Grade 8                     Unit 2 Fractions Review

 

1.1  Adding Fractions

 

Adding fractions with the same denominators:

 

Example:             + =

 

When two fractions have the same denominator (in this case 5) we simply add the numerators (1+3) and write the result (4) over the given denominator.

 

Therefore,

 

Adding fractions with different denominators:

 

Example:           

 

When two fractions have different denominators (in this case 3 and 5) we must first find the LCD (least common denominator) which is the LCM (least common multiple of the denominators, in this case the LCD is 15.

 

We then write each of the given fractions as equivalent fractions with a denominator of 15. See below:

 

 &

 

We may now solve the expression as follows:

 

             

 

Symbolically this is shown below.

 

+= +=

 

Note: Now that the denominators are the same, we simply add the numerators as above.

 

1.2  Subtracting Fractions

 

The rules for subtracting are similar to those for addition.

 

Subtracting fractions with the same denominators:

 

Example:             - =

 

When two fractions have the same denominator (in this case 5) we simply subtract the numerators (3-1) and write the result (2) over the given denominator.

 

Therefore,

 

Subtracting fractions with different denominators:

 

Example:

 

When two fractions have different denominators (in this case 5 and 3) we must first find the LCD (least common denominator) which is the LCM (least common multiple of the denominators, in this case the LCD is 15.

 

We then write each of the given fractions as equivalent fractions with a denominator of 15. See below:

 

 &

 

We may now solve the expression as follows:

 

 

Note: Now that the denominators are the same, we simply subtract the numerators as above.

 

Symbolically,

 

-= -=

 

 

1.3  Multiplying With Fractions

 

When multiplying fractions we DO NOT need a common denominator as we do in addition and subtraction of fractions.

 

  1. Simplify the fractions if not in lowest terms.
  2. Multiply the numerators of the fractions to get the new numerator.
  3. Multiply the denominators of the fractions to get the new denominator.

 

Example:

 

In the example above the fraction was first reduced to since we can divide both the numerator and the denominator by 2 (GCF of 4 and 6 is 2).

Also, the “answer” is not in simplest form (since we can divide both the Numerator and denominator by 3) this results in a final answer of .

 

Multiplying a natural number by a fraction:

 

Natural numbers may be written in fractional form where the denominator is 1.

 

Example:

 

Note: The answer in this case was  and improper fraction. We rewrite it as a corresponding mixed number .

 

Symbolically,

 

=

 

1.4  Dividing With Fractions

 

When dividing fractions:

 

  1. Multiply the number by the reciprocal of the fraction.
  2. Simplify the resulting fraction if possible.
  3. Check your answer: Multiply the result you got by the divisor and be sure it equals the original dividend.

Note: To determine the reciprocal of a fraction simply switch its numerator and denominator.

 

Example:   which can be simplified to give  by dividing the numerator and denominator by 3 (the GCF of 12 and 15).

 

Order of Operations With Fractions

 

1.         B – Brackets

2.         E – Exponents

3.         D – Division

M –Multiplication

(In the order they appear left to right.)

4.         A – Addition

S – Subtraction

(In the order they appear left to right.)

 

Example:

 

Solution:

 

                In this example the operation in BRACKETS is to be completed first.

 

                The operation inside the brackets is addition therefore we must write the fractions as equivalent fractions with the LCD 6.

 

                          We add the fractions by adding the numerators (the denominator remains 6)

 

                           We multiply the numerators together and the denominators together.

 

                              This fraction is not in simplest form since the numerator and denominator have a common factor of 6.

 

                                Dividing both the numerator and denominator by 6 gives us our final answer.