Question

The quotient of a number and - 2/3 is -9/10

Answer 1

Hey there!

For this problem, I believe that they're saying that a number divided by –2/3 is equal to –9/10. 

We can tell immediately that the mystery number is a positive number, since two negative numbers being divided by one another will give you a positive quotient. 

For actually solving the problem, you can refer to what you learned (presumably) a while ago about number families:

9 / 3 = 3
3 * 3 = 9

Using that, you can assume the following will get you your mystery number:

x / –2/3 = –9/10
–9/10 * –2/3 = x

For multiplying fractions, all you need to do is multiply the numerators and the denominators together. The denominator doesn't have to be the same on both fractions. 

(–9/10) * (–2/3) = 18/30 = 9/15

To check, all you have to do is remember the original problem:

(9/15) / (–2/3) =
(9/15) * (–3/2) = –27/30 = –9/10

When multiplying fractions, remember that the negative applies to both the denominator and numerator. Also, when dividing fractions, you will multiply the (untouched) first fraction by the second fraction with the numerator and denominator, aka the reciprocal. 

Hope this helped you out! :-)