Question

. Multiply to find the quotient of the original problem. Show your work. (2 points)

Answer 1

`\sf (5)/(9)`

Explanation:

`\sf (2)/(3) / (6)/(5)`

In order to find the quotient of this we can follow these steps:

Invert the divisor to find its reciprocal:

`\sf (6)/(5) \textsf{ to } (5)/(6)`

We can rewrite the division as multiplication by the reciprocal:

`\sf (2)/(3) / (6)/(5) = (2)/(3) * (5)/(6)`

Multiply the fractions:

`\sf (2)/(3) * (5)/(6) = ((2 * 5))/((3 * 6)) = (10)/(18)`

Simplify the fraction by finding the greatest common divisor (GCD) of 10 and 18, which is 2. Divide both the numerator and denominator by 2:

`\sf (10)/(18) = (10 / 2)/(18 / 2) = (5)/(9)`

So, the quotient is:

`\sf (5)/(9)`