Multiplying Mixed Numbers - Math Antics Extras

Learn how to multiply mixed numbers by converting them to improper fractions and multiplying, with clear step-by-step examples.

Ask about this video. Answers come from its transcript only — with the timestamp, so you can check them.

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Key Takeaways

Multiplying mixed numbers is easier by converting them to improper fractions first.
Conversion involves multiplying the whole number by the denominator and adding the numerator.
Multiply numerators and denominators directly once in improper fraction form.
Convert the product back to a mixed number by dividing numerator by denominator.
Simplify the final mixed number answer for clarity.

What the video covers

The video explains that multiplying mixed numbers directly is complicated and suggests converting them to improper fractions instead.
It shows how to convert mixed numbers to improper fractions by multiplying the whole number by the denominator and adding the numerator.
Examples include multiplying 4 1/2 by 1 2/3 and 2 1/3 by 3 3/4.
The video demonstrates multiplying the numerators and denominators of improper fractions.
It explains converting the product back into a mixed number using division to find whole parts and remainders.
Simplification of the resulting mixed number is also covered.
The video emphasizes practice and understanding through multiple examples.
It reassures viewers that the method is straightforward once the conversion is understood.

Chapters

Why convert mixed numbers to improper fractions before multiplying?

Converting mixed numbers to improper fractions simplifies multiplication because you only multiply numerators and denominators directly, avoiding the complexity of the distributive property.

How do you convert an improper fraction back to a mixed number?

Divide the numerator by the denominator to find the whole number part, and use the remainder as the numerator of the fractional part, keeping the same denominator.

Can the final mixed number answer be simplified?

Yes, after converting the improper fraction to a mixed number, you can simplify the fractional part by dividing numerator and denominator by their greatest common divisor.

Full Transcript — Download SRT & Markdown

Speaker A

Do you ever wonder how to multiply mixed numbers? I’ll let you in on a little secret… you don’t have to. Sure, there is a way to multiply mixed numbers directly using the distributive property, but it’s a little complicated. Fortunately, there’s another option where you don’t actually multiply mixed numbers at all. Instead, you just convert them into improper fractions and multiply those, which you already know how to do. So that’s it for this video. Keep practicing and I’ll…

Speaker A

I’m just kidding. Even though that’s all there is to it, it might help to see some examples. Our first example is 4 and 1/2 times 1 and 2/3. The first thing we need to do is convert our mixed numbers into improper fractions. To do that, we multiply the whole number part of our mixed number by a whole fraction with the same denominator as the fraction part of our mixed number. And then we add that to the fraction part of our mixed number. To convert 4 and 1/2 we have 4 times 2/2 + 1/2.

Speaker A

I’m just kidding. Even though that’s all there is to it, it might help to see some examples. Our first example is 4 and 1/2 times 1 and 2/3. The first thing we need to do is convert our mixed numbers into improper fractions. To do that, we multiply the whole number part of our mixed number by a whole fraction with the same denominator as the fraction part of our mixed number. And then we add that to the fraction part of our mixed number. To convert 4 and 1/2 we have 4 times 2/2 + 1/2.

Speaker A

Since our original problem was multiplying mixed numbers, we should convert our answer into a mixed number. To convert this into a mixed number, we need to find out how many whole fractions there are hiding in this improper fraction. And we can do that with division. We divide the numerator by the denominator, so 45 divided by 6 is 7 with a remainder of 3. The answer of the division tells us how many whole fractions there were in the improper fraction, 7.

Speaker A

4 times 2/2 is 8/2. And 8/2 + 1/2 equals 9/2. To convert 1 and 2/3 we have 1 times 3/3 + 2/3. 1 times 3/3 is just 3/3. And 3/3 + 2/3 equals 5/3. Now that we’ve converted our mixed numbers into improper fractions, we multiply those together, so our multiplication problem is 9/2 times 5/3 which is much easier to do. We just multiply the numerators and multiply the denominators. 9 times 5 is 45 and 2 times 3 is 6. So our answer is 45/6, but we don’t want to leave our answer as an improper fraction.

Speaker A

To convert 2 and 1/3 we multiply the whole number part ‘2’ by a whole fraction with the same denominator as the fraction part, so ‘3/3’ and then we add the fraction part of our mixed number ‘1/3’. 2 times 3/3 is 6/3. And 6/3 + 1/3 = 7/3. To convert 3 and 3/4 we multiply the whole number part ‘3’ by a whole fraction with the same denominator as the fraction part, so ‘4/4’. And then we add the fraction part of our mixed number ‘3/4’. 3 times 4/4 is 12/4. And 12/4 + 3/4 = 15/4.

Speaker A

Since our original problem was multiplying mixed numbers, we should convert our answer into a mixed number. To convert this into a mixed number, we need to find out how many whole fractions there are hiding in this improper fraction. And we can do that with division. We divide the numerator by the denominator, so 45 divided by 6 is 7 with a remainder of 3. The answer of the division tells us how many whole fractions there were in the improper fraction, 7.

Speaker A

The answer to our division problem tells us how many whole fractions there were in the improper fraction, ‘8’. So 8 is the whole number part of our mixed number. The remainder tells us what the left over fraction part will be. So the numerator will be 9 and the denominator will stay the same, ’12’. That means the mixed number form of our answer is 8 and 9/12 and that can be simplified to 8 and 3/4. So 2 and 1/3 times 3 and 3/4 = 8 and 3/4. Okay, now you know how to multiply mixed numbers.

Speaker A

So 7 is the whole number part of our mixed number. And the remainder tells us what the leftover fraction will be. So the numerator will be 3 and the denominator stays the same, 6. So the mixed number form of our answer is 7 and 3/6. But that can be simplified to 7 and 1/2. So 4 and 1/2 times 1 and 2/3 equals 7 and 1/2. Let’s do another example to make sure you’ve got it. Our next example is 2 and 1/3 times 3 and 3/4. Once again, we convert our mixed numbers into improper fractions.

Topics:multiply mixed numbersimproper fractionsmathanticsfraction multiplicationconvert mixed numbersmath tutorialmath basicsfraction simplificationmultiplying fractionsmath examples

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