All ACT Math Resources
Example Question #1 : Complex Fractions
Which of the following is equal to ?
First we must take the numerator of our whole problem. There is a fraction in the numerator with as the denominator. Therefore, we multiply the numerator of our whole problem by , giving us .
Now we look at the denominator of the whole problem, and we see that there is another fraction present with as a denominator. So now, we multiply the denominator by , giving us .
Our fraction should now read . Now, we can factor our denominator, making the fraction .
Finally, we cancel out from the top and the bottom, giving us .
Example Question #2 : Complex Fractions
Rewrite into the following form:
Change the division sign to a multiplication sign by flipping the 2nd term and simplify.
Example Question #3 : Complex Fractions
The expression can be rewritten as:
Change the division sign to a multiplication sign and take the reciprocal of the second term. Evaluate.
Example Question #4 : Complex Fractions
The expression can be simplified as follows:
We can simplify each fraction by multiplying the numerator by the reciprocal of the denominator.
From here we add our two new fractions together and simplify.
Example Question #5 : Complex Fractions
Simplify the following:
Begin by simplifying your numerator. Thus, find the common denominator:
Next, combine the fractions in the numerator:
Next, remember that to divide fractions, you multiply the numerator by the reciprocal of the denominator:
Since nothing needs to be simplified, this is just: