Question #09eb7

First convert `2/7` to a whole number.

It can be done by multiplying it by `7` = `2/7xx7` = `2`

As, the ratio has to be kept same, `7` has to be multiplied to `6` as well = `7xx6` = `42`

Now ratio of `2/7`:`6` is same as `2`:`42`

To make `2`:`42` in the simplest form, divide it till it can only be divisible by `1` or by itself.

So, for `2`:`42`, divide both sides by `2` and you get `1:21`

A ratio is always given as a comparison between whole numbers. There may not be any fractions or decimals.

A ratio should also always be in the simplest form,

Write the given ratio with both values as fractions:

`2/7" ":" " 6/1`

To get rid of any denominators, multiply each part by the `LCD` which in this case is `7`

`2/7color(blue)(xx7/1)" ":" " 6/1color(blue)(xx7/1)`

Cancel the denominators and simplify:

`2/cancel7color(blue)(xxcancel7/1)" ":" " 6/1color(blue)(xx7/1)`

`2" ":" " 42`

Divide both sides by the `HCF`, which in this case is `2`

`2 div 2" ":" "42 div2`

`" "1" ":" "21`

A ratio is actually a fraction
Setting the problem up as a complex fraction makes the problem easier to understand.

The complex fraction of the ratios would be

`(2/7)/ (6/1)`

To simplify the complex fraction multiple both the top and the bottom fractions by the inverse of the bottom fraction. The product of a fraction and its inverse is one simplifying the fraction.

`( 2/7 xx 1/6)/ (6/1 xx 1/6) = 2/42`

Dividing out the common factor of 2 will simplify the answer into its simplest form

`( 2/2)/(42/2)= 1/21`

The ratio in its simplest form is
1:21