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An Intro to Multiplying Fractions

By Arden Suvalle

Edited by Emma Davis

The mathematical world is filled with varying concepts, from simple addition, to the Quadratic Formula, to trigonometric functions. One of the most common mathematical concepts is fractional multiplication. Fractions come up many times in math, whether it be using them in functions, dividing, or simply fractions on their own. An important concept to be comfortable with, in relation to fractions, is how to multiply them.

Multiplying fractions is a generally straightforward thing to do. It is essentially one multiplication problem stacked on top of another. Below are two examples of fraction multiplication, which will be explained in further detail.

A Fraction Multiplied By a Fraction

In many cases, you may find that the fraction you are multiplying will be adjacent from another fraction. For the first equation in the image above, we have ⅚ times ¾.

The first thing we should do is find our new numerator. The numerator is the number that goes above the fraction line. To do this, simply take both numerators and multiply them. Our first numerator is 5, so we will take that and multiply it by the other numerator, 3. The answer to this simple equation is 15. The numerator of our new fraction will be 15.

Now we must find the denominator. The denominator is the number that goes below the fraction line. To find the new denominator, we take the denominator of each fraction and multiply them, just like we did for our numerator. Our first denominator is 6, so we will take that number and multiply it by 4, the other denominator. The number we will get is 24. 24 is our new denominator.

Now we have our new fraction which is 15/24. Sometimes you may have a fraction that can be further simplified into a smaller fraction, but for this one we’re left with the fraction in its simplest form.

A Fraction Multiplied By a Whole Number

The other example shown in the image above is a fraction that is being multiplied by a whole number. This is also a common mathematical expression. The multiplication problem we are given in this equation is ⅚ times 8.

The first thing we are going to want to do is give that 8 a denominator. Think of 8 as 8/1.

Next, we want to do the exact same thing we did when multiplying a fraction by another fraction, multiply the numerators. Our numerators this time around are 5 and 8, which we can multiply to get 40. Our new numerator is 40.

Now, once again, we have to find our denominator. This time around should be very easy, because one of our denominators is 1. The other denominator is 6, so we can multiply 6 times 1 to once again be left with 6.

Our new fraction is 40/6, a number that can further be simplified. The easiest way to simplify is to divide 40 by 6. 6 goes into 40 six different times, so we would be left with a whole number of 6. We are still left over with 4 that did not go into 40, so this will become our new fraction. Our fraction is now 6 and 4/6 which can still be divided down once more. The fraction can be divided by 2 to get ⅔. Our final fraction in simplest form is 6 and ⅔.

Hopefully this guide has helped you begin your journey to multiplying fractions! Remember to always simplify unless asked otherwise!

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