# ACT Math : How to add complex fractions

## Example Questions

### Example Question #1 : How To Add Complex Fractions

Calculate

Explanation:

To add complex fractions, 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 #1 : How To Add Complex Fractions

Calculate

Explanation:

To add complex fractions, 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 #11 : Complex Fractions

Calculate

Explanation:

To add complex fractions, 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 #1 : How To Add Complex Fractions

Calculate

Explanation:

To add complex fractions, 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 #5 : How To Add Complex Fractions

Calculate

Explanation:

To add complex fractions, 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 : How To Add Complex Fractions

Calculate

Explanation:

To add complex fractions, 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 #1 : How To Add Complex Fractions

Simplify,

Explanation:

To add complex fractions, 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 #8 : How To Add Complex Fractions

Simplify:

Explanation:

Begin by simplifying the first fraction:

Next, handle the division of each fraction by multiplying by the reciprocal in each case:

Now, with a common denominator, you are done!

### Example Question #9 : How To Add Complex Fractions

Simplify:

.

Explanation:

With a complex fraction like this, begin by simplifying the numerator of the first fraction:

Next, find the common denominator of the numerator's fractions:

Next, simplify the left division by multiplying by the reciprocal:

Finally, combine the fractions:

Simplifying, this is:

### Example Question #10 : How To Add Complex Fractions

Susan is training to run a race. The week before the race she ran four times. The first time she ran  miles, her second run was  miles, her third run was  miles and her final run was  miles. How many miles did Susan run this week?