3
Addition and subtraction are partners
Discover Mathematics P2: Term 2, Lessons 81–90
GoalUse fact families and use addition to check subtraction.
New words
fact family · addition and subtraction sentences that use the same three numberspartners · two things that work togethercheck · to see if an answer is right
Explanation
Addition and subtraction are partners. Three numbers can make a fact family. The numbers 8, 9 and 17 make four sentences: 8 + 9 = 17, 9 + 8 = 17, 17 − 8 = 9 and 17 − 9 = 8. The biggest number, 17, is the whole. We can use this to check subtraction. If 83 − 47 = 36, then 36 + 47 must be 83. Add: 6 + 7 = 13, 3 + 4 + 1 = 8. It is 83, so the answer is right. If the sum does not give the starting number, there is a mistake.
Worked examples
The fact family of 8, 9 and 17: 8 + 9 = 17, 9 + 8 = 17, 17 − 8 = 9, 17 − 9 = 8.
The fact family of 25, 30 and 55: 25 + 30 = 55, 30 + 25 = 55, 55 − 25 = 30, 55 − 30 = 25.
Check 83 − 47 = 36 by adding: 36 + 47 = 83. It matches, so the answer is right.
Class activity
Family cards. Choose three numbers such as 6, 9 and 15, where the biggest is the sum of the other two. Write all four sentences of the fact family on a card. Make three more cards. Then mix the sentences and match them back into families.
Practice
1
Write the other three sentences in the family of 6 + 9 = 15.
9 + 6 = 15, 15 − 6 = 9, 15 − 9 = 6.
2
Find the missing number: 14 + __ = 31.
31 − 14 = 17, so the missing number is 17.
3
Find the missing number: 40 − __ = 25.
40 − 25 = 15, so the missing number is 15.
4
Check 72 − 38 = 34 by adding.
34 + 38 = 72, so it is right.
5
Mina says 61 − 28 = 43. Check by adding. Is she right?
43 + 28 = 71, not 61, so she is wrong. The right answer is 33, because 33 + 28 = 61.