New York City SHSAT 2017

POSITIVES AND NEGATIVES

There are few things to remember about positives and negatives. You will not see many problems that focus specifically on
positives and negatives, but you must know the basics because these concepts will show up as part of harder problems.

Adding a negative number is basically subtraction.

Subtracting a negative number is basically addition.

MULTIPLYING AND DIVIDING POSITIVES AND NEGATIVES

Negative ×/÷ negative = positive

Positive ×/÷ negative = negative

Multiplying and Dividing positives and negatives is like all other multiplication and division, with one catch. To figure out whether
your product is positive or negative, simply count the number of negatives you had to start. If you had an odd number of negatives,
the product is negative. If you had an even number of negatives, the product is positive.

Similarly,

6 + (−4) is really 6 − 4 or 2.

4 + (−6) is really 4 − 6 or −2.

6 − (−4) is really 6 + 4 or 10.

−6 − (−4) is really −6 + 4 or −2.

6 × (−4) = −24 (1 negative ➞ negative product)

(−6) × (−4) = 24 (2 negatives ➞ positive product)

(−1) × (−6) × (−4) = −24 (3 negatives ➞ negative product)

−24 ÷ 6 = (−1) × (​−6) × (−4) (1 negative ➞ negative quotient)

−24 ÷(−4) = 6 (2 negatives ➞ positive quotient)