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Multiplying fractions and whole numbers 2

Video transcript
Multiply 6 times 1/4. Simplify your answer and write it as a mixed number. So let's just do the multiplication. So at first when you try to multiply 6 times 1/4, you'll be like, well, gee, I know how to multiply a fraction times a fraction. I know how to multiply a whole number times a whole number, but what about a whole number times a fraction? And kind of the key insight you need here is that any whole number can be written as a fraction. We can rewrite 6 as 6/1, right? 6 divided by 1 is 6. 6 ones is 6. Depending how you think about it, this is exactly the same thing as 6. So we just rewrote our whole number as a fraction. You can do it for any number. 10 is the same thing as 10/1. So this become 6/1 times 1/4, and then we just multiply the fraction. We multiply the numerators, so this is equal to 6 times 1 as our numerator. Let me do that in another color. So this becomes 6 times 1 for our numerator and 1 times 4 for our denominator, for the number on the bottom. And so this will become 6 over 4. And right now, it's just as an improper fraction and it's also not in lowest terms. You immediately see 6 and 4 are both divisible by 2, so let's divide them both by 2. If you divide 6 by 2-- and I'll do it in a new color again. If you divide 6 by 2, you get 3. If you divide 4 by 2, you get 2, so this is equal to 3/2. So it's still written as an improper fraction. We now have to write it as a mixed a number. And the process for writing it as a mixed number, you just divide the denominator into the numerator, so this just becomes 2 into 3. Divide 2 into 3. 2 goes into 3 one time. 1 times 2 is 2. You subtract. You have a remainder of 1. So this will become one whole and 1/2 left over. So this is 1 and 1/2. So that's our right answer. We've just simplified the answer and wrote it is a mixed number or we could simplify it at this stage. We could say right here, well, look, we could divide what's eventually going to be in the numerator by 2 and get a 3 there, and divide what's eventually in the denominator by 2 and get a 2 there. 3 times 1 is 3. 1 times 2 is 2, so it's 3/2. And you do this exact same process. You say that 3/2 is the same thing as 1 and 1/2. Either one of those will work. Now let's think about why this makes sense. Let's think about what 6 times 1/4 is. Let me draw 1/4. Let's say that that is 1/4 right there, and let's do six of them. So that's 1/4, that's 2/4 that's 3/4, that's 4/4, which would be a whole, and then you have 5/4, and then you have 6/4. So this is 6 times 1/4. This right here is 4/4. This right here is 4 over 4, which is equal to a 1, so this is equal to 1. And then this right here is two 1/4's, or this right here is 2/4. You can imagine this is two out of a potential, if a whole has to have two more of them, has to have four of them. so this is 1 and-- let me do it in the same colors-- 1 and 1/2, right? 2 out of 4 is the same thing as 1/2, so this right here is one out of a possible one, and then two. So this is 1 and 1/2, which is exactly what we got before.