Question

How do you add `4\frac { 1} { 8} + 3\frac { 2} { 3} + 5\frac { 1} { 2}`?

Answer 1

`13 7/24`

Explanation:

`"A "color(blue)"mixed number"` is made up of a whole number and a fraction, being added to it.

One way of adding them is to ADD the whole number parts together and the fraction parts together and combine the 2 results.

`rArr4 1/8+3 2/3+5 1/2`

`=4+1/8+3+2/3+5+1/2`

`=4+3+5+(1/8+2/3+1/2)`

`=12+(1/8+2/3+1/2)larrcolor(red)" whole numbers added"`

Before adding the fractions, we require them to have a `color(blue)"common denominator".` That is the same value on the denominator of each fraction.

This can be achieved by finding the `color(blue)"lowest common multiple"`
( LCM) of 8 , 3 and 2

The LCM of 8 , 3 and 2 is 24

We can change each fraction to this denominator.

`(1/8xx3/3)+(2/3xx8/8)+(1/2xx12/12)`

`=3/24+16/24+12/24`

Now they have a common denominator, we can add the numerators, leaving the denominator.

`rArr(3+16+12)/24=31/24=1 7/24larrcolor(red)" fractions added"`

Combing the 2 additions.

`rArr12+1 7/24=12+1+7/24=13 7/24`