Question

1/2 < ___< 4/5 a. 1/3 b.2/4 c. 2/3

Answer 1

To solve for this, we need to figure out the value of each fraction.

Let's put the fractions into decimals.
1/2 = 0.5
4/5 = 0.8

Our inequality is:

0.5 < x < 0.8
Now let's convert our answers into decimals.

1/3 = 0.33
2/4 = 0.5
2/3 = 0.66

1/3 doesn't work, as it's less than 0.5, and we are looking for a number that's greater than 0.5 but less than 0.8.

2/4 doesn't work because 0.5 isn't greater than 0.5, they're equal.

2/3 works because 0.66 is greater than 0.5 and less than 0.8

Your answer is C.) 2/3
I hope this helps!

Answer 2

There are several ways in which you might attack this problem.  One is to eliminate improbable answers until you are left with one answer.  Note that 1/3 is not greater than 1/2, so we must eliminate answer a.  Note that 2/4 is equal to 1/2, so we must also eliminate answer b.  That leaves 2/3 as the correct answer.

Another approach would be to convert all of these fractions so that every denominator is the LCD.  Here the LCD is 60.

Then:  30/60 < _____ < 48/60     a.  20;  b.  30/60;  c.  40/60.  Again, c is the correct answer.