Math 7 · Unit 4, Lesson 1: Hand It Out, Take It Back · Tile 2 of 3
What If There's Subtraction or Division?
Change them into addition and multiplication first
The properties only work for addition and multiplication. So before you do anything else, change every subtraction into addition and every division into multiplication. Then all the properties work again.
Write it down. Do every change on paper, one line per step. Changing signs in your head is the number one reason for missed problems. If you changed something, it should be on the paper.
Change 1. Subtracting is adding the opposite.
The minus sign belongs to the term on its right. It goes with that term wherever the term moves.
Why it matters: try 10 − 4 − 2. In your head it is easy to do 4 − 2 first and get 8. That is wrong. On paper: 10 + −4 + −2 = 4, in any order you like.
Change 2. A minus in front of parentheses is an invisible −1.
The −1 is handed to every term inside, so every sign inside flips.
Change 3. Dividing is multiplying by the reciprocal.
Ask: what do you multiply the divisor by to get 1? That number is the reciprocal.
Why it works: write 20 ÷ 4 as the fraction 204. Multiply the top (numerator) and the bottom (denominator) by 14. The bottom (denominator) becomes 1, and the top (numerator) is 20 × 14. So 20 ÷ 4 = 20 × 14 = 5.
Tidy up at the end
Tests write answers with minus signs. When you are done, write + −5 as − 5.
Rewrite subtraction as adding the additive inverse.
Change minus to plus the opposite.
Rewrite division as multiplying by the multiplicative inverse.
Change divide to times the flipped number, the reciprocal.
NC standards: NC.7.NS.1, NC.7.NS.2.