### All ACT Math Resources

## Example Questions

### Example Question #5 : Complex Fractions

Simplify,

**Possible Answers:**

**Correct answer:**

Convert the numerators and denominators into single fractions, then simplify.

Start by finding the lowest common denominator in both the numerator and denominator of the complex fraction.

Add fractions with like denominators.

Simplify. Divide complex fractions by multiplying the numerator by the reciprocal of the denominator.

Solve.

### Example Question #6 : Complex Fractions

Subtract:

**Possible Answers:**

**Correct answer:**

The least common multiple can be found by multiplying the denominators: 2, 3, and 5. The common denominator of these numbers is 30. Multiply the numerator with what was multiplied to the denominator of each term, and then solve.

### Example Question #7 : Complex Fractions

What is ?

**Possible Answers:**

**Correct answer:**

First, simplify both sides. becomes and becomes . The LCF between and is 36. Thus, This simplifies to .

### Example Question #8 : Complex Fractions

Simplify:

**Possible Answers:**

**Correct answer:**

Begin by simplifying the denominator of the first fraction:

Now, remember that division of fractions is done by multiplying the numerator by the reciprocal of the denominator. Thus:

Simplify a bit:

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