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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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