Adding and subtracting fractions
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Adding Fractions with Like Denominators
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Adding fractions with common denominators
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Subtracting Fractions
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Subtracting fractions with common denominators
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Adding and subtracting fractions
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Adding Fractions with Unlike Denominators
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Adding fractions (ex 1)
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Adding fractions
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Subtracting fractions
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Adding and subtracting fractions
Adding fractions examples
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- Let's add some rational numbers.
- And I'm using that word because that's the word that
- this book uses, but in more popular terminology we'll be
- adding fractions.
- So let's just go through all of these, actually, just to
- see all of the examples.
- So first we're going to have 3/7 plus 2/7.
- Our denominators are the same, so we can just add the
- numerators.
- So our denominator is 7, 3 plus 2 is 5.
- That is a.
- Let me do every other.
- It would take forever to do all of them.
- Not forever, but just more time than I want to spend.
- So c is 5/16 plus 5/12.
- Our denominators are not the same.
- We have to find a common denominator, which has to be
- the least common-- it actually could be any common multiple
- of these, but for simplicity let's do the
- least common multiple.
- So what's the smallest number that's a multiple
- of both 16 and 12?
- So let's see, 16 times 2 is 32, not there yet.
- Times 3, 48.
- That seems to work.
- 12 goes into 48 four times.
- So let's use 48 as our common denominator.
- So we had to multiply 16 times 3 to get to 48, so we're going
- to have to multiply this 5 times 3.
- We're just multiplying the numerator and the denominator
- by the same number, so we're not really changing it.
- So 5 times 3 is 15.
- And then to get from this 12 to this 48 right there, we had
- to multiply times 4.
- So then to get to 5 to this numerator over here, we have
- to multiply times 4.
- 5 times 4 is 20.
- Now we have the same denominator.
- So this is going to be equal to, our denominator is 48.
- And so we can add 15 plus 20, which is 35.
- And can we reduce this?
- Let's see, 5 does not go into 48.
- 7 does not go into 48.
- It looks like we're all done.
- Let's do e right there.
- 8/25 plus 7 over 10.
- Once again, we don't have a common denominator.
- But we can solve that.
- Let's make, let's see, 50 is the smallest number that both
- of these go into.
- 25 times 2, so that's 50.
- 8 over 25, to go to 50 we multiply by 2.
- So the 8, we're going to have to multiply by 2.
- So it's going to be 16 over 50.
- And then the 7 over 10, we're going to want
- to put it over 50.
- We multiply the 10 times 5, so we have to
- multiply the 7 times 5.
- So it's going to be 35 over 50.
- Now that our denominators are the same, we have it over 50.
- 16 plus 35, what is that?
- 10 plus 35 is 45, plus 6 is 51.
- So it is 51 over 50.
- Problem g.
- Let me do it in a new color.
- Problem g.
- So here we have 7 over 15-- I'll write the second one in a
- different color-- plus 2 over 9.
- Once again, the denominators are different.
- Find a common denominator.
- What is the smallest number that both 15 and 9 go into?
- Let's see, 15 times 2 is 30.
- Nope, not divisible by 9.
- 15 times 3 is 45, that works.
- 45 is divisible by 9.
- So we use 45.
- 15 times 3 is 45, so 7 times 3 is 21.
- These two fractions are equivalent.
- Plus we're going over 45.
- To get from 9 to 45, we have to multiply times 5.
- So to get our numerator over here, we have to
- multiply it times 5.
- So 2 times 5 is 10.
- 2/9 is the same thing as 10/45.
- So now we can add.
- We're adding fractions of 45.
- 21 plus 10 is 31, and we are done.
- Let's do one more problem down here, a word problem.
- Nadia, Peter and Ian are pooling their money to buy a
- gallon of ice cream.
- Nadia's the oldest and gets the greatest allowance.
- She contributes 1/2 the cost. So Nadia is contributing 1/2
- the cost. So that is Nadia right there.
- Ian is next oldest and contributes 1/3 of the cost.
- So Ian contributes 1/3.
- That is Ian.
- Peter, the youngest, gets the smallest allowance and
- contributes 1/4 of the cost. So Peter gives 1/4 of the
- cost. Peter contributes 1/4 of cost.
- They figure that this will be enough money.
- When they get to the checkout, they realize that they forgot
- about sales tax and worry there will
- not be enough money.
- Amazingly, they have exactly the right amount of money.
- What fraction of the cost of ice cream was added as tax?
- Well, let's see, if we add 1/2 plus 1/3, plus 1/4 of the
- cost, let's see what we get.
- So we have to find a common denominator, some number that
- is the least common multiple of 2, 3, and 4.
- And let's see, 4, it would have to be 12, right?
- 12 is divisible by 2, it's divisible by 3, and it's
- divisible by 4.
- So 1/2 is the same thing as 6/12.
- 2 times 6 is 12.
- 1 times 6 is 6.
- These are equivalent.
- 6 is 1/2 of 12.
- 1/3, if we use 12 as a common denominator, to go from 3 to
- 12 you have to multiply by 4.
- So you take that 4 and you multiply it by 1.
- 4/12 is the same thing as 1/3.
- And then 1/4, if you use your denominator 12, to go from 4
- to 12 you have to multiply by 3, so multiply the numerator
- by 3 as well, you get 3.
- So let's add these.
- So 6/12 plus 4/12, plus 3/12 is going to be equal to-- our
- denominator's going to be 12-- it's going to be 6 plus 4,
- plus 3, which is equal to 6 plus 4 is 10, plus 3 is 13.
- So it's going to be equal to 13/12.
- And this is as an improper fraction.
- Or we could say that this is the same thing, this is equal
- to 12/12 plus 1/12, or we could say the same thing as
- 12/12 is just 1, right?
- 12 divided by 12 is 1.
- So this is 1 and 1/12.
- So when they pool their money, they get 1 and 1/12 of the
- price of the ice cream that they want to buy.
- So they say what fraction of the cost of ice cream was
- added as tax?
- This is the exact amount that they needed to pay.
- So clearly, 1 is the non-taxed price of the ice cream, so
- this 1/12 was the amount added as tax.
- So the answer to the question is 1/12 of the price
- was added as tax.
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