Integer Operations Word Problems Reference Cheat Sheet

Key Facts

• A positive integer represents a gain, increase, deposit, above-zero value, or movement right on a number line, such as $+8$.
• A negative integer represents a loss, decrease, withdrawal, below-zero value, or movement left on a number line, such as $-8$.
• To add integers with the same sign, add the absolute values and keep the common sign, such as $-6 + (-4) = -10$.
• To add integers with different signs, subtract the smaller absolute value from the larger absolute value and keep the sign of the number with greater absolute value, such as $-9 + 5 = -4$.
• To subtract an integer, add its opposite, so $a - b = a + (-b)$ and $7 - (-3) = 7 + 3 = 10$.
• The product or quotient of two integers with the same sign is positive, such as $(-6)(-2) = 12$ and $12 \div 3 = 4$.
• The product or quotient of two integers with different signs is negative, such as $(-6)(2) = -12$ and $12 \div (-3) = -4$.
• In a word problem, a total change can be written as $\text{final value} = \text{starting value} + \text{change}$.

Vocabulary

Integer

An integer is a whole number, its opposite, or zero, such as $-3$, $0$, or $5$.

Positive number

A positive number is greater than $0$ and often represents a gain, increase, or amount above a starting point.

Negative number

A negative number is less than $0$ and often represents a loss, decrease, or amount below a starting point.

Absolute value

Absolute value is a number's distance from $0$ on a number line, written as $|x|$.

Opposite

Opposite numbers are the same distance from $0$ but on different sides, such as $7$ and $-7$.

Net change

Net change is the overall increase or decrease after all signed changes are combined.