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# Multiplying and Dividing Fractions

## Multiplication

Multiply straight across: Multiply the numerators to get the new numerator. Multiply the denominators to get the new denominator.

## Division

The first fraction is said to be “divided by” the second fraction. The fraction you are “dividing by” is called the “divisior.” To divide, “invert” the divisor (turn it upside down), then multiply.

(When a fraction is inverted we call the resulting fraction the “reciprocal” of the original number. Any whole number can be thought of as a fraction with 1 in the denominator. Since , the reciprocal of 2 is .)

## Chain Multiplication and Division

There are times (especially in science classes in high school and beyond) when you need to multiply and divide a whole series of fractions and whole numbers. This is actually easy to do. Think of making a shish kabob: a skewer loaded up with chunks of meat, tomatoes, onions, bell pepper, mushrooms, etc. and cooked on a grill. Think of one long fraction bar as a skewer. To multiply a fraction in the list, simply skewer it on. To divide by a fraction, flip it over and skewer it on. Any whole number can be thought of as a fraction with 1 in the denominator, so can treat it like any other fraction. Multiplying by a whole number puts the whole number into the numerator. Dividing by a whole number puts the whole number into the denominator. (Once everything is in place we can ignore the 1’s.)