Question

Which of the following shows the correct order for -1 2/5, (-1)^2, -1.4 and (1/2)^2?

A) (-1)^2 < -1.4 < -1 2/5 < (1/2)^2
B) -1.4 < -1 2/5 < (1/2)^2 < (-1)^2
C) -1 2/5 < -1.4 < (1/2)^2 < (-1)^2

Answer 1

The answer is B or C.
`-1.4<-1(2)/(5)<((1)/(2))^2<(-1)^2`

Explanation:

In order to determine the correct order, we have to compare every number with a same way notation.

We can choose between fraction or decimal, but it is much better to compare in fraction, because some fractions could be result in a repeating decimal.

The numbers are:

`-1(2)/(5)=-(1*5+2)/(5)=-(7)/(5)`

`(-1)^2=(1)/(1)`

`-1.4=-(14)/(10)`

`((1)/(2))^2=(1)/(4)`

This time every number has a fraction notation. Then we determine the common denominator of all numbers. The number is 20, so we increase every denominator up to 20:

`(7*4)/(5*4)=-(28)/(20)`

`(1*20)/(1*20) =(20)/(20)`

`-(14*2)/(10*2)=-(28)/(20)`

`(1*5)/(4*5)=(5)/(20)`

Then, to compare fractions, if all fractions have the same denominator, we have to compare the numerator. The order is:

`-(28)/(20)=-(28)/(20)<(5)/(20)<(20)/(20)\\-1.4=-1(2)/(5)<((1)/(2))^2<(-1)^2`

Every possible option is wrong but the most close answer is B or C.

`-1.4<-1(2)/(5)<((1)/(2))^2<(-1)^2`

Answer 2

To answer this question you have to make some calculations that permit makind the comparisson to place the numbers in order.

1) -1 2/5 is - (1 and 2/5) = - (1 + 2/5) = - (5 + 2)/5 = - 7/5

2) (-1)^2 = 1

3) -1.4 = - 14/10 = -7/5

4) (1/2)^2 = 1/4

So,

1) - 1.4 = - 7/5;
2) all the negative numbers are less than any positive numbers.
3) the fraction 1/4 is less than 1.

Therefore, the order is: -1.4 = - 7/5 < 1/4 < (-1)^2.

That option is not among the answers, so there is an error either in the statement of the question or in the set of choices.

Answer: -1.4 = - 7/5 < 1/4 < (-1)^2