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整數乘以分數的乘法 (英)

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整數乘以分數的乘法 (英) : 整數乘以分數的乘法

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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.

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整數乘以分數的乘法 (英)

整數乘以分數的乘法 (英) : 整數乘以分數的乘法