## Key Concepts

• .Convert an improper fraction to a mixed number by dividing the denominator into the numerator. Write the mixed number as $\text{quotient}\dfrac{\text{remainder}}{\text{divisor}}$.
• .Convert a mixed number to an improper fraction by multiplying the whole number by the denominator, adding the numerator, then placing the result over the original denominator.
• .To multiply or divide mixed numbers, first convert them to improper fractions then follow the rules for fraction multiplication or division.
• To simplify a complex fraction, simplify the numerator and denominator separately, then rewrite the fraction as a division problem and follow the rules for fraction division.
• To simplify an expression containing a fraction bar, first simplify the numerator and denominator separately then simply the fraction
• To add mixed numbers with a common denominator, first add the whole numbers then add the fractions.
• To subtract mixed numbers with a common denominator, first write them in vertical form. If the top fraction is smaller than the bottom fraction, borrow one from its whole number to add to the fraction. Then subtract the fractions and subtract the whole numbers. You may also write the mixed numbers as improper fractions first, then subtract and convert the result back to a mixed number.

## Glossary

complex fraction
a fraction that contains a fraction in the numerator or denominator
improper fraction
a fraction in which the numerator contains a larger number than the denominator does
mixed number
a number with a whole number part and a fraction part such as “three and one half,” e.g. $3\dfrac{1}{2}$