Question

What is the quotient of three-fourths and startfraction 5 over 6 endfraction?

1) three-fourths
2) startfraction 9 over 10 endfraction
3) 4 and one-half
4) cannot be determined

Answer 1

To find the quotient of three-fourths (3/4) and five-sixths (5/6), you multiply 3/4 by the reciprocal of 5/6, which is 6/5, to get 18/20, and then simplify to 9/10.

Step-by-step explanation:

The question is asking to find the quotient of two fractions: three-fourths (3/4) and five-sixths (5/6). To divide fractions, you multiply the first fraction by the reciprocal (the inverse) of the second fraction. In this case, the reciprocal of 5/6 is 6/5. So, you would multiply 3/4 by 6/5:

3/4 × 6/5 = (3 × 6) / (4 × 5) = 18/20

Now, simplify this fraction by dividing both the numerator and the denominator by their greatest common factor, which is 2:

18/20 = (18÷2)/(20÷2) = 9/10

Therefore, the quotient of three-fourths and five-sixths is 9/10.