Missing-number multiplication problems
Use gaps such as 7 × □ = 56 to link facts with division and algebra.
Quick answer
Missing-number multiplication problems like 7 × □ = 56 help you find the missing number by thinking about what number times 7 gives 56. You can solve this by using division or by thinking of the multiplication fact you already know.
Learning outcome
By the end of this page, you will be able to find the missing number in multiplication problems like 7 × □ = 56 using your times tables and division.
- You can solve multiplication problems with a missing number.
- You know how to use division to find the missing number.
- You understand how multiplication and division are connected.
- You can check your answer using the multiplication fact.
Why this matters
Missing-number multiplication problems are important because they help you understand how multiplication and division are connected. When you see a problem like 7 × □ = 56, you're not just doing maths – you're learning how to think backwards and forwards. This helps you solve more complex problems later, like algebra equations. It also helps you in real life, like when you're sharing 56 cookies among 7 friends and need to figure out how many each friend gets.
How it works
When you see a missing number in a multiplication problem, you can solve it in two ways:
- Think of the multiplication fact you already know.
- Use division to find the missing number.
Let’s look at the problem: 7 × □ = 56
Step 1: Think of the multiplication fact you know. You know that 7 × 8 = 56. So the missing number is 8.
Step 2: You can also use division. Since 7 × □ = 56, you can divide 56 by 7 to find the missing number: 56 ÷ 7 = 8. So the missing number is 8.
Examples you can see
Let’s try a few examples to make it clear:
| Problem | How to solve it | Answer |
|---|---|---|
| 5 × □ = 30 | Think: 5 × 6 = 30 | 6 |
| 9 × □ = 81 | Think: 9 × 9 = 81 | 9 |
| 4 × □ = 28 | Divide: 28 ÷ 4 = 7 | 7 |
| 6 × □ = 42 | Think: 6 × 7 = 42 | 7 |
| 3 × □ = 21 | Divide: 21 ÷ 3 = 7 | 7 |
Try it as a mini adventure
Imagine you are a treasure hunter! You found a map with a riddle:
“To find the treasure, you must solve: 8 × □ = 64.”
Your mission is to find the missing number to unlock the treasure chest. How many steps must you take?
Step 1: Think of the multiplication fact. You know that 8 × 8 = 64.
Step 2: So the missing number is 8.
Step 3: You take 8 steps and find the treasure!
Now, try this riddle: 6 × □ = 36. What number do you need to find?
Answer: 6 × 6 = 36, so the missing number is 6.
Common mistakes
- Mistake: Thinking that 7 × □ = 56 means 7 + □ = 56.
Why it happens: Mixing up multiplication and addition.
Fix: Remember that multiplication is repeated addition. So 7 × 8 means 7 added 8 times, not 7 plus 8. - Mistake: Forgetting that division can help solve missing-number problems.
Why it happens: Not knowing how multiplication and division are connected.
Fix: Remember that if 7 × □ = 56, then 56 ÷ 7 = □. - Mistake: Guessing the answer without checking it.
Why it happens: Not taking time to double-check.
Fix: After finding the answer, multiply it back to check: 7 × 8 = 56.
Parent and carer guide
Helping your child with missing-number multiplication problems is easy and fun!
- Start with simple facts: Begin with times tables your child knows well, like 2s, 5s, and 10s.
- Use real objects: Use counters, blocks, or snacks to show how multiplication works.
- Ask them to explain: Ask your child to explain how they solved a problem. This helps them think clearly.
- Check together: After solving, help them check by multiplying the answer back.
- Be patient: It’s normal for children to make mistakes. Use them as learning moments.
Remember, the goal is not speed, but understanding. Keep it light and fun!
Practice questions
- 3 × □ = 21
Answer: 7 - 4 × □ = 36
Answer: 9 - 5 × □ = 45
Answer: 9 - 6 × □ = 54
Answer: 9 - 8 × □ = 72
Answer: 9 - 9 × □ = 63
Answer: 7 - 2 × □ = 18
Answer: 9 - 10 × □ = 80
Answer: 8 - 7 × □ = 49
Answer: 7 - 11 × □ = 66
Answer: 6
FAQ
What is a missing-number multiplication problem?
A missing-number multiplication problem is a problem where one of the numbers is missing, like 7 × □ = 56. You need to find the missing number.
How do I solve 7 × □ = 56?
You can solve it by thinking: what number times 7 equals 56? You know that 7 × 8 = 56, so the missing number is 8. You can also divide: 56 ÷ 7 = 8.
Why is it helpful to know division when solving multiplication problems?
Because multiplication and division are linked. If 7 × □ = 56, then you can use division to find the missing number: 56 ÷ 7 = □.
Can I use a times table chart to solve these problems?
Yes! A times table chart can help you quickly find the answer. For example, if you see 7 × □ = 56, look for 56 in the 7 row and see which column it is in.
How can I practice more?
You can use online games, apps, or worksheets that have missing-number multiplication problems. Try to solve them using both multiplication facts and division.