Summary: Multiplying and Dividing Fractions
Key Concepts
- Equivalent Fractions Property
- If are numbers where , , then and .
- Simplify a fraction.
- Rewrite the numerator and denominator to show the common factors. If needed, factor the numerator and denominator into prime numbers.
- Simplify, using the equivalent fractions property, by removing common factors.
- Multiply any remaining factors.
- Fraction Multiplication
- If , and are numbers where and , then .
- Reciprocal
- A number and its reciprocal have a product of .
Opposite Absolute Value Reciprocal has opposite sign is never negative has same sign, fraction inverts
- A number and its reciprocal have a product of .
- Fraction Division
- If , and are numbers where , and , then
- To divide fractions, multiply the first fraction by the reciprocal of the second.
Glossary
- reciprocal
- The reciprocal of the fraction is where and .
- simplified fraction
- A fraction is considered simplified if there are no common factors in the numerator and denominator.