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Multiply 6 times 1/4.

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Simplify your answer and write it as a mixed number.

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So let's just do the multiplication.

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So at first when you try to multiply 6 times 1/4, you'll

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be like, well, gee, I know how to multiply a

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fraction times a fraction.

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I know how to multiply a whole number times a whole number,

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but what about a whole number times a fraction?

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And kind of the key insight you need here is that any

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whole number can be written as a fraction.

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We can rewrite 6 as 6/1, right?

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6 divided by 1 is 6.

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6 ones is 6.

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Depending how you think about it, this is exactly the same

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thing as 6.

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So we just rewrote our whole number as a fraction.

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You can do it for any number.

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10 is the same thing as 10/1.

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So this become 6/1 times 1/4, and then we just

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multiply the fraction.

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We multiply the numerators, so this is equal to 6 times 1 as

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our numerator.

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Let me do that in another color.

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So this becomes 6 times 1 for our numerator and 1 times 4

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for our denominator, for the number on the bottom.

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And so this will become 6 over 4.

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And right now, it's just as an improper fraction and it's

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also not in lowest terms. You immediately see 6 and 4 are

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both divisible by 2, so let's divide them both by 2.

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If you divide 6 by 2-- and I'll do it

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in a new color again.

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If you divide 6 by 2, you get 3.

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If you divide 4 by 2, you get 2, so this is equal to 3/2.

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So it's still written as an improper fraction.

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We now have to write it as a mixed a number.

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And the process for writing it as a mixed number, you just

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divide the denominator into the numerator, so this just

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becomes 2 into 3.

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Divide 2 into 3.

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2 goes into 3 one time.

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1 times 2 is 2.

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You subtract.

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You have a remainder of 1.

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So this will become one whole and 1/2 left over.

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So this is 1 and 1/2.

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So that's our right answer.

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We've just simplified the answer and wrote it is a mixed

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number or we could simplify it at this stage.

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We could say right here, well, look, we could divide what's

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eventually going to be in the numerator by 2 and get a 3

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there, and divide what's eventually in the denominator

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by 2 and get a 2 there.

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3 times 1 is 3.

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1 times 2 is 2, so it's 3/2.

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And you do this exact same process.

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You say that 3/2 is the same thing as 1 and 1/2.

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Either one of those will work.

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Now let's think about why this makes sense.

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Let's think about what 6 times 1/4 is.

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Let me draw 1/4.

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Let's say that that is 1/4 right there, and

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let's do six of them.

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So that's 1/4, that's 2/4 that's 3/4, that's 4/4, which

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would be a whole, and then you have 5/4, and

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then you have 6/4.

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So this is 6 times 1/4.

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This right here is 4/4.

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This right here is 4 over 4, which is equal to a 1, so this

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is equal to 1.

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And then this right here is two 1/4's, or this

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right here is 2/4.

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You can imagine this is two out of a potential, if a whole

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has to have two more of them, has to have four of them. so

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this is 1 and-- let me do it in the same colors-- 1 and

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1/2, right?

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2 out of 4 is the same thing as 1/2, so this right here is

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one out of a possible one, and then two.

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So this is 1 and 1/2, which is exactly what we got before.

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