Usually, one of the first topics covered in pre-algebra entails executing arithmetic operations on negative numbers, decimals and fractions. Students should already have some background knowledge of working with these types of numbers, such as adding two positive fractions. In pre-algebra, they’ll extend upon this knowledge. For example, students will practice combining different types of numbers, including expressions with negative numbers and fractions. They’ll work with square roots and solve word problems. Students may also explore the concept of absolute value, defined as distance from zero on a number line.
In pre-algebra, students expand upon their understanding of exponents, oftentimes encountering negative exponents for the first time. Students write negative exponents as fractions and then evaluate them. Students also use the order of operations to simplify lengthier problems involving exponents. They may also encounter exponents during a discussion of scientific notation, a way of writing very small or very large numbers. For instance, students may convert 470,000 to its equivalent in scientific notation, 4.7 x 10 to the fifth power.
Pre-algebra students learn about the three basic number properties of addition and multiplication: commutative, associative and distributive. The commutative property means that you can reverse the order in addition or multiplication – for instance, 7 x 4 produces the same result as 4 x 7. The associative property means that you can group numbers differently when adding or multiplying and the outcome is still the same. For example, 5+(8+1) and (5+8)+1 both equal 14. The distributive property states the equivalence of multiplying a number outside a set of parentheses with all of the numbers inside it. For instance, 3(2+5) produces the same result as 6+15. Students may also explore other number properties, such as the identity, inverse and zero properties.
Learning to work with variables is an integral part of any pre-algebra class. A variable is a letter that represents an unknown number or numbers. Students initially use variables to evaluate or simplify expressions, for instance, rewriting 5+3x–6–2x as -1+x. They then solve one-step equations for a given variable. For example, in b+4=-8, students subtract four from both sides of the equation to obtain an answer of b=-12.
Upon entering pre-algebra, many students already know how to convert fractions and decimals to percentages, but instructors may review the process. Pre-algebra students solve percentage-based word problems, such as “What percent of 52 is 36?” Pre-algebra students also solve simple proportion problems through cross-multiplication. Graphing on the coordinate plane is another integral part of pre-algebra. Students learn how to interpret ordered pairs, such as (-1, 7), and plot the corresponding points on a graph. Students also learn how relationships involving inputs and outputs can form a function, or equation. They learn how to identify a function’s slope and may practice graphing simple linear equations in the coordinate plane.