A fraction consists of two parts, a numerator (top number) and a denominator (bottom number). A proper

fraction is a fraction in which the numerator is less than the denominator. An improper fraction has a

numerator larger than the denominator.

Fraction = Numerator

Denominator

When adding or subtracting fractions, the denominator in each fraction must always be the same number.

1+ 1= 2

3

3

3

When denominators are not the same, the Least Common Denominator (LCD) must be found. One way to

find the LCD is to multiply the denominators together.

1+ 1

2 3 = 2x3=6

Now change all denominators to 6. Multiply the first fraction by 3/3 (since 3/3 is the same as 1, it does not

affect the value of the fraction).

3

1= 3

3 x2

6

To change the second fraction to sixths, multiply the fraction by 2/2.

1

2= 2

3 x 2

6

Now both denominators are equal and you can add the fractions.

3

2= 5

6 + 6

6

Another way to find the LCD is to divide the smaller denominator into the larger one.

3

1

4 + 8 = 8,,4=2

If the number divides evenly then the larger number is the LCD. For this problem, you now have to change

all the denominators to 8.

3

1

6

1

7

4 + 8 =8 + 8 = 8

To multiply a fraction, just multiply across (numerator times numerator; denominator times denominator).

3 5 = 15

4 x7

28

When multiplying many fractions, a method called cancellation can be used to simplify the process.

Cancellation is simply the striking out or reduction of numerators and denominators by dividing.

To divide fractions, turn over the divisor and multiply. Use cancellation to speed up the process.

3 ,, 9 = 3 x 64 = 1 x 4 = 4 = 1 1/3

16 64

16

9

1 3 3

A mixed number is a whole number and a fraction. To add or subtract mixed numbers you must first reduce

them to improper fractions and find the LCD. To multiply mixed numbers reduce them to improper fractions

and multiply.

Example: 1 1/8 + 3 3/8 = 4 4/8 = 4 1/2

To convert a fraction to a decimal divide the denominator into the numerator. The answer can be brought

out to as many decimal places as accuracy requires.

Example: 1/4 = 1,,4 = .25

9-3

QM 5092