Formula sheet · Grades 6 to 8

Pre-Algebra formulas

8 formulas from this course. Each one gives the rule in math, one line on what it means, and a worked example that uses it.

Order of operations (PEMDAS)

\text{PEMDAS: parentheses, exponents, } \times \div, \text{ then } + -

Work through the operations in this order, left to right.

(-a)(-b) = ab,\qquad (-a)(b) = -ab

Two matching signs give a positive result; two different signs give a negative result.

a + (-b) = a - b,\qquad -a + b = b - a

Adding a negative moves left on the number line, and subtracting a negative moves right.

|x| = \text{distance from } 0

Absolute value is never negative because distance ignores direction.

\text{unit rate} = \frac{\text{amount}}{\text{quantity}}

The amount for one unit, found by dividing the amount by the quantity.

\frac{a}{b} = \frac{c}{d} \Rightarrow ad = bc

Cross-multiplying turns a proportion into a simple equation.

a : b = \frac{a}{g} : \frac{b}{g}

Divide both parts by the greatest common factor g to write the ratio in lowest terms.

a : b = c : d \iff ad = bc

Two ratios are equivalent exactly when their cross-products are equal.

Practice problems with answers for every Pre-Algebra topic.