Find Unknown in Multiplication Equations - 3rd Grade Math

A teacher arranges $48$ students into $6$ equal groups for a project. How many students are in each group?
Answer: $8$ students Dividing 48 students into 6 equal groups gives 48 divided by 6, which is 8 students per group. Choice B, 6 students, is the number of groups, not the number of students in each group. Choice C, 42 students, comes from subtracting 6 from 48 instead of dividing. Choice D, 288 students, comes from multiplying 48 by 6 instead of dividing.
Which number completes the equation: $20 \div ? = 4$ ?
Answer: 5 5 is correct because 20 divided by 5 equals 4. 6 is incorrect because 20 divided by 6 does not equal 4. 4 is incorrect because it repeats a number already in the equation instead of solving for the unknown. 24 is incorrect because it does not match the given equation.
Find the unknown value: $5 \times \square = 30$ .
Answer: 6 Since 5 times 6 equals 30, the unknown value is 6. Choice A, 5, is the given factor itself, not the unknown. Choice B, 25, comes from multiplying 5 by 5 instead of finding the missing factor. Choice D, 7, is close to the answer but does not make the equation true.
Solve: $56 \div ? = 7$ . What is $?$ ?
Answer: 8 This question tests determining the unknown whole number in multiplication or division equations (CCSS.3.OA.4), specifically finding the missing value that makes an equation true. To find the unknown in an equation, identify what's missing (factor, product, dividend, divisor, or quotient), then use the relationship between multiplication and division. For multiplication: If one factor and the product are known, divide to find the other factor (8×?=48, so ?=48÷8=6). If both factors are known, multiply to find product (8×6=?, so ?=8×6=48). For division: If dividend and divisor are known, divide to find quotient (48÷8=?, so ?=48÷8=6). If dividend and quotient are known, multiply to find divisor (48÷?=6, so ?=48÷6=8). If divisor and quotient are known, multiply to find dividend (?÷8=6, so ?=6×8=48). In this problem, the equation is 56 ÷ ? = 7. The unknown is the divisor. To solve, we need to divide 56 by 7 or multiply 7 by 8. Choice A is correct because checking: 56÷7=8, but wait, no: the equation is 56÷?=7, so ?=56÷7=8, confirming 8 is correct. This value makes the equation true. Choice B is incorrect because this number doesn't make the equation true: 56÷7=8, not 7. This error occurs when students make calculation errors. To help students find unknowns in equations: Teach the inverse relationship (multiplication ↔ division). Use fact families: If 8×6=48, then 48÷8=6, 48÷6=8, and 6×8=48 (all related). Model thinking aloud: "56 divided by what equals 7? I know 7×8=56, so ? is 8." Cover up the unknown with your finger, say the known information, and think what number fits. Practice with manipulatives or arrays (56 objects divided into groups of ?, with 7 groups). Always check by substituting back: Does 56÷8 really equal 7? Yes! Watch for students who add/subtract instead of multiply/divide, or who don't understand the three numbers are related through multiplication and division.
What is the value of $n$ in $9 \times n = 81$ ?
Answer: 9 This question tests determining the unknown whole number in multiplication or division equations (CCSS.3.OA.4), specifically finding the missing value that makes an equation true. To find the unknown in an equation, identify what's missing (factor, product, dividend, divisor, or quotient), then use the relationship between multiplication and division. For multiplication: If one factor and the product are known, divide to find the other factor (8×?=48, so ?=48÷8=6). If both factors are known, multiply to find product (8×6=?, so ?=8×6=48). For division: If dividend and divisor are known, divide to find quotient (48÷8=?, so ?=48÷8=6). If dividend and quotient are known, multiply to find divisor (48÷?=6, so ?=48÷6=8). If divisor and quotient are known, multiply to find dividend (?÷8=6, so ?=6×8=48). In this problem, the equation is 9 × n = 81. The unknown is a factor. To solve, we need to divide 81 by 9. Choice A is correct because 9×9=81, so 9 makes the equation 9×n=81 true. This value makes the equation true. Choice D is incorrect because selecting 81 (the product) instead of solving for the unknown doesn't make the equation true: 9×81=729, not 81. This error occurs when students don't solve for the unknown. To help students find unknowns in equations: Teach the inverse relationship (multiplication ↔ division). Use fact families: If 8×6=48, then 48÷8=6, 48÷6=8, and 6×8=48 (all related). Model thinking aloud: "9 times what number equals 81? I know 9×9=81, so n is 9." Cover up the unknown with your finger, say the known information, and think what number fits. Practice with manipulatives or arrays (9 rows of ? objects = 81 total, count 9 per row). Always check by substituting back: Does 9×9 really equal 81? Yes! Watch for students who add/subtract instead of multiply/divide, or who don't understand the three numbers are related through multiplication and division.
Which number completes the equation: $72 \div ? = 8$ ?
Answer: 9 Since $8\times 9=72$ , the missing number is 9, so Choice D is correct. Choice A (7) confuses this fact with a nearby multiplication fact, such as $8\times 7=56$ . Choice B (10) is close to the correct answer but does not satisfy the equation. Choice C (8) repeats a number already given in the equation instead of solving for the unknown.
Determine the missing number in $? \div 6 = 8$ .
Answer: 48 Since the missing number divided by 6 equals 8, multiplying 6 by 8 gives the missing number, 48. Choice B (6) repeats the divisor instead of solving for the missing number. Choice C (42) is close to the correct answer but not the actual product. Choice D (14) comes from adding 6 and 8 instead of multiplying.
What is the value of $n$ in $9 \times n = 81$ ?
Answer: 9 Since $9 \times n = 81$ , dividing both sides by 9 shows that $n = 9$ . Choice A (8) is off by one from the correct value. Choice B (81) repeats the product instead of solving for $n$ . Choice C (18) comes from doubling the correct answer instead of dividing correctly.
What number makes the equation true: $8 \times ? = 48$ ?
Answer: 6 Since 8 x 6 = 48, the missing number is 6, making Choice C correct. Choice A (5) and Choice B (7) are close numbers that do not satisfy the equation. Choice D (48) repeats one of the given numbers instead of solving for the unknown factor.
Maria has $7$ boxes of crayons, with the same number of crayons in each box. She counts $42$ crayons in total, then gives away $2$ boxes to a friend. Which multiplication equation finds the number of crayons Maria has left after giving away the 2 boxes?
Answer: $5 \times 6 = ?$ Each box has 42 divided by 7, which is 6 crayons, and after giving away 2 boxes, Maria has 7 minus 2, which is 5 boxes left, so the crayons she has left is 5 x 6, making Choice A correct. Choice B finds crayons per box, which is a needed step but not the final answer to how many crayons are left. Choice C finds how many crayons were given away, not how many remain. Choice D does not correspond to any step in solving this problem.
What number makes the equation true: $30 \div \square = 5$ ?
Answer: 6 Since $30 \div 6 = 5$ , the missing number is 6. Choice A (25) comes from subtracting 5 from 30 instead of dividing. Choice C (5) repeats a number already in the equation instead of solving for the missing one. Choice D (30) repeats the dividend instead of finding the missing divisor.
Solve: $56 \div 7 = ?$ What is $?$
Answer: 8 Since 7 x 8 = 56, the answer to 56 divided by 7 is 8, making Choice C correct. Choice B (7) repeats the known factor instead of solving for the unknown one. Choice D (9) is close to the correct value but does not satisfy the division. Choice A (49) comes from squaring 7 instead of dividing 56 by 7.
Determine the missing number in $6 \times \square = 42$ .
Answer: 7 Since 6 times 7 equals 42, the missing number is 7. Choice B, 36, comes from multiplying 6 by 6 instead of finding the missing factor. Choice C, 8, is close to the answer but does not make the equation true. Choice D, 6, is the given factor itself, not the missing number.
Jake arranged stickers in equal rows. He used $36$ stickers total and made $4$ rows. Later, he decided to rearrange the same stickers into $6$ equal rows instead. Which equation helps find how many stickers will be in each new row?
Answer: $6 \times ? = 36$ Jake has $36$ stickers total and wants $6$ equal rows, so $6 \times ? = 36$ finds stickers per row. Choice A calculates stickers in the original arrangement. Choice C finds stickers per row in the original $4$ rows but doesn't help with the new arrangement. Choice D multiplies total stickers by rows, which doesn't make sense for this problem.
Which number completes the equation $5 \times ? = 30$ ?
Answer: 6 This question tests determining the unknown whole number in multiplication or division equations (CCSS.3.OA.4), specifically finding the missing value that makes an equation true. To find the unknown in an equation, identify what's missing (factor, product, dividend, divisor, or quotient), then use the relationship between multiplication and division. For multiplication: If one factor and the product are known, divide to find the other factor (8×?=48, so ?=48÷8=6). If both factors are known, multiply to find product (8×6=?, so ?=8×6=48). For division: If dividend and divisor are known, divide to find quotient (48÷8=?, so ?=48÷8=6). If dividend and quotient are known, multiply to find divisor (48÷?=6, so ?=48÷6=8). If divisor and quotient are known, multiply to find dividend (?÷8=6, so ?=6×8=48). In this problem, the equation is 5 × ? = 30. The unknown is a factor. To solve, we need to divide 30 by 5. Choice B is correct because 5×6=30, so 6 makes the equation 5×?=30 true. This value makes the equation true. Choice A is incorrect because this number doesn't make the equation true: 5×35=175, not 30. This error occurs when students make calculation errors. To help students find unknowns in equations: Teach the inverse relationship (multiplication ↔ division). Use fact families: If 8×6=48, then 48÷8=6, 48÷6=8, and 6×8=48 (all related). Model thinking aloud: "5 times what number equals 30? I know 5×6=30, so ? is 6." Cover up the unknown with your finger, say the known information, and think what number fits. Practice with manipulatives or arrays (5 rows of ? objects = 30 total, count 6 per row). Always check by substituting back: Does 5×6 really equal 30? Yes! Watch for students who add/subtract instead of multiply/divide, or who don't understand the three numbers are related through multiplication and division.
Find the unknown number: $7 \times \square = 56$ .
Answer: 8 Since 7 times 8 equals 56, the unknown number is 8. Choice A, 49, comes from multiplying 7 by 7 instead of finding the missing factor. Choice B, 7, is the given factor itself, not the unknown. Choice D, 9, is close to the answer but does not make the equation true.
Which number completes the equation $5 \times ? = 30$ ?
Answer: 6 Since $5 \times 6 = 30$ , the missing number is 6. Choice A (7) is off by one from the correct answer. Choice C (5) repeats the known factor instead of solving for the missing one. Choice D (35) is the sum of 5 and 30, not the missing factor.
What number makes the equation true: $30 \div \square = 5$ ?
Answer: 6 6 is correct because $30 \div 6 = 5$ . 5 is incorrect; it's the quotient given in the equation, not the missing divisor. 25 is incorrect because dividing 30 by 25 doesn't equal 5. 30 is incorrect; it's the dividend itself, not the missing number.
Roberto saves the same number of coins each week. After 7 weeks, he has saved 84 coins. He wants to have 120 coins in total. If he keeps saving the same number of coins each week, how many more weeks does he need?
Answer: 3 more weeks Roberto saves 84 divided by 7, which is 12 coins each week, and he still needs 120 minus 84, which is 36 more coins, so 36 divided by 12 is 3 more weeks. Choice A (5 more weeks) comes from a division error when finding the coins needed per week. Choice B (17 more weeks) comes from dividing 120 by 7 instead of using the correct weekly rate. Choice C (10 more weeks) comes from dividing the coins still needed by the wrong number.
Find the unknown number: $7 \times \square = 56$ .
Answer: 8 Since 7 times 8 equals 56, the unknown number is 8. Choice B, 49, comes from multiplying 7 by 7 instead of finding the missing factor. Choice C, 9, is close to the answer but does not make the equation true. Choice D, 7, is the given factor itself, not the unknown.

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