ADDING AND SUBTRACTING FRACTIONS
Consider the following example: Find the sum of
Need a lowest common denominator!
8
13
.
and
60
90
To find the Least Common Denominator, find the
prime factorization of 60 and 90 using the Factor
Tree.
60
90
6
10
3
2
2
5
3
9
10
3
2
Write the prime factorization using exponents.
60 2 2 3 5
Write a specific formula for LCD by multiplying
each factor (big number) with the highest
exponent.
LCD
(Note: If the factors have the same exponent,
then just write the factor once).
Build equivalent fractions with the denominator
180.
8 ?
60 ?
Ask yourself: 60 ?
2 2 32 5
90 2 32 5
2 2 3 3 5 180
?
180
180 ? (If you can’t think about the factor, just divide 180 60 3 )
Now, multiply both the numerator and
denominator by the same number.
8 3
60 3
24
180
Repeat the process for the second fraction.
13 ?
90 ?
?
180
Ask yourself: 90 ?
and
180 ? (If you can’t think about the factor, just divide 180 90 2 )
Now, multiply both the numerator and
denominator by the same number.
13 2
90 2
Since both fractions have the same denominator,
you are ready to add them. Simply add the
numerators (top numbers) and keep the
denominator the same.
8
60
If possible, reduce the fraction.
50 10
180 10
5
18
The sum is
5
.
18
Give a sentence answer:
26
180
13
90
24 26
180 180
50
180
SUBTRACTING FRACTIONS: The process is the same as with addition, except when you build
equivalent fractions subtract the numerators.
5
MULTIPLYING FRACTIONS
Example: Find the product of
Don’t need a lowest common denominator!
15
24
.
and
16
25
Method 1:
15 24
16 25
Multiply the numerators and denominators and
then reduce the fraction.
360 10
400 10
36 4
40 4
9
is the product
10
Method 2: “Cross-cancelling Method.”
Rewrite each numerator and denominator as a
product of 2 factors. Cancel common factors
between any numerator and any denominator.
3x5 4x6 3x1 2x3
15 24
16 25
3 6
4 5
3 3
2 5
9
is the product
10
4x4 5x5 2x2 5x1
DIVIDING FRACTIONS
Example: Find the quotient of
Don’t need a lowest common denominator!
15
24
.
and
16
25
In essence, rewrite the problem as multiplying by the reciprocal of the 2nd fraction (“flip” the 2nd
fraction).
15
16
24
25
15 25
16 24
Now the process is the same as when multiplying
fractions.
3x5 5x5
15 25
16 24
4x4 3x8
5 25
16 8
125
is the quotient
128