### All ACT Math Resources

## Example Questions

### Example Question #9 : Complex Fractions

Simplify

**Possible Answers:**

**Correct answer:**

Simplify the complex fraction by multiplying by the complex denominator:

### Example Question #11 : Complex 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:

and

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 .