Answer
$\text{(a) Adding Integers}$
When adding two integers with the same sign, add the absolute values of the two integers then copy the sign of the integers.
When adding two integers with different signs, subtract the smaller absolute value from the larger absolute value, then copy the sign of the integer with the bigger absolute value.
$\text{(b) Subtracting Integers}$
When subtracting two integers, add the opposite of the subtrahend to the minuend then perform the addition using the rules in part $\text{(a)}$ above.
$\text{(c) Multiplying Integers}$
The product of two integers with the same sign is positive, while the product of two integers with different signs is negative.
$\text{(d) Dividing Integers}$
The quotient of two integers with the same sign is positive, while the quotient of two integers with different signs is negative.
Refer to the examples given below.
Work Step by Step
$\text{(a) Adding Integers}$
When adding two integers with the same sign, add the absolute values of the two integers then copy the sign of the integers.
Examples:
$\begin{align*}
2+3&=|2|+|3|\\
&=5
\end{align*}$
$\begin{align*}
-2+(-3)&=-(|-2|+|-3|)\\
&=-(2+3)\\
&=-5
\end{align*}$
When adding two integers with different signs, subtract the smaller absolute value from the larger absolute value, then copy the sign of the integer with the bigger absolute value.
Examples:
$\begin{align*}
2+(-3)&=-(|-3|-|2|)\\
&=-(3-2)\\
&=-1
\end{align*}$
$\begin{align*}
-4+7&=|7|-|-4|\\\
&=7-4\\
&=3
\end{align*}$
$\text{(b) Subtracting Integers}$
When subtracting two integers, add the opposite of the subtrahend to the minuend then perform the addition using the rules in part $\text{(a)}$ above.
Examples:
$\begin{align*}
2-5&=2+(-5)\\
&=-3
\end{align*}$
$\begin{align*}
2-(-5)&=2+5\\
&=7
\end{align*}$
$\text{(c) Multiplying Integers}$
The product of two integers with the same sign is positive, while the product of two integers with different signs is negative.
Examples:
$3(9)=27$
$-3(-10)=30$
$3(-9)=-27$
$\text{(d) Dividing Integers}$
The quotient of two integers with the same sign is positive, while the quotient of two integers with different signs is negative.
Examples:
$-10 \div (-2) = 5$
$-10 \div 2 = -5$
$15 \div 5 =3$
