Chapter 10 Math 275
5
+
4
+
4
=
13
= 1
3
10 10 10 10 10
Subtracting fractions is done through the same process used to add
fractions. First, fi nd a common denominator, then subtract the numerators,
and write the answer using the common denominator.
Multiplying Fractions
When multiplying fractions, it is not necessary to fi nd a common
denominator. Instead, simply multiply across the fraction (numerator ×
numerator, and denominator × denominator).
Example:
3
×
2
=
6
4 3 12
(3 × 2 = 6 and 4 × 3 = 12) = 6/12
The fraction 6/12 needs to be reduced (or simplifi ed). You are trying to
get the smallest possible number for both the numerator and denominator.
To reduce this fraction, you would divide 6 into the top number, and 6 into
the bottom number (6 goes into 6 once, 6 goes into 12 twice).
The fraction 6/12 becomes 1/2.
Dividing Fractions
The process of dividing fractions is very unique and requires the use of
the reciprocal fraction. To identify a fraction’s reciprocal, turn the second
fraction in the problem upside down to switch the numerator and denomi-
nator. For example, the fraction 5/8 would become 8/5. Then, multiply the
fi rst fraction and the inverted second fraction. There is no need for a com-
mon denominator.
Example:
3
÷
5
=
3
×
8
=
24
=
6
= 1
1
4 8 4 5 20 5 5
Note that the answer was reduced from 24/20 to 6/5 by dividing the
numerator and denominator each by 4. The fraction 6/5 was then con-
verted to a mixed number. When dividing mixed numbers, you will need
to convert them to fractions fi rst.
Converting Mixed Numbers to Fractions. A mixed number is composed
of a whole number and a fraction
(5½).
If you want to convert
5½
into a
fraction, you must fi rst multiply the whole number (5) by the denomina-
tor of the fraction (2). Now you have solved how many 1/2s there are in
5 (10). Next, add the numerator (1) to give you 11/2. 11/2 is another way
of expressing
5½.