Prealgebra is the mathematical bridge between arithmetic and algebra. It introduces algebraic thinking while building on arithmetic skills. Students progress from basic arithmetic operations to working with variables and simple equations, preparing them for more advanced algebraic concepts.
Prealgebra works with different types of numbers. Integers include positive and negative whole numbers and zero. Rational numbers are fractions that can be expressed as ratios of integers. Irrational numbers like square root of 2 and pi cannot be written as simple fractions. Understanding these number systems is essential for algebraic thinking.
Variables are letters that represent unknown numbers, allowing us to work with general relationships. Expressions combine variables with numbers and operations. For example, in the expression 3x plus 5, the number 3 is the coefficient, x is the variable, and 5 is the constant term. We can translate word problems into algebraic expressions, like 'a number increased by 7' becomes x plus 7.
Equations show that two expressions are equal. To solve equations, we must keep both sides balanced using inverse operations to isolate the variable. For example, to solve x plus 7 equals 12, we subtract 7 from both sides. This gives us x equals 5. The balance scale helps visualize this concept of maintaining equality.
Ratios compare two quantities, while proportions show that two ratios are equal. In recipe scaling, if we have 2 cups flour to 1 cup sugar, and we want to use 4 cups flour, we can set up a proportion. Using cross-multiplication, 2 times x equals 4 times 1, so x equals 2 cups of sugar.