Some word
problems are solved using multiplication and division of fractions.
These can be common fractions or mixed numbers. This page will
use division problems. A link at the bottom of this page
will take you to a lesson with multiplication problems!
Let's review
some terms used with fractions!
common fraction- contains
a numerator and denominator and is less than one whole
mixed number-contains a
whole number and a common fraction and is greater than one whole
reciprocal (sometimes
called the multiplicative inverse)-"switch" the fraction around-
the numerator becomes the denominator and the denominator becomes
the numerator!
The rule is simple:
to divide fractions, multiply by the reciprocal of the second
number.
First,
I need to know that you know what a reciprocal is, so let's do some
together!
Find the reciprocal of ¾ by
switching the numerator and the denominator:
Find the
reciprocal of 1½ by: changing it to an improper
fraction and then switching the numerator and the
denominator:
reciprocal is
Second
, I need to check your knowledge, so
please do the following problems! Find the reciprocals of these
fractions:
1½
¾
⅜
⅞
2¾
Now, I repeat, the rule is simple: to
divide fractions, multiply by the reciprocal of the second number.
Let's try some!
Remember, the first number
doesn't change!
Remember, always put
answers in lowest terms!
Now let's examine
a word problem in which you use division of fractions to solve.
The Ecology
Club is going to clean up a section of highway which measures 10½
miles. If each member can clean ⅜mile, how many
members are needed to clean one side of the length of highway?
Set up
equation:
Rewrite
equation (multiply by reciprocal of the second number):
reciprocal is
