Fractions

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Enter expression, e.g. (x^2-y^2)/(x-y)

Enter expression, e.g. x^2+5x+6

Enter expression, e.g. (x+1)^3

Enter a set of expressions, e.g. ab^2,a^2b

Enter equation to solve, e.g. 2x+3=4

Enter equation to graph, e.g. y=3x^2-1

Depdendent Variable

Number of equations to solve:

Equ. #1:

Equ. #2:

Equ. #3:

Equ. #4:

Equ. #5:

Equ. #6:

Equ. #7:

Equ. #8:

Equ. #9:

Solve for:

Enter inequality to solve, e.g. 2x+3>4

Enter inequality to graph, e.g. y<3x^2-1

Dependent Variable

Number of inequalities to solve:

Ineq. #1:

Ineq. #2:

Ineq. #3:

Ineq. #4:

Ineq. #5:

Ineq. #6:

Ineq. #7:

Ineq. #8:

Ineq. #9:

Solve for:

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A. Parts of a fraction:

The numerator represents the number of parts of the unit being used.

The denominator represents the total number of parts within the one whole unit.

B. Types of fractions:

1. Proper fractions: fractions where the numerator is less than the denominator.

Examples include:

2. Improper fractions: fractions where the numerator is greater than the denominator.

Examples include:

3. Mixed number fractions: numbers that contain a whole number and a fraction.

Examples include:

4. Fractions in lowest terms: fractions where the numerator and denominator cannot be divided by a common number.

Examples include:

Examples of fractions that are not in lowest terms include:

a. because 5 and 10 are both divisible by 5 to become

b. because 5 and 10 are both divisible by 5 to become

Operations with fractions:

When ADDING or SUBTRACTING FRACTIONS, all denominators have to be the same number. If all denominators are not the same, you must find the lowest common denominator. The lowest common denominator is the smallest number that all the denominators will divide into evenly. After you find the common denominator, you must change each fraction into an equivalent fraction. An equivalent fraction has the same value as the original fraction but accommodates the new denominator. Once you find the common denominator and change the fractions into equivalent fractions, ADD or SUBTRACT the numerators, but do not add or subtract the denominators. Keep the common denominator as part of the answer. Reduce the answer to its lowest term if needed.

ADD:

Find the lowest common denominator, lcd.

15 is the lcd. Make the equivalent fractions. 3 will divide into 15

5 times. 5 times 2 = 10…. 5 will divide into 15

3 times. 3 times 4 = 12.

Add the numerators and keep the denominator. Reduce answer

to its lowest term.

When multiplying and dividing fractions, it is not necessary to find a common denominator. When multiplying fractions, multiply numerators together then multiply denominators together. Simplify the resulting fraction to its lowest term.

Ex:

Note: Cancellation may be used if any numerator will simplify with any denominator.

Ex: the numerator 2 will divide into itself 1 time and into the denominator 8 times.

Ex:

Divide: When dividing fractions, invert the second fraction and multiply.

Ex: