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

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Answer 1 · 2017-10-08T04:43:00

$-3/2,-3/7,0.75,2$

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

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: $-3/2,-3/7,0.75,2$

Answer 2 · 2017-10-08T05:27:27

$-3/2 < -3/7 <0.75<2$

Negative numbers are always smaller than positive numbers.

So an initial sort gives us:

$-3/7 and -3/2$ are both smaller than $2 and 0.75$

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

$-3/2 = -1 1/2$ This is between $-1 and -2$ and is therefore to the left of $-3/7$ which is between $0 and -1$

$-3/2 <-3/7$

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

This gives the order as: $-3/2 < -3/7 <0.75<2$

How do you order the following from least to greatest without a calculator 2, -3/7, 0.75, -3/22, -3/7, 0.75, -3/2?