Download To Multiply fractions:

Multiplying/Dividing Fractions
To Multiply fractions:
1. Change a mixed number or whole number
so that it is a ratio of two integers (i.e. an
improper fraction).
 Put whole number over 1.
 Change mixed number to an
improper fraction by multiplying
the whole number times the
denominator, then add the
numerator of the fraction part to
the product, and put the sum over
the denominator.
2. Simplify a numerator and a denominator if
5
3  12  ?
6
23
5
1. For 3 : 3x6  18  5  23 , giving
;
6
6
12
For 12: the fraction is
1
Ex1.
2. 23 x 12
6
1 Since 12  6  2 & 6  6  1
23 x 2
1
1
3.
possible by dividing the numerator and
denominator by the same number.
3. Multiply the numerator times the other
numerator and multiply the denominator
times the other denominator.
4. If the products result in an improper
fraction, then change it to a mixed number
(by dividing the numerator by the
denominator); add the whole numbers sum
to the fraction part.
5. Simplify the fraction if needed.
To Divide fractions:
1. Change mixed number or whole number so
that it is a ratio of two integers (i.e. an
improper fraction).
 Put whole number over 1.
 Change mixed number to an
improper fraction by multiplying
the whole number times the
denominator, then add the
numerator of the fraction part to
the product, and put the sum over
the denominator.
2. Change the division sign to a
multiplication sign and change
the divisor (the 2nd term) to its
reciprocal (i.e. “flip” the
Ex2:
23 2 46
x 
 46 Answer: 46
1 1 1
8 3
x
9 14
1. Step 1 is not needed since it’s already in
a ratio of two integers.
2. 8 x 3
9 14 Since 8/2=4 & 14/2=7
Since 3/3=1 & 9/3=3, then
4 x1
2
7
3.
Ex3.
4 1 4
x 
3 7 21
33  1
Answer:
4
21
5
6
1.
33
11
& 1x6  6,6  5  11 , then
1
6
2.
33 11 33 6
 
x
1 6
1 11
(Note - The reciprocal of
11 6
is
)
6 11
3. 33 x 6
1
11
Since 33  11  3 & 11  11  1
Then 3 x 6
1
1
Multiplying/Dividing Fractions
numerator and the
denominator).
3.
Simplify a numerator and a denominator if
possible by dividing the numerator and
denominator by the same number.
4.
Use the rule for multiplying fractions:
multiply a numerator times a numerator
and multiply a denominator times a
denominator.
5.
If it’s an improper fraction, then change to
mixed number (i.e. divide the numerator by
the denominator) and add the whole
numbers to the sum.
4.
Ex4:
3 6 18
x 
 18 Answer: 18
1 1 1
8 6

9 27
1. Step 1 is not needed since it’s already in
a ratio of two integers.
2.
8 27
8 6

x
=
9 6
9 27
3. 8 x 27
9 6 Since 8/2=4 & 6/2=3
Since 9/9=1 & 27/9=3, then
4 x 3
1 3
6.
Simplify the fraction if needed.
4.
4 3 12
x 
1 3 3
5.
12
4
3
Answer: 4