# ADDING-SUBTRACTING-FRACTIONS

# REVIEW OF ADDING &

SUBTRACTING FRACTIONS

You cannot add or subtract fractions unless they have a
common denominator.

The LEAST COMMON DENOMINATOR is the smallest number that contains

all the prime factors of both numbers.

1) Write the prime factorization of each denominator.

2) Circle all the prime factors of the first denominator.

Go to the next denominator’s prime factorization and
scratch out factors that are

in the first denominator. Then circle all the prime factors of the second

denominator that DON ’T appear in the first denominator's prime factors.

Notice that 21 = 3·7, which has a 3 in the prime factorization. The second

denominator is 18 = 2 ·3 ·3, which has two 3’s. One 3 already appeared in

the prime factorization of 21.

The LCD is the circled factors. LCD = 3·7·2 3=126

3) Rewrite each fraction into an equivalent fraction with
the LCD as the

denominator.

**4) Now perform the subtraction by subtracting the
numerators and leaving
the denominator the same.**

**Example**

Subtract:

Are the denominators, y and 18, the same?

Then, find the LCD of y and 18.

But we don’t know what y is, so how could we know if it goes into

18?

When you have denominators where one is a variable term and the

other is a constant term, find the Least Common Multiple of the

coefficient and the constant , and then find the Least Common

Multiple of the variables.

The coefficient of y is 1. The other denominator is just 18.

What is the LCM of 1 and 18?

Remember, LCM means what’s the smallest number that both 1 and

18 will go into?

LCM = 18 ____

However, the Least Common Denominator will have to include the

the LCM of the variables. Since the other denominator doesn’t have

a variable, the LCD of the variables is just y.

So the LCD is 18y_

Now rewrite each fraction so that the denominator is ____

The new expression which now has like terms is:

Example

Subtract:

Are the denominators, 3y and 6y^{2}, the same?

Then, find the LCD of 3y and 6y^{2}.

The coefficient of 3y is 3. The coefficient of 6y^{2} is 6.

What is the LCM of 3 and 6?

Remember, LCM means what’s the smallest number that both 3 and

6 will go into?

LCM = __6__

However, the Least Common Denominator will have to include the

the LCM of the variables. What’s the LCM of y and y^{2}? _y^{2}

So the LCD is _6y^{2}____

Now rewrite each fraction so that the denominator is ____

The new expression which now has like terms is:

**Add :**

Factor each denominator before finding the LCD.

Like doing prime factorization, we circle the factors in
the

first denominator, and then circle the factors in the second

denominator that are NOT in the first denominator.

**LCD = x(x-2)(x+2)**

Now change each fraction to have the LCD for its

denominator.

**Add :**

Subtract:

Before trying to find an LCD, notice that 3 - x = -(x - 3)

So the expression can be rewritten as:

REMEMBER, when additing fractions, once you have a least

common denominator, you ONLY add the numerators and you

leave the denominator the same.

COMPLEX FRACTIONS are just fractions inside fractions.

They are easily simplified by just multiplying the numerator and

denominator of the “main” fraction by the LCD of all the

fractions.

**Example 1:
Simplify :**

The denominators in this complex fraction are: x, 2, x^{2}
and 4.

Yeah! No more complex fractions!

Now factor this rational expression in order to

cancel common factors and reduce it .

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