Plz help with this problem

[Annie]

Which fraction is between 2/3 and 3/4?
A. 4/7
B. 2/4
C. 7/10
D. 4/5

 

[MarkFL]

Hello, and welcome to FMH!

Let's convert all of the fractions such that they all have the same denominator, like 420. Then the problem becomes:

Which fraction is between 280/420 and 315/420?

A. 240/420
B. 210/420
C. 294/420
D. 336/420

How did I pick 420? 3*4*7*5 = 420...this is the smallest number that all of the given denominators evenly divide.

 

[Steven G]

MarkFl method always works.

There are some shortcuts if the numbers are friendly.

You should know that 2/3 =.666666666 for ever and that 3/4 = .75.

What looks straight at me is 7/10 which is .7
.7 is between .6666666 and .75.

 

[amathproblemthatneedsolve]

Well as Jomo has already answered. My method would be similar(dividing all the fractions to decimals). it might not be the best method but I prefer it.

"You should know that 2/3 =.666666666 forever and that 3/4 = .75."

A. 4/7 = 0.57142 (just use long division)
B. 2/4 = it's just 1/4 + 1/4 which is 0.5
C. 7/10 = 0.7 (this one is easy too)
D. 4/5 = 0.8 (1/5 is 0.2)

 

[HallsofIvy]

Which fraction is between 2/3 and 3/4?
A. 4/7

I would note that 2/3= 4/6 and since 6<7, 4/7< 4/6 so 4/7 is not larger than 2/3 so not between 2/3 and 3/4.

B. 2/4

I hope you immediately recognized that 2/4= 1/2 so is less than 2/3 so is not between 2/3 and 3/4.

C. 7/10

7/10= 0.7 which is between 2/3= 0.666... and 3/4= 0.75.

D. 4/5

4/5= 8/10= 0.8 which is larger than 3/4= 0.75 so is not between 2/3 and 3/4.