# 1.06.01 Multiplying fractions

This is a very simple procedure. You just multiply the numerators and denominators of the fractions individually to produce the answer which is then expressed in its lowest form.

examples

- 2/5 x 3/4 = ?
- 2 x 3 = 6
- 5 x 4 = 20
**2/5 x 3/4 = 6/20**- 6/20 = 3/10 in its lowest form

- 3/7 x 4/5 = ?
- 3 x 4 = 12
- 7 x 5 = 35
**3/7 x 4/5 = 12/35**

**Simplifying the problem**

To keep the result of the multiplications as small as possible both fractions being multiplied should be in their lowest form. This is done as shown earlier by dividing where possible the numerator and denominator of each fraction by a common number (greater than 1) before carrying out the multiplication. In fact we can extend this method by also dividing where possible the numerator of one fraction and the denominator of the other fraction by a common number (greater than 1). If this is done as far as possible then the multiplications carried out will be as simple as possible and the answer obtained will give a fraction that is already in its lowest common form.

example

- 3/8 x 4/24 = ?
- 3/8 is already in its lowest form
- 4/24 :- dividing both numerator and denominator by 4 gives 1/6
- Therefore 3/8 x 4/24 = 3/8 x 1/6
- The numerator of the first fraction and the denominator of the second can both be divided by 3
- Therefore 3/8 x 4/24 = 3/8 x 1/6 =
**1/8 x 1/2** - 1 x 1 = 1
- 8 x 2 = 16
- 1/8 x 1/2 = 1/16
**Therefore 3/8 x 4/24 = 1/6**

# 1.06.02 Dividing fractions

This is again a very simple procedure. You just invert the second fraction and multiply as shown previously.

examples

- 2/3 divided by 1/3 = ?
- 2/3 x 3/1 = ?
- 2 x 3 = 6
- 3 x 1 = 3
- 2/3 x 3/1 = 6/3
- 6/3 = 2
**Therefore 2/3 divided by 1/3 = 2**

- 4/5 divided by 1/6 = ?
- 4/5 x 6/1 = ?
- 4 x 6 = 24
- 5 x 1 = 5
- 2/3 x 3/1 = 24/5
- 24/5 = 4
^{4}/_{5} **Therefore 4/5 divided by 1/6 = 4**^{4}/_{5}