Answer:
The last one, (1/2)^2 < 2/3 < 0.75
Explanation:
So lets try to put each number in the same form, and see what their values are.
Lets start with (1/2)^2
This is squaring the 1 and 2 in 1/2. 1^2 is 1. 2^2 is 4. So its now:
1/4
Lets look at the others:
2/3
Lets just give it a common denominator. To do this, lets find the lowest number that both 3(from 2/3) and 4(from 1/4) go into. This is also known as the LCM.
This will be 12.
Since 3(from 2/3) goes into 12 4 times, we multipy both numerator and denominator of 2/3 by 4:
4*2=8, 3*4=12:
8/12
Since 4(from 1/4) goes into 12 3 times, we multiply both the numerator and denominator by 3:
1*3=3, 4*3=12:
3/12
So lets just go over what we know so far:
(1/2)^2 = 3/12
2/3 = 8/12
Now lets find our last value:
0.75
When converted into fraction form, we will get:
3/4
We already have a LCM, which is 12, that goes into this.
The denominator goes into 12 3 times, so again, we multiply numerator and denominator in this:
3*3=9, 4*3=12:
9/12
So:
(1/2)^2 = 3/12, 2/3 = 8/12, and 0.75 = 9/12
3/12 is smaller than 8/12, and 8/12 is smaller than 9/12. This can be written as:
3/12 < 8/12 < 9/12
And this basically means that:
(1/2)^2 < 2/3 < 0.75
This is the last answer in your answer list.
Hope this helps!