Operations with fractions

Addition
The concept of addition is the same for fractions as for whole numbers.  When adding whole numbers your combining two sets of objects.  When adding fractions your combining two amounts.

Unlike denominators
Finding the least common denominator
http://www.onlinemathlearning.com/adding-fractions-2.html

Addition of fractions for fractions a/b and c/d
a + c = ad + bc = ad + bc
b    d    bd    bd         bd

Mixed numbers
They are the combinations of wholes numbers and fractions.  The sum of two mixed numbers can be found by adding the whole umbers and the fractions speratly.  If the denominators are unequal you must find a common denominator

Exaples on adding fractions
http://www.themathpage.com/arith/add-fractions-subtract-fractions-1.htm

Subtraction
Make sure the denominators are the same.  Then subtract the numerators and put the answer over the same denominator.

Examples on subtracting fractions with unlike denominators
http://cuip.uchicago.edu/~jwoods/wit/fsubex2.htm

Examples on subtracting mixed numbers

http://www.youtube.com/watch?v=yXiG2iv1Vq8

Multiplication

 whole number times a fraction (repeated addition)

 

• First change 3 into a fraction (1/3)
• Multiply the numerateor (3x3)=9
• Multiply the denominator (1x4)=4

The answer is 9/4

Whole number times a fraction

k x a= ka

      b    b

Example

3 x 2 = 3(2) = 6 = 2

      9      9       9     3

Fraction times a fraction

2/3 x 1/7

• Multiply numerators (2x1) = 2
• Multiply denominators (3x7) =21
• The answer is 2/21

Division

a/b  and c/d when c/d does not = 0

a/b divided by c/d = a/b x d/c = ad/bc

Great video explaining how to divide fractions

http://www.youtube.com/watch?v=OGUaN-F80NA