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.)
