Question

6/7=1/7+5/3r

Answer 1

6/7 =1/7 +5/3r
6/7 -1/7=5/3r
5/7 =5/3r
15r=35
r=35/15 =7/3

Answer 2

which one?

Answer 3

6/7=1/7+(5/3)(r)
(I find that it helps beginners to separate multiplication with parenthesis to make sure that you have the set up right.) Anyway, first you subtract 1/7 from both sides

6/7-1/7=5/7 Since they both have the same denominator (bottom number), you can just add/subtract the numerator (top number)

5/7=(5/3)r
Now divide by the quantity that is being multiplied by the r and you get the problem: (5/7)/(5/3)
When dividing by a fraction, it is often easier to think of it as multiplying by the reciprocal (which is basically the fraction flipped upside down where the numerator is the denominator and vise versa). So we then are looking at (5/7)(3/5)

You can either simplify here or later. I always like to simplify at then end to avoid making mistakes in harder problems. So, 5(3)=15 and 7(5)=35. Thus you are left with

r=15/35 or (simplified) r=3/7