Operations

In this section, you will find the Laws of signs, examples, and also an interactive quiz. Enjoy!

Absolute Value

Absolute value is the distance (always positive) between a number and a zero on the number line; the positive value of a number.

Ex:
• $|3| = 3$
• $|-3| = 3$
• $|-5| = 5$

Addition

When adding numbers, follow these rules.

a) If both numbers are positive, add them; the sign of the answer will be positive.

b) If both numbers are negative, add them; the sign of the answer will be negative.

c) If one number is negative and the other is positive (in any order), subtract the two numbers (even if they are joined by a plus sign); the sign of the answer will be the same sign as the sign of the number that has the larger absolute value.

Ex:
• $4 + (-9) = -5$
• $(-32)+(-2)=-34$
• $(-12)+14=2$

Subtraction

1. Subtraction numbers can be accomplished by adding the opposite of the number to be subtracted.

2. After changing the sign of the number in back of the minus sign, follow the rules of addition as stated above.

Ex:
• $8-(-3)=8+(+3)=11$
• $(-32)+(-2)=-34$
• $(-15)-(9)=(-15)+(-9)=-24$

Multiplication

When multiplying numbers, follow these rules.

a) If the signs of the numbers are the same, multiply and make the answer positive.

b) If the signs of the numbers are different, multiply and make the answer negative.

Ex:
• $(-4)(5)=-20$
• $(-3)(-2)=6$
• $(7)(-10)=-70$

Division

When dividing numbers, follow these rules.

a) If the signs of the numbers are the same, divide them and make the answer positive.

b) If the signs of the numbers are different, divide them and make the answer negative.

Ex:
• $(-30)/(5)=-6$
• $(-22)/(-2)=11$
• $(70)/(-10)=-7$