Question

What is `4 2/15 - 2 11/45`?

Answer 1

`1 8/9`

Explanation:

`"one way to calculate the difference is to change the"`
`"mixed numbers into improper fractions"`

`4 2/15=((15xx4)+2)/15=62/15`

`2 11/45=((45xx2)+11)/45=101/45`

`4 2/15-2 11/45`

`=62/15-101/45`

`"before we can subtract we require the fractions to have"`
`"common denominators"`

`"multiply numerator/denominator of "62/15" by 3"`

`=186/45-101/45larrcolor(blue)"subtract numerators"`

`=85/45`

`"cancel the fraction by dividing numerator/denominator by 5"`

`=17/9larrcolor(red)"in simplest form"`

`"since the question used mixed numbers, give the solution"`
`"as a mixed number"`

`=1 8/9`

Answer 2

`=1 8/9`

Explanation:

You can subtract fractions by working with the whole numbers first. This keeps the numbers smaller but you sometimes have to convert a whole number to a fraction.

`color(blue)(4) 2/15 -color(blue)(2) 11/45`

`= color(blue)(2) (6-11)/45" "larr` make equivalent fractions with LCD

`= color(blue)(1 +1) (6-11)/45`

`= color(blue)(1 +45/45) +(6-11)/45`

`= 1+ (45+6-11)/45`

`= 1 40/45`

`=1 8/9`

Note: this looks like a long process but the step by step details have been shown for clarity. It can be done as follows:

`= color(blue)(2) (6-11)/45`

`= 1 (color(blue)(45)+6-11)/45`

`=1 40/45`

`=1 8/9`