### ACCUPLACER Review: Elementary Algebra Problem 1 – Mathematics with Dan Avedikian

Bristol Community College, Mathematics with

Dan Avedikian, ACCUPLACER Review, Elementary Algebra Problem 1. This is the Elementary

Algebra ACCUPLACER Review, Problem number 1, we have 2 numbers to multiply, we have

2 and ½ times 3 1/3 and we have 4 possible options that our answer could be. So we have

a positive value times a positive value and 2 of our options are negative. I will eliminate

those right away. Option B is negative 6 and 1/6. It can’t be negative. And option D

is negative 8 1/3. My answer can’t be negative. It has to be one of the 2 positive options.

So if you can eliminate a few that is always good to do on a multiple choice exam. Now

to actually do the multiplication, we can’t multiply it when it’s in this mixed number

form. We have to convert them both to an improper fraction which means just the numerator and

denominator and the numerator is going to be bigger. So this 2 and ½ I am going to

come up this way and multiply the bottom 2 times the front 2. 2 times 2 is 4, and I am

going to take that result of 4 and I am going to add coming up the 4 that I got plus 1 more

that was the numerator so for and 1 more is 5. The denominator stays 2. And that is going

to be multiplied times 3 and 1/3. So same process the denominator of 3 times the 3 that

is in front we will multiply take the answer that we get which is 9 and add coming up to

the top so the 9 that we got plus 1 more is 9 and 1 more is 10, keep the denominator which

is 3. Now we can multiply top times top, bottom time’s bottom. Top times top 5 times 10

is 50. And then bottom time’s bottom 2 times 3 is 6. Now 50 over 6 does not match any of

my options. Since the denominator is 6, I am leaning towards a right away. So we should

try for a better match, than I think it’s a. So first of all, this is even, so I can

at least cut them in half. So half of 50 is 25. And then half of 6 is 3. So now that is

starting to look like option C which has a denominator of 3. That is good why it’s

good to finish it to the end and not just jump at an answer. Now the 25 over 3 still

doesn’t match either of my available options. A is 6 and 1/6 and c which is 8 and 1/3. So

what I want to do is put this back into a mixed number form with a number in front and

a fraction. So 25/3. 24/3 is pretty close. 25/3, 24/3. 24/3 will reduce to 8. And if

I have 24/3, 25/3 is one more 1/3 so 8 and 1/3 which is positive. So the answer is C.

8 and 1/3 is a perfect match once I simplify my answer.