Finding Unknown Values in Multiplication and Division
Year 5 · Maths · Free — no account needed
Finding Unknown Values
Sometimes a number in a multiplication or division equation is missing. This missing number can be shown as a box (□), a question mark (?), or a letter like n or x. No matter how it's written, it stands for exactly one number that makes the equation true.
Multiplication and division undo each other
Multiplication and division are inverse operations — one undoes the other. If 6 × 7 = 42, then 42 ÷ 7 = 6 and 42 ÷ 6 = 7. This means you can always swap between multiplying and dividing to find a missing number.
Finding a missing factor
If □ × 5 = 35, ask "what is 35 divided by 5?" 35 ÷ 5 = 7, so □ = 7. Whenever a factor is missing, divide the product by the factor you already know.
Finding a missing number that's being divided
If □ ÷ 4 = 9, the missing number is the one being shared out — this is called the dividend. Use the inverse: multiply the answer by the divisor. 9 × 4 = 36, so □ = 36.
Balancing equations
Some equations have numbers or symbols on both sides, like 8 × 3 = 4 × □. Both sides must equal the same amount. Work out the side you know first (8 × 3 = 24), then find what makes the other side match (24 ÷ 4 = 6).
Using properties to help
Because multiplication can be done in any order — this is called the commutative property — 6 × 9 gives the same answer as 9 × 6. Spotting this can make it quicker to see matching factors when solving for an unknown.
Always check your answer
Once you find the missing number, put it back into the equation and check that both sides really are equal.
Worked Example
Find the value of the letter: 6 × k = 4 × 12 Step 1: Work out the side of the equation that has no unknown: 4 × 12 = 48. Step 2: Now the equation reads 6 × k = 48. Step 3: Since k is a missing factor, divide the product by the known factor: 48 ÷ 6 = 8. Step 4: So k = 8. Check: 6 × 8 = 48, and 4 × 12 = 48 — both sides match!
Practice
Determine the value of □ in 9 × □ = 63.
Flashcards
What does 'inverse operation' mean?
An operation that undoes another — division undoes multiplication, and multiplication undoes division.
How do you find a missing factor, like in □ × 6 = 42?
Divide the product by the known factor: 42 ÷ 6 = 7, so □ = 7.
How do you find a missing dividend, like in □ ÷ 3 = 9?
Multiply the answer by the divisor: 9 × 3 = 27, so □ = 27.
How do you solve a balance equation like 5 × 4 = 2 × □?
Work out the known side first (5 × 4 = 20), then divide by the other factor (20 ÷ 2 = 10).
What is the commutative property of multiplication?
You can multiply numbers in any order and get the same answer, e.g. 6 × 9 = 9 × 6.
How can you check if you've found the correct unknown value?
Put the number back into the equation and check both sides give the same answer.
All 14 practice questions
Determine the value of □ in 9 × □ = 63.
- 9
- 8
- 54
- 7
Show the answer to question 1
Answer: 7
63 ÷ 9 = 7, so □ = 7.
What number does the letter m stand for in 7 × m = 56?
- 7
- 49
- 8
- 9
Show the answer to question 2
Answer: 8
56 ÷ 7 = 8, so m = 8.
Calculate □ in this equation: □ ÷ 5 = 6
- 5
- 11
- 1
- 30
Show the answer to question 3
Answer: 30
6 × 5 = 30, so □ = 30.
I think of a number, multiply it by 4, and the answer is 32. What is my number?
- 8
- 28
- 4
- 36
Show the answer to question 4
Answer: 8
32 ÷ 4 = 8, so the number is 8.
Balance this equation by finding the missing number: 6 × 4 = 3 × □
- 9
- 8
- 7
- 2
Show the answer to question 5
Answer: 8
6 × 4 = 24, and 24 ÷ 3 = 8, so □ = 8.
Eight identical boxes hold 96 marbles altogether. How many marbles are in each box?
- 11
- 12
- 13
- 8
Show the answer to question 6
Answer: 12
96 ÷ 8 = 12, so each box holds 12 marbles.
In the equation 9 × n = 9 × 5, what is n?
- 45
- 9
- 5
- 1
Show the answer to question 7
Answer: 5
Since both sides have a factor of 9, n must equal 5 to make the equation balance, so n = 5.
Work out the missing number: 72 ÷ ? = 9
- 9
- 8
- 81
- 63
Show the answer to question 8
Answer: 8
72 ÷ 9 = 8, so ? = 8.
A number divided by 6 gives 7. What is the number?
- 1
- 36
- 42
- 13
Show the answer to question 9
Answer: 42
7 × 6 = 42, so the number is 42.
Balance the equation: 5 × 8 = □ × 10
- 5
- 4
- 50
- 8
Show the answer to question 10
Answer: 4
5 × 8 = 40, and 40 ÷ 10 = 4, so □ = 4.
Which value of a makes 3 × a = 5 × 6 true?
- 15
- 2
- 10
- 90
Show the answer to question 11
Answer: 10
5 × 6 = 30, and 30 ÷ 3 = 10, so a = 10.
Solve for x: 64 ÷ x = 8.
- 8
- 56
- 72
- 64
Show the answer to question 12
Answer: 8
64 ÷ 8 = 8, so x = 8.
Josh multiplies a number by 7 and gets 84. What was Josh's number?
- 77
- 7
- 91
- 12
Show the answer to question 13
Answer: 12
84 ÷ 7 = 12, so Josh's number was 12.
Complete the balance: 9 × 6 = 2 × □
- 52
- 3
- 27
- 56
Show the answer to question 14
Answer: 27
9 × 6 = 54, and 54 ÷ 2 = 27, so □ = 27.
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