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### Course: Arithmetic > Unit 13

Lesson 1: Fractions with denominators of 10 and 100- Visually converting tenths and hundredths
- Equivalent fractions with fraction models (denominators 10 & 100)
- Equivalent fractions (denominators 10 & 100)
- Decomposing hundredths
- Adding fractions (denominators 10 & 100)
- Adding fractions: 7/10+13/100
- Equivalent expressions with common denominators (denominators 10 & 100)
- Add fractions (denominators 10 & 100)

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# Adding fractions (denominators 10 & 100)

Sal adds 3/10+7/100 by finding a common denominator. Created by Sal Khan.

## Want to join the conversation?

- but what if the numerator is bigger the denomanator? I mean like 16/10 + 6/100(7 votes)
- If your comparing numbers like 7/14 and 14/7 try multiplying the denominators into the same number, then multiply the numerator with the same amount that you multiplied for the denominator.For 7/14 you will get 28/28 and for 14/7 you will get 28/28.Then you see which numerator is bigger if none are then they are equivalent.(7 votes)

- hey whats the denominator again(6 votes)
- the one on the bottom.(7 votes)

- ok so this did help me and let me understand a little bit when the person doing the voice over is making it a little harder to ya know, understand? all im asking is for them to explain a TINY bit more... thankyou and hope you understand...(5 votes)
- Okay! Let's get a different situation. 7/10 + 4/100=?. We need to find out the sum. The first thing we need to do is that we need to make the denominators the same. We have to make the denominators 100, because you cannot divide 4 by 10 without decimals. So we times 10 by 10=100. Then we have to times the numerator by 10 too! 7x10=70. It becomes 4/100+70/100+?. Now, 70+4=74 so, the answer is 74/100. Hope this helps and have a good day!(4 votes)

- is that the only way you can add fractions or?(4 votes)
- When adding fractions, you always need to have a common denominator. So, yes. The process shown in the video are the steps you would need to take.(5 votes)

- GCD means Greatest Common Factor right?(3 votes)
- Actually, "greatest common denominator" does not make good sense since because a common denominator can be as large as one likes. (For example, if the denominators of two fractions are 4 and 6, then the numbers 12, 24, 36, 48, 60, and so on forever are all common denominators!)

GCD actually means greatest common divisor, which means the same thing as GCF (greatest common factor) because a divisor of a number means the same thing as a factor of a number. For example, the GCD of 4 and 6 is the GCF of 4 and 6, which is 2.

Have a blessed, wonderful day!(2 votes)

- What is the variable of 5a(3 votes)
- A variable is a letter that represents an unknown number. A variable can be any letter so it would mean the same thing if it said 5s . so in your case a is the variable(2 votes)

- Do I have to use a number line?(3 votes)
- No you just have to figure out what it's going to equal times our added I don't get it completely either(2 votes)

- Why do we need fractions and numerator and denominators?(2 votes)
- In case we need to show a part of something. You could just use decimals, but fractions in my opinion are a much better way to visually represent a part of a whole(3 votes)

- why does he do 10 times 10 at1:40? I don't get it.(2 votes)
- In order to add or subtract a fraction, each fraction must have the same denominator (bottom number). This is done by multiplying one or both of the fractions by a number that will change the denominator, but not the value of the fraction as a whole. So, in the video he is attempting to add 3/10 and 7/100. He can't do so since they have different denominators, so he multiplies 3/10 by 10/10 (any number over itself is equal to 1) and obtains the necessary denominator of 100, but it also changes his numerator as well, leaving him with 30/100. In the video he was just referencing the denominators alone at that1:40mark because the denominator is the most important aspect of adding and subtracting fractions.

Hope this helped!(3 votes)

- after solving do you simplify too?(2 votes)
- Yes. But if it is already in the simplest form, then you don't need to.(3 votes)

## Video transcript

Let's see if we can
add 3/10 to 7/100. And I encourage you to
try adding these two fractions on your own first
before I work through it, and I'll give you one hint. Right now, it's very hard
to add these fractions. You're adding 3/10 to 7/100. You're adding two
different fractions with two different denominators. So what I would
encourage you to do is try to rewrite
3/10 in a way that it has 100 as a
denominator, or so it's expressed in terms
of hundredths, and then see if
you can add them. Well, I'm assuming
you've given a go at it. Let's see how we
can rewrite 3/10, and I'll try to visualize it. So what I've done here, so this
you could consider a whole, and this is a whole as well. And this whole is divided into
tenths-- 1,2, 3, 4, 5, 6, 7, 8, 9, 10. So what would 3/10 look like? Well, it would be one, two,
and three of the tenths. Now, what would happen if
you took each of those tenths and you divided them
into 10 more sections? So you're essentially
taking each of those tenths and you're dividing
them into 10 sections. Well, you have 10 sections
and then each of them will have 10 subsections in it. So you're going to
have hundredths. Then the sections are going
to describe hundredths. So 10-- let me
write it this way. 10 times 10. You are then going
to have hundredths. And 3/10 would be equivalent to
how many of these hundredths? Well, each of these
tenths will now become 10. So you're going to
have 10, 20, and-- let me color them in better. So that's 10, 20, and
then 30 hundredths. So this part right over here. This-- let me get my tool
right-- this part right over here, this is going
to be 3 times 10, which is going to be equal to 30. 10 times 10 is equal to 100. So this is how we're going
to change the denominator. Instead of thinking
in terms of tenths, we're going to think
in terms of hundredths. And now our numerator, 3/10,
is equivalent to 30 hundredths so we can rewrite this fraction. We essentially multiplied
the numerator by 10, and we multiplied
the denominator by 10, which didn't change
the value of the fraction. It still represents
the same-- it still represents 3/10 of the whole. So when you do
that, you end up-- we can rewrite this
thing as 30 over 100. Three tenths is
equivalent to 30 over 100. We add that to 7 over 100. Or another way of thinking
about it, three tenths is the same thing
as 30 hundredths. And we add that to 7 hundredths. Well, now we're going to
have 30 plus 7 hundredths. So now, we're going to
have 30 plus 7 hundredths. Or we could say that this is
now going to be 37 hundredths. So this extra 7 that we're
adding here-- maybe I'll do this in-- that's
the same color. This extra sevenths-- let
me do this in a new color. This 7 hundredths that we're
adding, that's going to be one, two-- let me paint that
in a little bit clearer. So that's 1, 2, so it
gets us all the way to 7. Let's see, 1, 2, 3, so 7
hundredths is right over there. So let me get back to my pen. So that, whoops, this right
over here is 7 out of the 100 so 30/100 plus 7/100 is
going to get us to 37/100.