means: what times 6 equals 42?' Practice fact families: if 7×6=427 \times 6=42, then 42÷7=642 \div 7=6 (division finds the other factor). Use arrays: '6 rows of how many equals 42 total? 6×?=426 \times ?=42' Model thinking aloud: 'I need to find 56÷756 \div 7. I think: 7 times what equals 56? I know 7×8=567 \times 8=56, so 56÷7=856 \div 7=8.' Have students write both equations (division and missing factor multiplication) side by side. Check division answers by multiplying (if 42÷6=742 \div 6=7, check: does 7×6=427 \times 6=42? Yes!). This reinforces the inverse relationship. Watch for students who can multiply but struggle with division—show them they already know division by knowing multiplication facts.

Question 16

What is 48÷648 \div 6?

  1. 7
  2. 6
  3. 42
  4. 8 (correct answer)
Explanation: Dividing 48 by 6 gives 8, since 6 times 8 equals 48, matching choice D. Choices A and B are close numbers but do not satisfy the division. Choice C comes from multiplying instead of dividing.

Question 17

What is 72÷972 \div 9?

  1. 8 (correct answer)
  2. 7
  3. 9
  4. 63
Explanation: 8 is correct because 9 times 8 equals 72, so 72 divided by 9 is 8. 7 is incorrect because 9 times 7 equals 63, not 72. 9 is incorrect because it repeats the divisor instead of the quotient. 63 is incorrect because it is the product of 9 and 7, not the quotient.

Question 18

What number makes this equation true? 9×?=729 \times ? = 72

  1. 7
  2. 8 (correct answer)
  3. 63
  4. 9
Explanation: 9 x 8 = 72, so the missing number is 8, making Choice B correct. Choice A (7) and Choice D (9) are close numbers that don't satisfy the equation. Choice C (63) comes from multiplying 9 x 7 instead of finding the correct factor.

Question 19

What is 48÷648 \div 6?

  1. 8 (correct answer)
  2. 7
  3. 42
  4. 6
Explanation: 8 is correct because 6 times 8 equals 48, so 48 divided by 6 is 8. 7 is incorrect because 6 times 7 equals 42, not 48. 42 is incorrect because it is the product of 6 and 7, not the quotient of 48 and 6. 6 is incorrect because it repeats the divisor instead of the quotient.

Question 20

What is 24÷624 \div 6?

  1. 18
  2. 4 (correct answer)
  3. 6
  4. 5
Explanation: 4 is correct because 4 times 6 equals 24, so 24 divided by 6 is 4. 18 is incorrect because it does not relate to dividing 24 by 6. 6 is incorrect because it repeats the divisor instead of the quotient. 5 is incorrect because 5 times 6 equals 30, not 24.