Page 58 - Mathematics of Business and Finance

38 Chapter 1 | Review of Basic Arithmetic

Addition and Subtraction of Signed Numbers

The following are rules to be followed while adding or subtracting signed numbers.
Adding Two Signed Numbers
a. If the signs of the two numbers are the same: disregard the sign of the numbers, add the numbers,
and keep the common sign.
For example,
■ Adding +7 and +3 ■ Adding –6 and –2
= +7 + (+3) = –6 + (–2)
= +(7 + 3) = –(6 + 2)
= +10 = –8
b. If the signs of the two numbers are different: disregard the sign of the numbers, subtract the smaller
Two signs should not be
written next to each other. number from the larger number, and keep the sign of the larger number.
Brackets should be used to For example,
separate the two signs.
For example, we write ■ Adding +8 and –15 ■ Adding –3 and +7
–7 – (+2) instead of –7 – +2 = +8 + (–15) = –3 + (+7)
+8 + (–5) instead of +8 + –5
+10(–2) instead of +10 × –2 = –(15 – 8) = +(7 – 3)
= –7 = +4
Subtracting Two Signed Numbers

Change the subtraction (minus) sign to addition (plus) and change the sign of the number being subtracted.
Then follow the above addition rules.
For example,
■ Subtracting –12 from +18 ■ Subtracting –5 from –7 ■ Subtracting –6 from –2
= +18 – (–12) = –7 – (–5) = –2 – (–6)
= +18 + (+12) = –7 + (+5) = –2 + (+6)
= +(18 + 12) = –(7 – 5) = +(6 – 2)
= +30 = –2 = +4

Multiplication and Division of Signed Numbers

The following are rules to be followed while multiplying or dividing two signed numbers:
Multiplying two
signed numbers a. If the sign of the two numbers are the same: their product or quotient will be positive.
(+) (+) = (+)
(−) (−) = (+) For example,
(+) (−) = (−)
(−) (+) = (−) ■ (+5)(+4) = +20 ■ (–5)(–4) = +20
+12 –12
■ = +4 ■ = +4
+3 –3
b. If the sign of the two numbers are different: their product or quotient will be negative.
For example,
Dividing two signed ■ (+5)(–4) = –20 ■ (–5)(+4) = –20
numbers
+12 –12
(+) (–) ■ –3 = –4 ■ +3 = –4
(+) = (+) (–) = (+)
(–) (+) ■ –25 = –5 or – 5 ■ +30 = +15 = –15 or – 15
(+) = (–) (–) = (–) +15 3 3 –4 –2 2 2
When multiplying or dividing more than two signed numbers, group them into pairs and determine
the sign using the rules for multiplication and division of signed numbers.