ACT Math : How to multiply complex fractions

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #1 : How To Multiply Complex Fractions

What is ?

Possible Answers:

Correct answer:

Explanation:

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

Example Question #2 : How To Multiply Complex Fractions

What is  equal to?

Possible Answers:

Correct answer:

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.

Therefore our answer becomes,

  .

Example Question #2 : How To Multiply Complex Fractions

Simplify:

Possible Answers:

Correct answer:

Explanation:

Begin by simplifying the denominator:

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

Do your simplifying now:

Finally, multiply everything:

 

Example Question #4 : How To Multiply Complex Fractions

Simplify:

Possible Answers:

Correct answer:

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:

Now, cancel your terms immediately:

, which is easy to finish:

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