Math 7 · Unit 3, Lesson 5: Dividing Signed Numbers · Tile 1 of 4
Multiplying Backward
Same signs, same rules
A multiplication problem in disguise
Every division problem is a multiplication problem in disguise. −12 ÷ 3 asks: what times 3 makes −12? The answer is −4, because −4 × 3 = −12. So dividing follows the same sign rules as multiplying.
One fact family.
−4 × 3 = −123 × (−4) = −12−12 ÷ 3 = −4−12 ÷ (−4) = 3
| Numbers | Quotient |
|---|---|
| positive ÷ positive | positive |
| negative ÷ negative | positive |
| positive ÷ negative | negative |
| negative ÷ positive | negative |
The same table as Lesson 4, Tile 2, with × changed to ÷.
The words
| Elle (math-speak) | Finn (plain English) |
|---|---|
| Quotient | The answer you get when you divide. Quotient comes from a Latin word that means how many times. |
| Divisor | The number you divide by. In −12 ÷ 3, the divisor is 3. |
Same signs, same rules
ElleMath-speak
The quotient of two numbers with the same sign is positive. The quotient of two numbers with different signs is negative.
FinnPlain English
Same rules as multiplying. Same signs, positive. Different signs, negative.
−12 ÷ 3What times 3 is −12?−4
15 ÷ (−3)Different signs, negative−5
−42 ÷ (−6)Same signs, positive7
0 ÷ (−7)Zero split into any number of groups is still zero0
The second example is from the North Carolina unpacking document for this standard.
NC standard: NC.7.NS.2.
Where to go next
Let me try a few7 problems on multiplying backward.
Next: Tile 2, The Fraction Bar Means DivideWhere the negative goes, and what a rational number is
All tilesAll 4 parts of this lesson.
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