Lesson 2: Fractions II

October 17, 2010
2.1. Finding the Lowest Common Denominator
Sometimes, it is interesting to find a common denominator as low as possible. Some applications of it will be adding and subtracting fractions and ordering fractions.

To find the lowest possible common denominator of 2 or more fractions:

  1. Simplify the fractions if possible
  2. Find the Lowest Common Denominator, which is the Lowest Common Multiple of all denominators.
  3. To work out the new numerator of each fraction, divide the Lowest Common Multiple  by each denominator and multiply the quotient by the corresponding numerator.

 You can undertand the technique on this link by clicking on the picture

fractionsYou can practise on


3. Comparing fractions

To compare fractions we can work out their values (dividing numerator by denominator) and compare them or we can apply the following criteria:

  • If the two fractions have the same denominator, the larger fraction is the fraction with larger numerator.
  • If the two fractions have equal numerator and different denominators, the larger fraction is the fraction with smaller denominator.
  • If the two fractions have different numerators and different denominators we reduce them to their Lowest Common Denominator and we apply the criterion before.


Descending order means from the largest to the smallest (or going down).
Ascending order means from the  smallest to the largest (or going up).

Do you remember signs “>” and “<“?

Sign  >  means  greater ( 2 > 1 means “2 is greater than 1”) 

Sign  <  means  smaller ( 2 < 99 means “2 is smaller than 99”)

Practise and play a funny game on


You will find harder exercises on


4. Operations

 4.1. Adding or subtracting fractions

 To add or subtract fractions with the same denominator you have to do is to add or subtract the numerators.

And it is always a good idea to make your result “nice” by simplifying if possible.


Find 1 + 2
5 5

Both fractions have the same denominator of 5, so we can simply add the numerators:

1 + 2 = 3
5 5 5

 To add or subtract fractions with different denominators we must first make the denominators the same (by finding the Lowest Common Denominator and using equivalent fractions), and finally add or subtract the new numerators and write the new denominator.

 Remember, simplify if possible!

 Here you can see examples step by step and progress  by practising. In order to advance you have to click on the right arrow placed at the bottom of the screen.






Here you are a video on adding fractions very easy to understand


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