I'm just wanting to confirm and understand why: 2/5 = 2 x 1/5 and why isn't it like before with mixed numerals where this is done: 2 x 1/5 = ((2 x 5)+1)/5 = 11/5 ? is there a conceptual difference i am missing? thanks in advance !! :)

Yes there's a conceptual difference. I believe you are confusing multiplication of a whole number and a fraction, with addition of a whole number and a fraction. Many students have difficulty in math, including higher levels such as algebra, ultimately because they confuse the fundamental concepts of addition and multiplication. ((2 x 5)+1)/5 is equivalent to the mixed number 2 and 1/5. This mixed number means 2 + 1/5, not 2 x 1/5. 2 x 1/5 can be thought of as the repeated addition 1/5 + 1/5, which is clearly 2/5.

Sal explained it in a simple way, but it is confusing for me. I am here to know whether to do reciprocal in the multiplication of fractions. Can someone pls clarify my question?

You do not have to use reciprocals when multiplying fractions, only when dividing.

*_why can't we just add it the normal way.like 1/5+3/4=4/9*_

You cant just add the denominators as well as adding the numerators, you need to find a common factor.

If 1/2 x 5 is 5/2 does that mean 5 x 1/2 is the same?

yes because 1/2 x 5 is the same as 1/2 x 5/1 (because 5 ones are five) and if you multipy 1 x 5 (the top) and 2 x 1( the bottom) you get 5/2 so you are correct

Do they ever answer us back?cause i asked them something from like 3 years ago

People DO answer your questions, but there are thousands of questions, so it's certainly possible that not every one gets an answer. Many of the people answering these questions are those who have taken the course and have mastered all of the concepts - in other words former students who are volunteering their time to answer questions.

If whatever happens to the denominator happens to the numerator why is the whole number only multiplied by the numerator and not the denominator? Are whole numbers +-x/ fractions only between the whole number and numerator?

Technically, A whole number n is the same as n/1. Since anything multiplied by 1 is itself, The denominator doesn't change. You only multiply both numbers by the whole number when you're finding a common denominator.

How would you solve 1/3 x 576?

Divide 576 by 3 to get your answer, which would be 192

How do you multiply by 1000000

Any time you're multiplying by a number that is a 1 followed by some number of 0's, you can simply add on that amount of 0's. If I were to multiply 37 by 10, my answer would be 370. Multiplying 42 by 100 results in 4200. Multiplying 13 by 1 million (1000000) results in 13 million (13000000)

Main content

4th grade

Course: 4th grade > Unit 9

Lesson 1: Multiplying fractions and whole numbers visually

Multiplying fractions and whole numbers visually

Name: Multiplying fractions and whole numbers visually
Uploaded: 2013-10-24T13:44:58Z
Description: Sal gives a visual explanation of multiplying a fraction and a whole number.

CCSS.Math:

Sal gives a visual explanation of multiplying a fraction and a whole number. Created by Sal Khan.

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Gigi V
Posted 4 years ago. Direct link to Gigi V's post “I'm just wanting to confi...”
I'm just wanting to confirm and understand why:
2/5 = 2 x 1/5
and why isn't it like before with mixed numerals where this is done:

2 x 1/5 = ((2 x 5)+1)/5 = 11/5 ?

is there a conceptual difference i am missing? thanks in advance !! :)
Button navigates to signup pageComment on Gigi V's post “I'm just wanting to confi...”
(49 votes)
Answer
- Ian Pulizzotto
  Posted 4 years ago. Direct link to Ian Pulizzotto's post “Yes there's a conceptual ...”
  Yes there's a conceptual difference.
  
  I believe you are confusing multiplication of a whole number and a fraction, with addition of a whole number and a fraction. Many students have difficulty in math, including higher levels such as algebra, ultimately because they confuse the fundamental concepts of addition and multiplication.
  
  ((2 x 5)+1)/5 is equivalent to the mixed number 2 and 1/5. This mixed number means 2 + 1/5, not 2 x 1/5.
  
  2 x 1/5 can be thought of as the repeated addition 1/5 + 1/5, which is clearly 2/5.
  Comment on Ian Pulizzotto's post “Yes there's a conceptual ...”
  (53 votes)
hasini.birlangi
Posted 3 years ago. Direct link to hasini.birlangi's post “Sal explained it in a sim...”
Sal explained it in a simple way, but it is confusing for me. I am here to know whether to do reciprocal in the multiplication of fractions. Can someone pls clarify my question?
Button navigates to signup pageComment on hasini.birlangi's post “Sal explained it in a sim...”
(22 votes)
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- Claire
  Posted 3 years ago. Direct link to Claire's post “You do not have to use re...”
  You do not have to use reciprocals when multiplying fractions, only when dividing.
  Comment on Claire's post “You do not have to use re...”
  (5 votes)
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I need 10 votes
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Gavin Hill
Posted 3 years ago. Direct link to Gavin Hill's post “*_why can't we just add i...”
*why can't we just add it the normal way.like 1/5+3/4=4/9*
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- M a x w e l l P 0 9 6 2
  Posted 2 years ago. Direct link to M a x w e l l P 0 9 6 2's post “You cant just add the den...”
  You cant just add the denominators as well as adding the numerators, you need to find a common factor.
  Comment on M a x w e l l P 0 9 6 2's post “You cant just add the den...”
  (8 votes)
KalebO
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whopper whopper whopper triple junior double whopper flame grilled with perfect toppers aibum aibum

pls up vote me
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ChristinaE
Posted a year ago. Direct link to ChristinaE's post “If 1/2 x 5 is 5/2 does th...”
If 1/2 x 5 is 5/2 does that mean 5 x 1/2 is the same?
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- U Nanny Mus
  Posted a year ago. Direct link to U Nanny Mus's post “yes because 1/2 x 5 is th...”
  yes because 1/2 x 5 is the same as 1/2 x 5/1 (because 5 ones are five) and if you multipy 1 x 5 (the top) and 2 x 1( the bottom) you get 5/2 so you are correct
  Comment on U Nanny Mus's post “yes because 1/2 x 5 is th...”
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Shafiqah McLaughlin
Posted 5 years ago. Direct link to Shafiqah McLaughlin's post “If whatever happens to th...”
If whatever happens to the denominator happens to the numerator why is the whole number only multiplied by the numerator and not the denominator? Are whole numbers +-x/ fractions only between the whole number and numerator?
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(5 votes)
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- lsdiana0701
  Posted 3 years ago. Direct link to lsdiana0701's post “Technically, A whole numb...”
  Technically, A whole number n is the same as n/1. Since anything multiplied by 1 is itself, The denominator doesn't change.
  You only multiply both numbers by the whole number when you're finding a common denominator.
  Button navigates to signup page
  (2 votes)
chady.lacroix
Posted 2 years ago. Direct link to chady.lacroix's post “Do they ever answer us ba...”
Do they ever answer us back?cause i asked them something from like 3 years ago
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(6 votes)
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- Stephen White
  Posted 2 years ago. Direct link to Stephen White's post “People DO answer your que...”
  People DO answer your questions, but there are thousands of questions, so it's certainly possible that not every one gets an answer.
  
  Many of the people answering these questions are those who have taken the course and have mastered all of the concepts - in other words former students who are volunteering their time to answer questions.
  Button navigates to signup page
  (3 votes)
27lzosta
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How do you multiply by 1000000
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- Cavan P
  Posted 2 years ago. Direct link to Cavan P's post “Any time you're multiplyi...”
  Any time you're multiplying by a number that is a 1 followed by some number of 0's, you can simply add on that amount of 0's. If I were to multiply 37 by 10, my answer would be 370. Multiplying 42 by 100 results in 4200. Multiplying 13 by 1 million (1000000) results in 13 million (13000000)
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BraydenBoi
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How would you solve 1/3 x 576?
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- Jo21Mixels
  Posted 3 years ago. Direct link to Jo21Mixels's post “Divide 576 by 3 to get yo...”
  Divide 576 by 3 to get your answer, which would be 192
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  (3 votes)

Video transcript

We've already seen that the fraction 2/5, or fractions like the fraction 2/5, can be literally represented as 2 times 1/5, which is the same thing, which is equal to literally having two 1/5s. So 1/5 plus 1/5. And if we wanted to visualize it, let me make a hole here and divide it into five equal sections. And so this represents two of those fifths. This is the first of the fifths, and then this is the second of the fifths, Literally 2/5, 2/5, 2/5. Now let's think about something a little bit more interesting. What would 3 times 2/5 represent? 3 times 2/5. And I encourage you to pause this video and, based on what we just did here, think about what you think this would be equivalent to. Well, we just saw that 2/5 would be the same thing as-- so let me just rewrite this as instead of 3 times 2/5 written like this, let me write 2/5 like that-- so this is the same thing as 3 times 2 times 1/5. And multiplication, we can multiply the 2 times the 1/5 first and then multiply by the 3, or we can multiply the 3 times the 2 first and then multiply by the 1/5. So you could view this literally as being equal to 3 times 2 is, of course, 6, so this is the same thing as 6 times 1/5. And if we were to try to visualize that again, so that's a whole. That's another whole. Each of those wholes have been divided into five equal sections. And so we're going to color in six of them. So that's the first 1/5, second 1/5, third 1/5, fourth 1/5, fifth 1/5-- and that gets us to a whole-- and then we have 6/5 just like that. So literally 3 times 2/5 can be viewed as 6/5. And of course, 6 times 1/5, or 6/5, can be written as-- so this is equal to, literally-- let me do the same color-- 6/5, 6 over 5. Now you might have said, well, what if we, instead of viewing 2/5 as this, as we just did in this example, we view 2/5 as 1/5 plus 1/5, what would happen then? Well, let's try it out. So 3 times 2/5-- I'll rewrite it-- 3 times 2/5, 2 over 5, is the same thing as 3 times 1/5 plus 1/5. 2/5 is the same thing as 1/5 plus 1/5. So 3 times 1/5 plus 1/5 which would be equal to-- well, I just have to have literally three of these added together. So it's going to be 1/5 plus 1/5 plus 1/5 plus 1/5 plus-- I think you get the idea here-- plus 1/5 plus 1/5. Well, what's this going to be? Well, we literally have 6/5 here. We can ignore the parentheses and just add all of these together. We, once again, have 1, 2, 3, 4, 5, 6/5. So once again, this is equal to 6/5. So hopefully this shows that when you multiply-- The 2/5 we saw already represents two 1/5s. We already saw that, or 2 times 1/5. And 3 times 2/5 is literally the same thing as 3 times 2 times 1/5. In this case, that would be 6/5.

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