Name the fraction that makes the following true.?

Question

1) a/b x = 30 2) 3a/2b x = 30 times 3/2 3) x = 45

Answer 1

Hi,

a/b = 2/3 because

2/3 * 45 = 30

(3*2)/(2*3) * 45 = 30 * 3/2

45 = 45

I hope that helps!! :-)

Answer 2

x = 45 -- replace that in all the problems

a/b (45) = 30
45a/b = 30
a/b = 30/45
if a = 30 and b = 45 then
a/b = 30/45

basically any multiple of 2/3 will work
a = 2, b = 3
a = 4, b = 6

etc etc

lets put this into the second problem
a = 30, b = 45, x = 45
3a/2b (x) = 30 * 3/2
(3*(30)*(45))/(2*45) = 30 * 3/2
(90*45)/90 = 90/2
45 = 45

so a = 30, b = 45, x = 45 is a fraction that makes all of the following true
or a = 2, b = 3, x = 45 will work as well

Answer 3

a/b = 2/3

Answer 4

2/3;

1) 2/3(45) = 30
2) 30(3/2)= 45: (3a)/(2b) (45) = 45

divide by 45

(3a)/(2b) = 1
(3/2)(a/b) = 1

divide by a/b
3/2=b/a
a/b=2/3