274 Essential Skills for Health Careers Success
Fractions with the Same Denominator
When adding or subtracting fractions with a common denominator
only the numerator is added or subtracted.
Example:
9
+
6
+
4
=
9 + 6 + 4
=
19
8 8 8 8 8
If adding the fraction leaves you with a numerator that is divisible by
the denominator, the fraction must be reduced. This can be done by divid-
ing the numerator by the denominator.
The answer
19
must be reduced by dividing 19 ÷ 8 = 2
3
8 8
Because 8 goes into 19 twice, the answer includes a 2 next to the remain-
ing fraction, which is 3/8. This creates the mixed number of
2⅜.
Subtraction of fractions with common denominators is similar to addition.
Example:
10
–
5
–
4
=
10 – 5 – 4
=
1
9 9 9 9 9
Fractions with Different Denominators
To add or subtract two or more fractions that have different denomina-
tors, a lowest common denominator must be found.
Example:
1
+
2
+
4
= ?
2 5 10
To fi nd the lowest common denominator for 2, 5, and 10, consider the
multiples of each number.
Multiples of 2: 2, 4, 6, 8, 10…
Multiples of 5: 5, 10, 15, 20…
Multiples of 10: 10, 20…
10 is the lowest common denominator.
For the fi rst two fractions that do not already have a denominator of 10
(1/2 and 2/5), you need to multiply both the numerator and denominator
by the number that will produce a denominator of 10. So the fraction 1/2
will have its numerator and denominator multiplied by 5 to equal 5/10.
The fraction 2/5 will have its numerator and denominator multiplied by 2
to become 4/10. The fraction 4/10 already has a common denominator of
10. So the problem becomes:
common denominator
the number that can be
divided evenly by all of the
denominators in a group of
fractions