Mark B. answered • 01/23/19

PhD Candidate and Math Tutor with 20 Years of Experience: All levels.

Good Morning, Alisa,

To determine the number of years Tina lived in the city, you must multiply her age by the amount of time she lived in the city which is stated in the problem as 4/9. Therefore:

18 * 4/9 =

Alisa, you will notice that the number 18, is the exact same as 18/1 which you will multiply 4/9's by.

Therefore:

18/1 * 4/9 =

Please notice that the denominator of the second fraction is 9, and also note that 9 goes into 18 the numerator of first fraction twice.,

When doing this you are now left with the following:

2/1 * 4/1 = 8

Please note that we simply multiply the numerators and denominators, meaning you will multiply 2 and 4 - the numerators - and 1 and 1 - the denominators, leaving you with 8.

Finally, one way to check your work is to multiply 5/9 by 18, Doing so, allows you to determine the number of years Tina **did not live in the city? **Why? Because if Tina lived 4/9 of her life in the city, then the remainder of her life - 5/9 - is the number of years Tina lived outside of the city, right? (4/9 + 5/9 = 9/9 which equals 1).

5/9 * 18/1 = 5 *18/9*1 = 90/9 which is the exact same as 10. Also, please note: we could easily use the same method I initially used in the first part of the solution. Do you remember what we did then? We divided the denominator of one fraction into the numerator of the other fraction. Beginning with 5/9 * 18/1, we simply divide the 9 into the eighteen which provides the following result: 5/1 * 2/1 which equals 10. When we add the ten to the eight, we arrive at 18 which accounts for Tina's entire life while checking our previous answer.

My deepest apologies for the length of my solution, however as a tutor I feel an obligation to explain everything so you can remember the process. I sincerely hope I have assisted you and wish you a great ending to your week. Should you need further clarity to the solution, wish to leave feedback, or have further questions, please just click the "Add Comment" prompt and your information will populate beneath this solution. Should you need one on one tutoring, please do not hesitate to reach out to me or **any** tutor. Best!