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

Question

6488 views around the world

You can reuse this answer
Creative Commons License

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#