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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

Respuesta :

Edufirst
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

Answer:

The answer is B or C. [tex]-1.4<-1\frac{2}{5}<(\frac{1}{2})^2<(-1)^2[/tex]

Step-by-step 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:

[tex]-1\frac{2}{5}=-\frac{1*5+2}{5}=-\frac{7}{5}[/tex]

[tex](-1)^2=\frac{1}{1}[/tex]

[tex]-1.4=-\frac{14}{10}[/tex]

[tex](\frac{1}{2})^2=\frac{1}{4}[/tex]

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:

[tex]\frac{7*4}{5*4}=-\frac{28}{20}[/tex]

[tex]\frac{1*20}{1*20} =\frac{20}{20}[/tex]

[tex]-\frac{14*2}{10*2}=-\frac{28}{20}[/tex]

[tex]\frac{1*5}{4*5}=\frac{5}{20}[/tex]

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

[tex]-\frac{28}{20}=-\frac{28}{20}<\frac{5}{20}<\frac{20}{20}\\-1.4=-1\frac{2}{5}<(\frac{1}{2})^2<(-1)^2[/tex]

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

[tex]-1.4<-1\frac{2}{5}<(\frac{1}{2})^2<(-1)^2[/tex]

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