### What’s 3-1/2 + 2-1/3? How about 3-1/2 – 2-1/3? Once you understand the last episode about adding and subtracting mixed fractions, these questions should be relatively easy to answer. And they naturally lead to a few additional questions. In particular, they may lead you to wonder about how the other two big arithmetic operations—multiplication and division—work when dealing with mixed fractions. In other words, what’s 3-1/2 x 2-1/3? Or 3-1/2 / 2-1/3? Are there any tricks to make this type of problem easier to solve? Stay tuned because those are precisely the questions we’ll be answering today.

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## How to Multiply Mixed Fractions

### Let’s say we need to solve a problem like 3-1/2 x 2-1/3. How do we get started? Well, you might not be surprised that the easiest way to get started is to convert the mixed fractions into improper fractions. I’ll let you work out the details, but when you do that you should find that 3-1/2 is equal to 7/2 and that 2-1/3 is equal to 7/3. Which means that the problem 3-1/2 x 2-1/3 is the same as the problem 7/2 x 7/3. What do we do now? All we have to do is use the technique we learned long ago for multiplying fractions. Namely multiply the two numerators to find that the numerator of the answer is 7 x 7 = 49, and multiply the two denominators to find that the denominator of the answer is 2 x 3 = 6. Which means that 3-1/2 x 2-1/3 = 49/6. Or, if we want or need to, we can convert this mixed fraction back into an improper fraction to find that 3-1/2 x 2-1/3 = 8-1/6.

Multiplying mixed fractions is very similar to adding or subtracting them.