Inverse Operations and Fact Families
Recognise and explain the connection between multiplication and division as inverse operations and use this to develop families of number facts.
Read this first
Multiplying and dividing undo each other. One fact gives you four.
6 x 7 = 42. So 42 shared into 6 rows gives 7.
Words you need
- Inverse
- An operation that undoes another.
- Fact family
- Four number facts made from three numbers.
- Product
- The answer when you multiply.
Worked example
e.g. Write the fact family for 6, 7 and 42.
- Start with a times fact. 6 x 7 = 42.
- Swap the order. 7 x 6 = 42.
- Now undo it. 42 divided by 6 = 7.
- And the other way. 42 divided by 7 = 6.
- Four facts from three numbers.
If you know one fact, you know all four.
Practice
The pictures fade as you go. By the last few you are on your own.
1What is 5 x 8?with a picture
Answer40.
2What is 40 divided by 5?with a picture
Answer8.
3Write the fact family for 4, 9 and 36.with a hint
Need a hint?
Two times facts and two divide facts.
Answer4x9=36, 9x4=36, 36/4=9, 36/9=4.
4You know 8 x 7 = 56. What is 56 divided by 8?with a hint
Need a hint?
Divide undoes multiply.
Answer7.
5Write the fact family for 3, 11 and 33.on your own
Answer3x11=33, 11x3=33, 33/3=11, 33/11=3.
6You know 12 x 5 = 60. What is 60 divided by 12?on your own
Answer5.
7Why does 6 x 7 equal 7 x 6?on your own
AnswerTurning the array does not change how many there are.
Think about it
1
Why is division called the inverse of multiplication?
One good answerIt puts the number back where it started.
2
How does a fact family help with hard divisions?
One good answerTurn it into a times question you already know.
Common mistakes
Learning each fact separately.
One fact gives you four. Learn the family.
Thinking division can be swapped like multiplication.
42 / 6 is not the same as 6 / 42.