# ACT Math : How to multiply complex fractions

## Example Questions

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

What is ?

Explanation:

Simplify both sides first.  simplifies to 6.  simplifies to . Finally 6   = .

### Example Question #2 : How To Multiply Complex Fractions

What is  equal to?

Explanation:

When multiplying fractions, we can simply multiply the numerators and then multiply the denominators. Therefore,  is equal to

We then do the same thing again, giving us .

Now we must find the least common denominator, which is .

We multiply the top by  and the bottom by . After we do this we can multiply our numerator by the reciprocal of the denominator.

.

### Example Question #3 : How To Multiply Complex Fractions

Simplify:

Explanation:

Begin by simplifying the denominator:

Then, you perform the division by multiplying the numerator by the reciprocal of the denominator:

Finally, multiply everything:

### Example Question #4 : How To Multiply Complex Fractions

Simplify:

Explanation:

Generally, when you multiply fractions, it is a very easy affair. This does not change for complex fractions like this. You can begin by simply multiplying the numerators and denominators directly. Thus, you know:

Now, simplify this to:

or

Now, remember that when you divide fractions, you multiply the numerator by the reciprocal of the denominator: