#1 - good

#2 - (assuming you don't know algebra)

make a list that match the description:

1/7 , 2/9, 3/11, 4/13, 5/15=1/3 , yeahhh

#3 - good

#4 - why not do what you did in #3, they are the same question.

however , if you picked 20/30 , the HCF would be 10 not 5

so the trick is to first reduce 4/6 to 2/3

now 2/3 -----> 10/15

notice the HCF of 10/15 is 5

and since 4/6 = 2/3 , and 10/15 = 2/3

4/6 <-----> 10/15

#5 no

the smallest prime number is 2, 1 is not considered a prime number, so you want

2/3

#6, the prime numbers are

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, ....

can you find a pair which adds up to 24 ?, then form the fraction

#1 Huh? 1:6/12 = 12/6 = 2

How does that relate to what they said?

You need to set the words to math:

(d-6)/d = 3/4

4(d-6) = 3d

4d-24 = 3d

d = 24

check:

18/24 = 2/3

yes.

As with most skills, with a little practice it gets easier.

#2

n/(2n+5) = 1/3

3n = 2n+5

...

#3

Since 2 and 5 have no factors in common, just make sure 3 is a factor in the equivalent fraction

2/5 = 6/15

GCF = 3, so that works

#4

4/6 .. 4 and 6 do not have 5 as a factor, so

4*5/6*5 = 20/30

However, GCF(20,20) = 10

So, reduce the fraction first to get rid of other factors

4/6 = 2/3

2*5/2*5 = 10/15

Now GCF(10,15) = 5 and 10/15 = 2/3

#5

With one exception, all primes are odd numbers, which differ by at least 2. The only even prime is 2, so the fraction is 2/3

#6

You need two odd numbers whose sum is 24, and they are both primes. So, what are the choices?

3+21, no

5+19, yes

7+17 yes

9+15 no

11+13 yes

That's all we need to check - stop halfway there, because then we start getting repeat values.