GED Mathematical Reasoning
Signed Numbers & Absolute Value
Numbers below zero are negative — a temperature of −8, a bank balance of −$40. The math is the same math you already do; the only new part is keeping track of the minus signs. Almost every mistake here is a bookkeeping slip, not a thinking slip.
The words first
- negative number
- a number less than zero, written with a minus sign in front
- absolute value
- how far a number sits from zero, written with two straight bars: |−8| = 8
- sum / difference
- the answer to an addition / a subtraction
The method
THE RULE FOR SUBTRACTING A NEGATIVE
a − (−b) becomes a + b
Two minus signs next to each other cancel into a plus.
THE RULE FOR ADDING A NEGATIVE
a + (−b) becomes a − b
THE RULE FOR MULTIPLYING AND DIVIDING
negative × negative = positive
negative × positive = negative
Count the minus signs. Even number of them → positive.
Odd number of them → negative.
Worked all the way through
The problem
What is −8 − (−3)?
- Step 1 — Spot the two minus signs.The problem is −8 minus negative 3. The second minus belongs to the 3, and there is a subtraction sign in front of it. That is two minus signs in a row.
- Step 2 — Turn them into a plus.−8 − (−3) becomes −8 + 3
- Step 3 — Now it is ordinary addition.Start at −8 on a number line and move 3 steps to the right (right is the positive direction): −8 → −7 → −6 → −5.
- Step 4 — Write the answer.−8 + 3 = −5
On the board
−8 − (−3)
the problem
−8 + 3
two minus signs became a plus
−5
count 3 to the right from −8
Answer
−5
A second one, in a different form
What is (−4) × (−6) + 3?
(−4) × (−6) + 3
the problem
24 + 3
negative × negative = positive
27
Answer
27
The usual mistake
Rushing the double negative and answering −11 instead of −5.
Check yourself
Sanity check: you started at −8 and added something, so the answer has to be bigger than −8. −5 is bigger than −8. If you had answered −11 you moved the wrong way.
Practice it
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