ACT Math : How to find a complex fraction

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #10 : Complex Fractions

Simplify \frac{x + \frac{1}{x}}{x}

Possible Answers:

\frac{x + 1}{x^{2}}

\frac{x^{2} + 2x + 1}{x}

\frac{x^{2} + 1}{x^{2}}

\frac{x + 1}{x}

\frac{x^{2} + 1}{x}

Correct answer:

\frac{x^{2} + 1}{x^{2}}


Simplify the complex fraction by multiplying by the complex denominator:

\frac{x + \frac{1}{x}}{x}\cdot \frac{x}{x}= \frac{x^{2} + 1}{x^{2}}

Example Question #3 : How To Add And Subtract Fractions

Steven purchased  of vegetables on Monday and  of vegetables on Tuesday. What was the total weight, in pounds, of vegetables purchased by Steven?

Possible Answers:

Correct answer:


To solve this answer, we have to first make the mixed numbers improper fractions so that we can then find a common denominator. To make a mixed number into an improper fraction, you multiply the denominator by the whole number and add the result to the numerator. So, for the presented data:



Now, to find out how many total pounds of vegetables Steven purchased, we need to add these two improper fractions together:


To add these fractions, they need to have a common denominator. We can adjust each fraction to have a common denominator of  by multiplying  by  and by :

 To multiply fractions, just multiply across:

We can now add the numerators together; the denominator will stay the same:

Since all of the answer choices are mixed numbers, we now need to change our improper fraction answer into a mixed number answer. We can do this by dividing the numerator by the denominator and leaving the remainder as the numerator:

This means that our final answer is .

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