Two fractions are equivalent if multiplying the numerator and denominator of one fraction by the same whole number yields the other fraction. |
To reduce a fraction to lowest terms or to its simplest equivalent fraction, factor both the numerator and denominator completely (i.e. into prime numbers). Then cancel every factor that occurs in both the numerator and denominator. What remains is the simplest equivalent fraction. |
Algebra Coach Exercises |
To add two or subtract like fractions (fractions that have a common denominator), just add or subtract the numerators and put the result over the common denominator, like this: |
Algebra Coach Exercises |
Multiplying fractions produces a new fraction. Multiply the numerators to get the new numerator and multiply denominators to get the new denominator, like this: Then simplify by reducing the new fraction to lowest terms. To multiply a fraction by a whole number, just multiply the fraction’s numerator by the whole number to get the new numerator, like this: Then simplify by reducing the new fraction to lowest terms. |
Algebra Coach Exercises |
4/5 and 5/4 are reciprocals because
8 and 1/8 are reciprocals because
Dividing fractions: The procedure is to replace a division by a fraction by the multiplication by the reciprocal of that fraction, like this: |
Here is why this procedure works: The key is that instead of seeing a fraction divided by a fraction, look for a single fraction whose numerator and denominator just happen to be fractions. In the first step we multiplied this fraction by a UFOO whose numerator and denominator just happen to be fractions. The UFOO was chosen so the fractions in the denominator would cancel and give 1. After another simplification that left only the final multiplication of fractions. |
Algebra Coach Exercises |