Math 7 · Unit 3, Lesson 5: Dividing Signed Numbers · Tile 2 of 4
The Fraction Bar Means Divide
Where the negative goes, and what a rational number is
The secret in every fraction
Here's a secret hiding in every fraction: the fraction bar is a division sign. 34 means 3 ÷ 4. So a negative fraction is a division problem with one negative number, and it doesn't matter which number gets the negative sign.
All three are −1 14, or −1.25.
Not on this list: −5−4. Two negatives make it positive: 54.
For integers p and q, with q not zero, the negative of p over q equals negative p over q, which equals p over negative q.
One negative sign, anywhere in the fraction, makes the whole thing negative. Two negative signs cancel out.
What a rational number is
| Elle (math-speak) | Finn (plain English) |
|---|---|
| Rational number | Any number you can write as one integer divided by another, as long as you don't divide by zero. Rational comes from ratio. |
Every one of these is rational
| Number | As an integer over an integer |
|---|---|
| 6 | 61 |
| −0.75 | −34 |
| 3 12 | 72 |
| 0 | 01 |
| −2.5 | −52 |
Each one can be written as an integer over an integer, so each one is rational. Integers, fractions, mixed numbers, and decimals that stop are all rational numbers. Lesson 6 shows that decimals that repeat are rational too. Some numbers cannot be written this way, and you'll meet them in 8th grade.
Never divide by zero
6 ÷ 0 asks what times 0 makes 6. Nothing works, because anything times 0 is 0. So dividing by zero has no answer. Math calls it undefined. That's why a rational number's bottom (denominator) can never be zero. Zero on top is fine: 06 = 0.
Elle and Finn talk it over
So what happens if I divide by zero?
Nothing. No number works, so there's no answer. It's undefined.
So it's like asking my cat to fetch.
Exactly. You can ask all day. Nothing is coming back.
NC standard: NC.7.NS.2.