Video: Finding in the Simplest Form the Result of Multiplying Three Fractions

Calculate 21/44 × 6/7 × 11/12, giving your answer as a fraction in its simplest form.


Video Transcript

Calculate 21 44ths times six-sevenths times 11 12ths, giving your answer as a fraction in its simplest form.

When you multiply fractions, you multiply all of the numerators and then you multiply all of the denominators and put your numerator over your denominator. However, when the numbers become larger like this, it’s actually easier to find common factors that you can cancel. This means you can take any numbers on the numerators and simplify them with any numbers on the denominators.

There are few places where we could simplify. For example, 21 and seven both have a common factor of seven. So we can take seven out of both of those numbers. If you take seven out of 21, it turns into a three. And if you take seven out of seven or divide by seven, you get one.

The next numerator and denominator I’m going to simplify is the six and the 12. Six and 12 are both divisible by six. So six divided by six is one and 12 divided by six is two. So the 12 will turn into a two. Finally, the 11 and the 44 can also reduce; 11 can go into 11 and 11 can go into 44. So 11 divided by 11 is one and 44 divided by 11 is four. So now we have three-fourths times one over one times one-half. So let’s go ahead and rewrite this.

Now that we have it all reduced, we can multiply all of the numerators together, write it as our new numerator, and then multiply all of our denominators together and write it as our new denominator. So for our numerator, three times one times one is three and for our denominator, four times one times two is eight. Therefore, three-eighths is our final answer.

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