# How to multiply fractions with variables

- Multiplying and Dividing Fractions
- Multiplying rational expressions: multiple variables
- Fractions in Algebra

## Multiplying and Dividing Fractions

Multiplying two algebraic fractions produces a new algebraic fraction. Multiply the two numerators to get the new numerator and multiply the two denominators to.

withIf you're seeing this message, it means we're having trouble loading external resources on our website. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. Multiplying rational expressions. Dividing rational expressions. Multiplying rational expressions: multiple variables. Dividing rational expressions: unknown expression.

Are you stumped when it comes to multiplying fractions by whole numbers?

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The method to multiply fractions is to multiply the numerators together, multiply the denominators together and then cancel down if necessary. The method to divide fractions is to keep the first fraction the same, turn the divide sign into a multiply and turn the second fraction upside down. This is known as multiplying by the reciprocal. The sum then becomes multiplying two fractions, which is done using the method above. Multiplying and dividing rational expressions works using the same methods. To multiply two rational expressions, multiply the numerators and denominators together.

Multiplying fractions is easy: you multiply the top numbers and multiply the bottom numbers. For instance:. When it's possible, you reduce the fraction by cancelling off common factors; that is, you cross out any factors from one side of the fraction line that are duplicated on the other side of the line. In the example above, however, nothing reduces, because 8 and 45 have no factors in common. Multiplying Fractions.

## Multiplying rational expressions: multiple variables

To multiply two fractions, just do the following: Multiply the two numerators top numbers to get the numerator of the answer; multiply the two denominators bottom numbers to get the denominator of the answer. Before you multiply, see whether you can cancel out common factors that appear in both the numerator and denominator.

## Fractions in Algebra

Teachers and students alike might argue this concept is more daunting than leaping from subtraction and addition to multiplication. Put simply, multiplication is adding the same number over and over. Good news for your students: if they can add, they can multiply! Here are some examples:. In addition to multiplying whole numbers, you can also multiply by integers, decimals and, today, fractions. A proper fraction has a numerator less than the denominator.

Many techniques will simplify your work as you perform operations with algebraic fractions. As you review the examples, note the steps involved in each operation and any methods that will save you time. Reducing algebraic fractions. To reduce an algebraic fraction to lowest terms, first factor the numerator and the denominator; then reduce , or divide out common factors. Warning: Do not reduce through an addition or subtraction sign as shown here. To multiply algebraic fractions, first factor the numerators and denominators that are polynomials; then, reduce where possible.

Step 3: Simplify the resulting fraction by reducing it to the lowest term, if needed. The resulting fraction after multiplication is already in its reduced form. That becomes our final answer! Divide the top and bottom by its greatest common divisor GCD which is The general idea remains the same just like when you multiply two fractions, as shown in previous examples.

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Divide rational expressions.

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