Mixed fractions are composed of **a whole number and a fraction**, and represent the total of the two -- 3 1/4, for instance, represents 3 and one-fourth. To multiply or divide a mixed fraction, convert it into a an improper fraction such as 13/4. You can then multiply or divide it like any other fraction.

## Convert Mixed Fractions to Improper Fractions

Before you can multiply or divide mixed fractions, you must convert the mixed fractions to *improper fractions*. An improper fraction, such as 7/4, is **a fraction whose numerator is larger than its denominator**. The *numerator* is the top number in the fraction, and the *denominator* is the bottom number. To convert a mixed fraction to an improper fraction, **multiply the whole number part of the mixed fraction by the fraction's denominator, then add it to the numerator.** For example, to convert the mixed fraction 8 1/3, multiply the whole number, 8, by the denominator, 3, getting the product 24. Add 24 to the numerator to find the equivalent improper fraction: 25/3. So **8 1/3 = 25/3**.

## Multiply Numerator and Denominator

Once you've converted the mixed numbers to improper fractions, you can multiply two fractions together. Say you're multiplying 3 1/2 by 1 1/3: 3 1/2 is equal to 7/2, and 1 1/3 is equal to 4/3, so you're multiplying 7/2 by 4/3. To multiply two fractions, **multiply the numerators together to find the new numerator, then multiply the denominators together to find the new denominator.** The numerators of the fractions are 7 and 4; multiplied together they produce the new numerator, 28. The denominators, 2 and 3, are multiplied together to produce the new denominator, 6. So the product of multiplying 7/2 by 4/3 is 28/6.

## Divide Fractions

When you divide one fraction by another fraction, **you switch the numerator and denominator of the divisor fraction, then multiply.** Say instead of multiplying 7/2 by 4/3, you're dividing 7/2 by 4/3. Switch the numerator and denominator of 4/3, getting 3/4, then multiply: **7/2 x 3/4 = (7 x 3)/(2 x 4) = 21/8**.

## Simplify Fractions

Once you've divided or multiplied your fractions, check to see if the result can be simplified. You can simplify a fraction **if both the numerator and denominator can be evenly divided by the same number**. For instance, in 28/6, both 28 and 6 are divisible by two. Simplify the fraction by dividing both numerator and denominator by 2, getting 14/3. There is no number by which both 14 and 3 can be evenly divided, so you cannot further simplify it.

## Convert Back to Mixed Fraction

Once you've simplified, if you still have an improper fraction, convert the fraction back into a mixed fraction. To do this, **divide the numerator by the denominator.** The result of the division will be the mixed fraction's whole number, and the remainder will be the new numerator. For example, to convert 14/3 into a mixed fraction, divide 14 by 3: 3 goes into 14 four times, with a remainder of 2. So 14/3 is equal to the mixed fraction 4 2/3.

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