SAT Mc Graw Hill 2011

CHAPTER 7 / ESSENTIAL PRE-ALGEBRA SKILLS 291

Visualize the Number Line

Visualize the number line when comparing, adding, or subtracting numbers. Greater thanalways means

to the right on the number lineand less thanmeans to the left on the number line. A negative number is

greaterthan another if it is closer to 0.

Example:

4 − 18 =−(18 −4) =− 14

Remember these helpful facts about subtracting:

• abis positiveif ais greater than band
  negativeif bis greater than a(regardless
  of the signs).


• abis always the oppositeof ba.

Products, Quotients, and

Powers of Negatives

Any product, quotient, or power is negativeif

it has an oddnumber of negatives and positive

if it has an evennumber of negatives.

Example:

− 12 × 5 ×7 is negative: it has an odd number (1) of

negatives.

is positive: it has an even number (4)

of negatives.

(−3)^12 (5)^7 (−2)^5 is negative: it has an odd number

(12 + 5 =17) of negatives.

Inequalities and Negatives

Any inequality must be “flipped” whenever you

multiply or divide both sides by a negative.

Example:

Solve  3 x> 6y– 3 for x.

To isolate x, you must divide both sides by 3. But,

since this changes the sign of both sides, you must

“flip” the inequality, so the solution is x<  2 y+ 1.

()− ()−

()− ()−

43

263

xx

xx

Lesson 6: Negatives

less greater

− 10 − (^10110)
Example:
Which is greater, −2/5 or −7/5? Answer: Visualize
the number line. Although 2/5 is less than 7/5, on
the negative side this relationship is “flipped.” −2/5
is closer to 0 than −7/5 is, so −2/5 is greater.
Adding and Subtracting with
Negatives
To add, visualize the number line. To add a
positive, jump to the right. To add a negative,
jump to the left.
Example:
To add − 5 +−12, start at −5 and move 12 spaces to
the left(negative), to land on −17.
(Or you could start at −12 and jump 5 spaces to the
left!)
To subtract, you can change the subtraction to
addition by changing the sign of the second
number.
Example:
To subtract − 5 −(−12), change it to addition by
changing the sign of the second number: − 5 + 12 =
12 − 5 =7.
To subtract, you can also “swap” the numbers
and change the sign of the result, because ab
is the opposite of ba.