Fractions, decimals and percentages:
Operations with fractions.
3rd year of secondary education.

Adding and subtracting fractions

In the mid-seventies the Hungarian architect Erno Rubik invented a magic cube, the Rubik's cube. The cube, illustrated on the right, is one of the most difficult and popular puzzles of all time.

It is made up of 27 little cubes. There are 3 cubes on each edge, so 33 =27. 

Each layer represents 1/3 of the cube; there are 8 corner cubes that have three faces showing, each one of a different colour, and these represent 8/27 of the cube. There are also 12 edge cubes that have two faces showing, each of a different colour, and these represent 12/27 of the cube.

How many little cubes are there in the centre of each face of the cube that only have one colour showing? What fraction of all the little cubes do these cubes represent?

How many little cubes are there that cannot be seen, i.e. have no colour face showing? What fraction of all the little cubes do they represent?

Remember that as the total number of little cubes is 27, when you add up all your fractions you should get a total of 27/27, or 1. This is because all the little cubes together make up the complete big cube.

Divide this unit in 27 parts (use the button at the bottom) and shade in 8 of these parts (by dragging point A). 

We now have the corner cubes represented: 8/27.

Now we are going to add the 12 two-coloured cubes, again dragging point A, until we get to 20/27.

Carry on selecting the different types of little cubes until you make up the complete UNIT.

From this we can reach the following conclusion:

To add fractions ensure that they have the same denominator.

If the fractions have the same denominator, add the numerators together and leave the denominator as it is.

If the fractions have a different denominator change them so that they have a common denominator and then repeat the same process as above.

Use this window for the following exercise.

Click on sol-1 to find out the sum of the fractions that have the SAME DENOMINATOR.

Introduce the lowest common multiple (LCM) of the two denominators for the fractions with DIFFERENT DENOMINATORS and then click on sol-2 to find out the sum.

NOTE: It is not a problem if you introduce a common multiple which is not the lowest of the denominators. However, if you introduce a number which is not a common multiple of the denominators all the workings out will be incorrect.

Exercise 5

Add the following fractions and check your answers in the this window.

a) 2/7 + 3/7
b) 2/3 + 5/7
c) 7/9 + 4/6
d) 7/6 + 9/6

You subtract fractions in the same way as you add them, but instead of adding the numerators you subtract them.


TO ADD fractions with the same denominator:

fracciones2_01.gif (1200 bytes)

TO SUBTRACT fractions with the same denominator:

fracciones2_02.gif (1177 bytes)

Exercise 6

Subtract the following fractions and check your answers in this window:

a) 3/4 - 3/5
b) 3/5 - 4/5
c) 37/18 - 14/9
d) 37/9 - 18/9

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  Ángela Núñez Castaín
Spanish Ministry of Education. Year 2001

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