Negative Number Operations Reference Cheat Sheet

Key Facts

• A negative number is less than $0$ and is written with a minus sign, such as $-6$.
• The absolute value $|a|$ is the distance from $a$ to $0$ on the number line, so $|-8| = 8$.
• When adding integers with the same sign, add the absolute values and keep the sign, such as $-4 + (-7) = -11$.
• When adding integers with different signs, subtract the smaller absolute value from the larger absolute value and use the sign of the number with the larger absolute value.
• Subtracting an integer means adding its opposite, so $a - b = a + (-b)$.
• The product of two numbers with the same sign is positive, so $(-3)(-5) = 15$.
• The product or quotient of two numbers with different signs is negative, so $-18 \div 3 = -6$.
• Use order of operations with negative numbers: parentheses first, then exponents, then multiplication and division, then addition and subtraction.

Vocabulary

Integer

An integer is a whole number, its opposite, or $0$, such as $-3$, $0$, or $7$.

Negative Number

A negative number is a number less than $0$ and is located to the left of $0$ on a number line.

Opposite

The opposite of a number is the number the same distance from $0$ on the other side, such as $5$ and $-5$.

Absolute Value

Absolute value is a number’s distance from $0$, written as $|a|$.

Additive Inverse

An additive inverse is a number that adds with another number to make $0$, so $a + (-a) = 0$.

Sign

The sign tells whether a number is positive or negative.