Question

How do you determine which fraction is greater 3/7 or 4/9?

Answer 1

Divide one into the other. The resulting value will indicate which is the greater: `color(white)(....)4/9>3/7`

Explanation:

Consider `4/9-:3/7` giving:

`4/9xx7/3 =28/27` which is greater than 1 so

`4/9>3/7`

Answer 2

`3/7 < 4/9`

Explanation:

A quick method is to cross multiply the fractions.

However, this only works if you multiply in the same direction every time. `color(red)("Red x Red")` first as shown below:

`color(red)(3)/color(blue)(7) and color(blue)(4)/color(red)(9)`

`color(red)(3xx9) and color(blue)(7xx4)`

`color(red)(27) < color(red)(28)`

`color(red)(3/7) < color(blue)(4/9)`

An alternative method is to get rid of the denominators

`xx LCD" "` which in this case is 63

`cancel63^9/1 xx3/cancel7 and cancel63^7/1xx4/cancel9`

`27 < 28`

`3/7 < 4/9`

Worst method - use a calculator!

Use a calculator to change them into decimals, then compare.

`3/7 = 0.42857...." "larr` smaller

`4/9 = 0.44444..." "larr` larger

You can also use a calculator to subtract the two fractions.
If you get a positive answer, then the first fraction was bigger.
If you get a negative answer then the first fraction was smaller.