Count the Negatives · Deep Dive 5

Count first

When there are lots of numbers to multiply, don't flip the sign over and over in your head. Count the negative signs first. An even number of negatives, and the answer is positive. An odd number, and it's negative. Then multiply the numbers without their signs.

Every pair of negatives makes a positive, so negatives cancel two at a time.
If one is left over, the answer is negative.

Zero. If any factor is 0, the product is 0. Zero groups of anything is nothing, no matter the signs.

ElleMath-speak

A product with an even number of negative factors is positive. A product with an odd number of negative factors is negative.

FinnPlain English

Count the minus signs. Even means positive. Odd means negative. Write the sign down first, then multiply.

Watch it work

⁻2(10)(⁻3)Count: 2 negatives, even, so positive2 × 10 × 3 = 6060

⁻2 × 5 × (⁻1) × (⁻3)Count: 3 negatives, odd, so negative2 × 5 × 1 × 3 = 30⁻30

56 × (⁻66)Count: 1 negative, so negative66 ÷ 6 = 11, and 11 × 5 = 55⁻55

(⁻0.5)(⁻12)Count: 2 negatives, so positivehalf of 12 is 66

Tip. To multiply a fraction by a whole number, it helps to divide first. 56 of 66: divide 66 by 6, then multiply by 5. Use the commutative property to put friendly numbers together, as in Lesson 3.

The first and third examples are from the North Carolina unpacking document for this standard.

Let me try a few

NC standard: NC.7.NS.2.

Where to go next

Let me try a few8 problems on count the negatives. Next: Tile 4, Real-World ProductsTemperatures, dives, and money over time All tilesAll 4 parts of this lesson. Tell us what you thought about this tileA few quick questions about just this tile. It takes a few minutes, and opens in a new tab so you keep your place.