Question

Susie has a bag with 8 hair pins, 6 pencils, 2 snacks, and 4 books. What is the ratio of books to pencils?

Answer 1

Ratio of books to pencils is `2/3` or written as 2:3

Explanation:

There are:

6 pencils
4 books

So the ratio of books to pencils is 4:6`larr" "`format some people use

Write this as `("books")/("pencils")-> 4/6`

But this is not in its simplest form as 2 will divide exactly into both numbers.

Divide top and bottom by 2 giving

`("books")/("pencils")-> (4-:2)/(6-:2) =2/3`

Ratio of books to pencils is `2/3` or written as 2:3
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("A further note just for information")`

This business of `4/6" being the same as "2/3` has a proper mathematical term.

They are 'equivalent fraction' as the answer to `4-:6` is exactly the same as the answer to `2-:3`

The correct way to write 'equivalent fractions' is `4/6-=2/3`

A lot of people write `4/6=2/3`

Answer 2

2:3

Explanation:

A ratio is a way of comparing 2 or more quantities.

A ratio may be expressed in 2 ways.

`color(orange)"(1) As a fraction"`

We require the ratio `color(red)"books"/color(blue)"pencils"`

Which 'looks' like a fraction, and if we insert the appropriate values.

That is `color(red)"books=4" " and " color(blue)"pencils=6"`

Then the ratio as a fraction is `color(red)"4"/color(blue)"6"`

This may be 'simplified' in the usual way by 'cancelling'.

`rArrcolor(red)cancel(4)^2/color(blue)cancel(6)^3=2/3`

`color(orange)"(2)Using a colon"`

instead of saying 2 'to' 3 we write 2:3 (which is read as 2 to 3)

Hence ratio = `color(red)"4":color(blue)"6"`

In this form we can multiply or divide each term in the ratio by the same number ( but not zero ).

Dividing each term by 2 the ratio becomes `4:6=2:3`

The ratio may be written as `2/3" or " 2:3`