Question

Today Ian wants to run less than 7/12 miles. Write a fraction with a denominator of 4 to represent a distance that is less than 7/12 miles.

Answer 1

the answer is 1/4 because 7/12 is larger than 1/2 but 1/4 is 2x smaller

Answer 2

A fraction with a denominator of
`4` that is less than
`(7)/(12)`miles is
`(1)/(4)`.

Explanation:

Let the fraction be

`(x)/(4)`

Since this fraction must be less than
`(7)/(12)` miles, we can write the inequality,

`(x)/(4)\:<\:(7)/(12)`

We now solve the inequality for
`x` to obtain,

`x\:<\:(7)/(12)* 4`

This simplifies to,

`x\:<\:(7)/(3)`

This implies that,

`x\:<\:2(1)/(3)`

This is distance so
`x` must be positive.

So we can choose
`x=1` or
`x=2`.

Therefore the possible fractions include
`(1)/(4)` or
`(2)/(4)`.

In the simplest form, the most appropriate fraction is
`(1)/(4)`