Question

How do you evalaute `\frac { 13} { 15} \div \frac { 2} { 5}`?

Answer 1

`13/6=2 1/6`

Explanation:

To divide two fractions:

1) turn the second fraction upside down ( i.e. find its multiplicative inverse)

2) change the operation from division to multiplication

3) calculate and cancel as required.

`13/15color(blue)(-:2/5)`

`=>13/15color(blue)(xx5/2`

`=>13/cancel(15)^3color(blue)(xxcancel(5)^1/2`

`=13/3xx1/2=(13xx1)/(3xx2)`

`=13/6`

this is top heavy, so change to a mixed number

`13/6->13-:6=2R1`

`:.13/6=2 1/6`

Answer 2

A = `2 1/6`

Explanation:

1. Find a common denominator (the number below the Vinculum)

= `13/15 divide (2*3)/(5*3)`
= `13/15 divide 6/15`

1. With a common denominator now, we can use both the numerators to form a new fraction: (This is personally my way)

= `13/6`

1. Now, we can convert the improper fraction in to a mixed number

= `2 1/6`

All the best!