Multiply Fractions

Multiplying fractions without a calculator is the best way to learn. Using a pencil and paper, here is how to multiply two fractions.

Multiplying fractions can be easy with a calculator (assuming you know the decimal equivalent of the fraction). Multiplying them on paper can be simple and a lot of fun, too, if you know how to do it. Here's how.

Let's first define a couple of terms that will be used. The numerator of a fraction is the number above the fraction line. The denominator is the number below the line. So in the fraction 1/2, 1 is the numerator and 2 is the denominator. In 3/4, 3 is the numerator and 4 is the denominator.

Let's multiply those two fractions mentioned above: 1/2 x 3/4. Very simply, you multiply the two numerators to get your numerator in your answer, and multiply the two denominators to get the denominators in your answer. So multiply 1 x 3, which equals 3. And multiply 2 x 4, which equals 8. The answer to 1/2 x 3/4 is 3/8.

Now we'll complicate it slightly. Let's multiply 3/4 x 2/3. If we multiply the same way as above, we have 3 x 2 on the top, which equals 6, and 4 x 3 on the bottom, which equals 12. Our answer is 6/12. But that can be simplified even further. What number can go into 6 and 12 to reduce it to the smallest fraction possible? 6, of course. 6 goes into 6 once, and 6 goes into 12 twice. That means 6/12 = 1/2. So 3/4 x 2/3 = 1/2.

Now let's go even one step further. Say you want to multiply whole numbers with fractions. For example, what is 2-3/8 x 1-3/4? The first thing to do is make them into fractions (get rid of the whole number). The way that is done is to take the whole number and multiply it by the denominator, then add the numerator. That answer would then be the new numerator, which would be placed over the denominator. So in 2-3/8, it would be the whole number (2) times the denominator (8) plus the numerator (3). That would be 19. Put that over the denominator

(8), and 2-3/8 is equal to 19/8. So in 1-3/4, it's (1 x 4) + 3, which is 7/4. So asking what 2-3/8 x 1-3/4 equals is the same as asking what 19/8 x 7/4 equals. 19 x 7 = 133. 8 x 4 = 32. Our answer is 133/32. To simplify that, divide 133 by 32, which is 4, with a remainder of 5. So 133/32 = 4-5/32.

Multiplying fractions may sound a little complicated, but if you practice a few of them, you'll see that it's actually a very simple process. Use a calculator to check your answers until you get some confidence in doing them. Once you do them for a while, you will master them without the help of a calculator.

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