Question

Evaluate the expression shown below and write your answer as a fraction in simplest form. Please

Answer 1

`(22)/(21)`

Explanation:

Firstly, we can see that this equation contains multiple different operators (in this case division and addition). So, we must keep in mind the order of operations. This can be remembered as PEMDAS or Paraenthasis, Exponents, Multiplication, Division, Addition, and Subtraction. When working on the problem using PEMDAS ALWAYS start from P and work your way down. PEMDAS is just used to determine the order in which a problem should be solved.

In our equation we have
`(2)/(3) / ( (3)/(11) +(4)/(11))`

So, by using PEMDAS we can see that we first need to deal with what is in the parathesis.

We can do this by adding the two fractions together, which will give us
`(7)/(11)`

We can add these together because the denominator or bottom numbers are the same.

Now we will have
`(2)/(3) / (7)/(11)`

Now, we can use a math trick called keep it, change it, flip it to solve for the answer.

The first fraction, 2/3, will remain the same (this is the keep it step). Then change the division to multiplication (this is the change it step). And finally, flip the numerator with the denominator of the second fraction. So 7/11 will now be 11/7.

Your equations should now be
`(2)/(3) *(11)/(7)`

Now solve! Multiply the numerators (top numbers) together and denominators (bottom numbers) together.

So, 2 x 11 = 22 and 3 x 7 = 21.

You should end up with
`(22)/(21)`

This number cannot be further decreased, so it is your final answer.

Hope this helps :)

Answer 2

Explanation:

3/11 + 4/11 = 7/11

2/3 divided by 7/11

Multiply by reciprocal

2/3 * 11/7 = 22/21 or 1 1/21