ACT Math : How to find a complex fraction

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #6 : Complex Fractions

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

Possible Answers:

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

\frac{x + 1}{x}

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

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

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

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 #24 : Problem Solving

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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