Pre-AlgebraPre-AlgebraMiddle school

Integers and Signed Numbers

Add, subtract, multiply and divide positive and negative numbers.

Integers are the whole numbers and their negatives: $\ldots, -2, -1, 0, 1, 2, \ldots$ . A number line makes their arithmetic visual: adding a positive moves right, adding a negative moves left, and subtracting a number is the same as adding its opposite.

For multiplication and division only the count of negative signs matters. An even number of negative factors gives a positive result and an odd number gives a negative result. This is why $(-1)^{10} = 1$ while $(-1)^{11} = -1$ .

Key terms

Sign rules: A product or quotient of two numbers with the same sign is positive; with different signs it is negative.
$(-3)(-4) = 12$

Key ideas

Rewrite every subtraction as addition of the opposite: $5 - (-3) = 5 + 3$ .
Same signs add and keep the sign; different signs subtract and take the sign of the larger absolute value.
Absolute value $|x|$ is the distance from zero, so it is never negative.
Division by zero is undefined; zero divided by a nonzero integer is $0$ .

Worked example

Evaluate $-7 - (-12) + (-3)(-4) \div (-2)$ .

Multiply and divide first: $(-3)(-4) = 12$ , then $12 \div (-2) = -6$ .
Rewrite: $-7 + 12 + (-6)$ .
Add left to right: $-7 + 12 = 5$ , then $5 - 6 = -1$ .

Answer: $-1$

Common mistakes

Writing $-7 - (-12) = -19$ by ignoring the double negative.
Assuming the answer to a subtraction must be smaller than the starting number.
Treating $|-5 + 2|$ as $|-5| + |2| = 7$ instead of $3$ .

Practice questions

Try each one, then open the answer. Numerical answers on this page are verified by an automated calculation check.

1.Evaluate $-15 + 9 - (-4)$ .
Show answer
$-2$
2.Evaluate $(-6)(3)(-2)$ .
Show answer
$36$
3.Evaluate $\frac{-48}{-6} - 10$ .
Show answer
$-2$

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