To Change a Mixed Number to an Improper Fraction Multiply the whole number by the denominator of the fraction and add the numerator to this product; write this sum over the denominator.

Example: 56/7 ( 7x5 = 35 ) + 6 = 4/7

Addition of Fractions In order to add fractions, you must determine a common denominator (a number that is evenly divisible by each of the denominators concerned).

Example: 1/2 + 1/3 + 5/6 = ?

1. Multiply the denominators by each other. This gives you a common denominator.

2x3x6 = 36

2. Divide each original denominator into this common denominator and multiply the quotient by the old denominator. This gives you new numerators.

18/36 + 12/36

3. Reduce each fraction to lowest terms.

18/36 + 12/36 + 30/36 = 3/6 + 5/6

4. Add the numerators only, place the sum over the common denominator, and reduce to lowest terms.

3/6 + 2/6 + 5/6 = 10/6 = 14/6 =

Therefore 1/2 + 1/3 + 5/6 = 12/3

## Subtraction of Fractions

1. Establish a common denominator.

2. Subtract one numerator from the other.

3. Reduce to lowest terms.

Example:

9/11 - 3/4 = 36/44 - 33/44 = (36 - 33)/44 = 3/44

Multiplication of Fractions

1. Multiply the numerators to determine the new numerator.

2. Multiply the denominators to determine a new denominator.

3. Write the new numerator over the new denominator and reduce to lowest terms.

Examples:

a. 1/2 x 1/2 = 1/4

b. 2/3 x 3/5 = 6/15 = 2/5

NOTE: If you have a mixed number to multiply, change to an improper fraction and proceed as above.

Example: 2 1/2 x 1 1/4 = 5/2 x 5/4 = 25/8 = 3 1/8

1. Invert the divisor.

2. Change the division sign to a multiplication sign and proceed as in multiplication.

3. Reduce to lowest terms.

Example: 1/4 ÷ 3/4 = 1/4 x 4/3 = 4/12 = 1/3

NOTE: If mixed numbers are involved, change to improper fractions and proceed as above.

Example: 13/8 ÷ 2/5 = 11/8 ÷ 2/5 = 11/8 x 5/2 = 55/16 = 3 7/16

## To Change a Fraction to a Decimal

Divide the numerator by the denominator. Some of the results can be stated in their exact equivalents such as 1/2, 1/4, or 2/5; others will not divide evenly and will be expressed as close approximates.

Examples:

# PERCENTAGE

Percentage means “parts per hundred” or the expression of fractions with denominators of 100. Thus a 10 percent solution may be expressed as 10%, 10/100. 0.10, or 10 parts per 100 parts.

It is often necessary for the pharmacist to compound solutions of a desired percentage strength.

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