Pre-AlgebraMiddle school3 topic explainers

Pre-Algebra course

Integers, exponents, expressions and simple equations, with the habits that prevent sign errors.

Topics in this course

1.Integers and Signed 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.
- 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.
Quick check: Evaluate $-15 + 9 - (-4)$ .
$-2$
Includes a worked example, 3 common mistakes and 3 practice questions with answers. Study integers and signed numbers
2.Exponents
An exponent counts repeated multiplication: $2^5 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 = 32$ . The exponent rules all follow from counting factors. Multiplying $a^3 \cdot a^4$ strings together seven factors of $a$ , so the exponents add.
- Product rule: $a^m a^n = a^{m+n}$ .
- Quotient rule: $\frac{a^m}{a^n} = a^{m-n}$ .
- Power rule: $(a^m)^n = a^{mn}$ and $(ab)^n = a^n b^n$ .
Quick check: Evaluate $2^{-3}$ .
$\frac{1}{8}$
Includes a worked example, 3 common mistakes and 3 practice questions with answers. Study exponents
3.One- and Two-Step Equations
An equation is a balance: whatever you do to one side you must do to the other to keep it true. A one-step equation needs a single inverse operation to isolate the variable. Addition undoes subtraction, multiplication undoes division, and vice versa.
- Identify the operation applied to the variable, then apply its inverse to both sides.
- For $\frac{x}{a} = b$ multiply both sides by $a$ ; for $ax = b$ divide by $a$ .
- Negative coefficients: divide by the negative number itself, as in $-4x = 20 \Rightarrow x = -5$ .
Quick check: Solve $x - 9 = -4$ .
$x = 5$
Includes a worked example, 3 common mistakes and 3 practice questions with answers. Study one- and two-step equations

Topics in this course

1.Integers and Signed Numbers

2.Exponents

3.One- and Two-Step Equations

Where to go next