Question

Find a number that is between 7/11 and 0.75 .

A. 25/44


B. 77/99


C.23/33


D.76/99

help please!

Answer 1

Let's first change .75 to a fraction:

.75 = 75/100 = 3/4

Do you agree @kira12341234 ?

Answer 2

So now, the question becomes

Find a number between 7/11 and 3/4

The easiest way to deal with this is to use equivalent fractions to re-write each fraction in a way so that the denominators of both are the same.

Answer 3

Notice that the Least Common Denominator or LCD is the Least Common Multiple of 4 and 11. \(4 \times 11 = 44\)

Answer 4

Multiply 7/11 by 4/4 and 3/4 by 11/11 to get

28/44 and 33/44

Answer 5

so in essence we need to find a fraction, x, such that

\(\dfrac{28}{44} < x < \dfrac{33}{44}\)

Answer 6

From here, one approach you can take is cross multiplication

Answer 7

We know that 25/44 won't work, so we won't bother with that.

Answer 8

Also, let's not forget that we can reduce the fractions in the given choices.

Answer 9

77/99 = 7/9

Answer 10

So let's see if

\(\dfrac{7}{11} < \dfrac{7}{9} < \dfrac{3}{4}\) will work

Answer 11

Notice that if we cross multiply 7/11 < 7/9 we get

63 < 77 which is true

If we cross multiply 7/9 < 3/4 we get

28 < 27 which is false so that doesn't work

Answer 12

Next test:

\(\dfrac{7}{11} < \dfrac{23}{33} < \dfrac{3}{4}\)

Answer 13

Cross multiply 7/11 < 23/33 to get

231 < 253 which is true

and then

23/33 < 3/4 to get

92 < 99 which is also true

So the correct answer is 23/33