Question

How do you subtract `5 1/16 - 1 13/18`?

Answer 1

`3 49/144`

Explanation:

There are 2 possible approaches to this calculation, both made fairly 'awkward' due to the values on the denominators of the fractions.

`color(red)"Approach 1"`

Change the `color(blue)"mixed numbers " "to "color(blue)"improper fractions"`

`rArr5 1/16=81/16" and "1 13/18=31/18`

The calculation is now.

`81/16-31/18`

Before we can subtract the fractions we require them to have a
`color(blue)"common denominator"`

We have to find the `color(blue)"lowest common multiple"` ( LCM) of 16 and 18

The LCM of 16 and 18 is 144

`rArr81/16xx9/9=729/144" and "31/18xx8/8=248/144`

`rArr729/144-248/144larrcolor(red)" is now the calculation"`

Since the denominators are now common we can subtract the numerators, leaving the denominator as it is.

`rArr729/144-248/144=(729-248)/144`

`=481/144=3 49/144larrcolor(red)" returning a mixed number"`

`color(red)"Approach 2"`

`"Using the fact that "5 1/16=5+1/16;1 13/18=1+13/18`

`"Then "5 1/16-1 13/18`

`=5+1/16-(1+13/18)=5+1/16-1-13/18`

We can now subtract the numbers and subtract the fractions separately.

`rArr5+1/16-1-13/18=(5-1)+1/16-13/18`

`=4+(1/16xx9/9-13/18xx8/8)`

`=4+(9/144-104/144)`

`=4+(-95/144)`

`=4-95/144`

`=576/144-95/144`

`=481/144`

`=3 49/144larrcolor(red)" as a mixed number"`