# How do you order the following from least to greatest without a calculator 2, -3/7, 0.75, -3/2?

Oct 8, 2017

$- \frac{3}{2} , - \frac{3}{7} , 0.75 , 2$

#### Explanation:

First, let's make all these common to decimals just to make it easier:
$2.0 , - 0.42 \ldots , 0.75 , - 1.5$

The smallest number here is $- 1.5$

The largest number here is $2.0$

Least to greatest (in decimal form is): $- 1.5 , - 0.42 , 0.75 , 2.0$

Least to greatest in the original form would be: $- \frac{3}{2} , - \frac{3}{7} , 0.75 , 2$

Oct 8, 2017

$- \frac{3}{2} < - \frac{3}{7} < 0.75 < 2$

#### Explanation:

Negative numbers are always smaller than positive numbers.

So an initial sort gives us:

$- \frac{3}{7} \mathmr{and} - \frac{3}{2}$ are both smaller than $2 \mathmr{and} 0.75$

On the number line, numbers decrease to the left and increase to the right.

$- \frac{3}{2} = - 1 \frac{1}{2}$ This is between $- 1 \mathmr{and} - 2$ and is therefore to the left of $- \frac{3}{7}$ which is between $0 \mathmr{and} - 1$

$- \frac{3}{2} < - \frac{3}{7}$

$0.75$ is a proper fraction and is between $0 \mathmr{and} 1$ and is smaller than the whole number $2$

This gives the order as: $- \frac{3}{2} < - \frac{3}{7} < 0.75 < 2$