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- Multiply 1 and 3/4 times 7 and 1/5.
- Simplify your answer and write it as a mixed fraction.
- So the first thing we want to do is rewrite each of these
- mixed numbers as improper fractions.
- It's very difficult, or at least it's not easy for me, to
- directly multiply mixed numbers.
- One can do it, but it's much easier if you just make them
- improper fractions.
- So let's convert each of them.
- So 1 and 3/4 is equal to-- it's still going to be over 4,
- so you're still going to have the same denominator, but your
- numerator as an improper fraction is going to be 4
- times 1 plus 3.
- And the reason why this makes sense is 1 is 4/4, or 1 is 4
- times 1 fourths, right?
- 1 is the same thing as 4/4, and then you have three more
- fourths, so 4/4 plus 3/4 will give you 7/4.
- So that's the same thing as 1 and 3/4.
- Now, let's do 7 and 1/5.
- Same exact process.
- We're going to still be talking in terms of fifths.
- That's going to be the denominator.
- You take 5 times 7, because think about it.
- 7 is the same thing as 35/5.
- So you take 5 times 7 plus this numerator right here.
- So 7 is 35/5, then you have one more fifth, so you're
- going to have 35 plus 1, which is equal to 36/5.
- So this product is the exact same thing as taking the
- product of 7/4 times 36/5.
- And we could multiply it out right now.
- Take the 7 times 36 as our new numerator, 4 times 5 as our
- new denominator, but that'll give us large numbers.
- I can't multiply 7 and 36 in my head, or I
- can't do it too easily.
- So let's see if we can simplify this first.
- Both our numerator and our denominator have numbers that
- are divisible by 4, so let's divide both the numerator and
- the denominator by 4.
- So in the numerator, we can divide the 36 by 4 and get 9.
- If you divide something in the numerator by 4, you need to
- divide something in the denominator by 4, and the 4 is
- the obvious guy, so 4 divided by 4 is 1.
- So now this becomes 7 times 9, and what's the 7 times 9?
- It's 63, over 1 times 5.
- So now we have our answer as an improper fraction, but they
- want it as a mixed number or as a mixed fraction.
- So what are 63/5?
- So to figure that out-- let me pick a nice color here-- we
- take 5 into 63.
- 5 goes into 6 one time.
- 1 times 5 is 5.
- You subtract.
- 6 minus 5 is 1.
- Bring down the 3.
- 5 goes into 13 two times.
- And you could have immediately said 5 goes into 63 twelve
- times, but this way, at least to me, it's a
- little bit more obvious.
- And then 2 times 5 is 12, and then we have sorry!
- 2 times 5 is 10.
- That tells you not to switch gears in the
- middle of a math problem.
- 2 times 5 is 10, and then you subtract, and you have a
- remainder of 3.
- So 63/5 is the same thing as 12 wholes and 3 left over, or
- 3/5 left over.
- And if you wanted to go back from this to that, just think:
- 12 is the same thing as 60 fifths, or 60/5.
- 60/5 plus 3/5 is 63/5, so these two things
- are the same thing.
- These two things are equivalent.
- This is as an improper fraction.
- This is as a mixed number or a mixed fraction.
- But this is our answer right there: 12 and 3/5.