look, I'm genuinely confused about this rational thing. he said that if an int is divided by an int then its rational right? but 2/7 = 0.285714 recurring I'm pretty certain that's not rational. my teacher couldn't explain this to me edit: would love if someone answered this quickly

So what makes you think it is not rational? If a decimal is repeating, it should be rational because some people such as myself can relatively easily find the two whole numbers to create a fraction. All truncating and repeating decimals are rational because they meet the definition of being a ratio of two integers or whole numbers. An irrational number has a decimal that NEVER repeats. So if it repeats, then it does not meet the qualification of NEVER.

can anyone of you can tell if this is true or not? 1+2+3+4+5.....to infinity= -1/12? want to know just upvote for this question

No, because this is not a geometric series whose terms are approaching zero. The terms are increasing by 1, and this is an arithmetic series. So, no, you can't calculate the sum of this series. It just approaches infinity.

How do you find out which is which? (Irrational & Rational)

Rational Numbers: The real numbers which can be represented in the form of the ratio of two integers, say P/Q, where Q is not equal to zero are called rational numbers. Irrational Numbers: The real numbers which cannot be expressed in the form of the ratio of two integers are called irrational num

At 2:06, when Sal added bn + bn, how come he didn't write it as 2bn? Since he added both of them together and they are the same quantity, shouldn't he have written it as 2bn?

Sal is adding 2 fractions. The "bn" are in the denominators. When we add fractions, we only add the numerators. For example: 5/8+2/8 = 7/8, not 7/16. Hope this helps.

is zero a rational number or a irrational number

It is a rational number. 0 is an integer. All integers are rational numbers. Integers can be written as a fraction using 2 integers (that's the definition of a rational number): 0 = 0/1 Hope this helps.

Main content

Algebra 1

Course: Algebra 1 > Unit 15

Lesson 2: Sums and products of rational and irrational numbers

Proof: sum & product of two rationals is rational

Name: Proof: sum & product of two rationals is rational
Uploaded: 2013-12-24T01:50:45Z
Description: Sal proves that the sum, or the product, of any two rational numbers will always be a rational number.

CCSS.Math:

HSN.RN.B.3

Google Classroom

Sal proves that the sum, or the product, of any two rational numbers will always be a rational number. Created by Sal Khan.

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theshadow6606
Posted 5 years ago. Direct link to theshadow6606's post “look, I'm genuinely confu...”
look, I'm genuinely confused about this rational thing.
he said that if an int is divided by an int then its rational right?
but 2/7 = 0.285714 recurring
I'm pretty certain that's not rational.
my teacher couldn't explain this to me

edit: would love if someone answered this quickly
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(8 votes)
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- David Severin
  Posted 5 years ago. Direct link to David Severin's post “So what makes you think i...”
  So what makes you think it is not rational? If a decimal is repeating, it should be rational because some people such as myself can relatively easily find the two whole numbers to create a fraction. All truncating and repeating decimals are rational because they meet the definition of being a ratio of two integers or whole numbers.
  An irrational number has a decimal that NEVER repeats. So if it repeats, then it does not meet the qualification of NEVER.
  Comment on David Severin's post “So what makes you think i...”
  (11 votes)
yash jaiswal
Posted 4 years ago. Direct link to yash jaiswal's post “can anyone of you can tel...”
can anyone of you can tell if this is true or not?
1+2+3+4+5.....to infinity= -1/12?

want to know just upvote for this question
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(5 votes)
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- GraceMoon124
  Posted 2 years ago. Direct link to GraceMoon124's post “No, because this is not a...”
  No, because this is not a geometric series whose terms are approaching zero. The terms are increasing by 1, and this is an arithmetic series. So, no, you can't calculate the sum of this series. It just approaches infinity.
  Button navigates to signup page
  (3 votes)
Dre Hill
Posted 2 years ago. Direct link to Dre Hill's post “How do you find out which...”
How do you find out which is which? (Irrational & Rational)
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(4 votes)
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- Malkom
  Posted 2 years ago. Direct link to Malkom's post “Rational Numbers: The rea...”
  Rational Numbers: The real numbers which can be represented in the form of the ratio of two integers, say P/Q, where Q is not equal to zero are called rational numbers. Irrational Numbers: The real numbers which cannot be expressed in the form of the ratio of two integers are called irrational num
  Button navigates to signup page
  (2 votes)
The first integral proponent
Posted 5 years ago. Direct link to The first integral proponent's post “What about irrational div...”
What about irrational divide irrational? rational divide irrational? irrational divide rational? irrational to a rational number's power? irrational to irrational? rational to irrational?
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(3 votes)
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aviralp
Posted 2 years ago. Direct link to aviralp's post “is zero a rational number...”
is zero a rational number or a irrational number
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(1 vote)
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- Kim Seidel
  Posted 2 years ago. Direct link to Kim Seidel's post “It is a rational number. ...”
  It is a rational number. 0 is an integer. All integers are rational numbers. Integers can be written as a fraction using 2 integers (that's the definition of a rational number):
  0 = 0/1
  Hope this helps.
  Button navigates to signup page
  (5 votes)
Vector Inc.
Posted 3 years ago. Direct link to Vector Inc.'s post “At 2:06, when Sal added b...”
At
2:06
, when Sal added bn + bn, how come he didn't write it as 2bn? Since he added both of them together and they are the same quantity, shouldn't he have written it as 2bn?
Button navigates to signup pageComment on Vector Inc.'s post “At 2:06, when Sal added b...”
(2 votes)
Answer
- Kim Seidel
  Posted 3 years ago. Direct link to Kim Seidel's post “Sal is adding 2 fractions...”
  Sal is adding 2 fractions. The "bn" are in the denominators. When we add fractions, we only add the numerators. For example: 5/8+2/8 = 7/8, not 7/16.
  
  Hope this helps.
  Comment on Kim Seidel's post “Sal is adding 2 fractions...”
  (3 votes)
m.prosser2022
Posted 5 years ago. Direct link to m.prosser2022's post “So If you do X + 34 + 9/3...”
So If you do X + 34 + 9/33 x 44 = y =555 what would add 33+9/33x44
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Evan Campbell
Posted 2 years ago. Direct link to Evan Campbell's post “this is very confusing fo...”
this is very confusing for me why must we do high school math in 8th grade?
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feven
Posted 2 years ago. Direct link to feven's post “what is the different bet...”
what is the different between irtional and rational
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(2 votes)
Answer
- Kim Seidel
  Posted 2 years ago. Direct link to Kim Seidel's post “Rational numbers can be w...”
  Rational numbers can be written in the form of a fraction (ratio) of 2 integers. The numbers that fall into this set are:
  -- All integers
  -- All fractions where the numerator and denominator are integers.
  -- All terminating decimals as they are just fractions in another form. For example 0.25 = 1/4
  -- All repeating decimals as they are also fractions in another form. For example 0.66666... = 2/3
  
  Irrational numbers are non-terminating and non-repeating decimals. Needless to say, we almost never write them in their decimal form if we want their exact value. The most common example is Pi. But there are many numbers that are radicals that can't be simplified. For example: sqrt(2); cubert(9); 4th root(6) would all be irrational numbers.
  
  Hope this helps.
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  (1 vote)
Smith Mark
Posted a year ago. Direct link to Smith Mark's post “this doesnt make sense”
this doesnt make sense
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Video transcript

What I want to do in this video is think about whether the product or sums of rational numbers are definitely going to be rational. So let's just first think about the product of rational numbers. So if I have one rational number and-- actually, let me instead of writing out the word rational, let me just represent it as a ratio of two integers. So I have one rational number right over there. I can represent it as a/b. And I'm going to multiply it times another rational number, and I can represent that as a ratio of two integers, m and n. And so what is this product going to be? Well, the numerator, I'm going to have am. I'm going to have a times m. And in the denominator, I'm going to have b times n. Well a is an integer, m is an integer. So you have an integer in the numerator. And b is an integer and n is an integer. So you have an integer in the denominator. So now the product is a ratio of two integers right over here, so the product is also rational. So this thing is also rational. So if you give me the product of any two rational numbers, you're going to end up with a rational number. Let's see if the same thing is true for the sum of two rational numbers. So let's say my first rational number is a/b, or can be represented as a/b, and my second rational number can be represented as m/n. Well, how would I add these two? Well, I can find a common denominator, and the easiest one is b times n. So let me multiply this fraction. We multiply this one times n in the numerator and n in the denominator. And let me multiply this one times b in the numerator and b in the denominator. Now we've written them so they have a common denominator of bn. And so this is going to be equal to an plus bm, all of that over b times n. So b times n, we've just talked about. This is definitely going to be an integer right over here. And then what do we have up here? Well, we have a times n, which is an integer. b times m is another integer. The sum of two integers is going to be an integer. So you have an integer over in an integer. You have the ratio of two integers. So the sum of two rational numbers is going to give you another. So this one right over here was rational, and this one is right over here is rational. So you take the product of two rational numbers, you get a rational number. You take the sum of two rational numbers, you get a rational number.