please solve 5/6÷X=3 4/7 step by step

Question

Please show me step by step, thanks

Answer 1

please solve 5/6÷X=3 4/7 step by step

5/6÷X = 3 4/7       convert to improper fraction

5/6÷X = 25/7        divide both sides by 5

1/6÷X = 5/7          cross-multiply

7÷X = 6*5

7÷X = 30             multiply both sides by X

7 = 30X               divide both sides by 30

7/30 = X

Answer: X = 7/30

Answer 2

Convert the mixed number on the right to an improper fraction: 25/7 (=(7*3+4)/7). 

(5/6)/X=25/7. Divide both sides by 5: (1/6)/X=5/7. This can be written 1/(6X)=5/7. Turn the fractions upside down: 6X=7/5 so X=7/30 (dividing both sides by 6).

Another way to do it: after converting to an improper fraction and dividing by 5, multiply both sides by X: 1/6=5X/7. Multiply both sides by 42 (LCD of 6 and 7): 7=30X. Divide both sides by 30: 7/30=X so X=7/30.