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# Inverse property of multiplication

Simple idea that multiplying by a number's multiplicative inverse gets you back to one. 5 × 1/5 = 1. Created by Sal Khan.

## Want to join the conversation?

- What would you do if you had to find a multiplicative inverse for a fraction?(12 votes)
- flip the fraction

multiplicative inverse of 2/5 = 5/2(21 votes)

- So the multiplicative inverse of 1 is 1/1?(7 votes)
- The multiplicative inverse of 1 is in fact 1/1 which is equal to 1. So 1 is its own multiplicative inverse.(3 votes)

- what about for 4/5 (4 over 5)? the additive inverse is 4/5 + (-4/5) = 0, but the multiplicative inverse!?(6 votes)
- It is the same concept as the video explains, except the video only demonstrates it using whole numbers. For example, with whole numbers, 15 is equivalent to 15/1 (15 over 1). To get that, you multiply by the multiplicative inverse of 15 - in this case, 1/15, by the original number, getting 1. Swapping the numerator and the denominator is the same concept. So for 4/5 (4 over 5), you would multiply it by 5/4 (5 over 4). It is the same steps, but your example is a fraction instead of a whole number. Let me know if I overcomplicated the answer to your question, and I will attempt to simplify it.(11 votes)

- What if we're dealing with negatives? Will this fraction thing still work?(5 votes)
- Yes it will still work. You just have to make sure that
**both numbers that you are multiplying are negative**so that you end up with a positive one. (-72 x -1 / 72 = 1) That's a very important thing to keep in mind for higher level math. Good Question!(6 votes)

- I have a hard question in math it is 1c-7 then it says c-7 how is that possible if u don't know what c is?(3 votes)
- that is not solvable(1 vote)

- Why are there no practices for this?(2 votes)
- You can try practising fraction multiplication and division in Subject: Arithmetic .(2 votes)

- does ever problem with 1/8 = 1?(1 vote)
- I don't know where you got the 1/8 from.

The inverse property of multiplication basically tells us:

any number * its reciprocal = 1

If you have a whole number like 5. Change it to its fraction 5/1. Its reciprocal = 1/5

The property tells us: 5/1 * 1/5 = 1

If you have a fraction like: 3/4. Its reciprocal = 4/3

The property tells us: 3/4 * 4/3 = 1

Hope this helps.(4 votes)

- I don't understand this concept one bit. My math teacher has tried to explain it but it's hopeless! Can someone please explain how to a problem such as a/13 =12?(2 votes)
- a/13=12 so, we already have the answer. All we need to do is multiply 13 times 12, because 13 under a is division. (You do the opposite thing) So, 13x12 is 156. a=156 Make sure you check your answer!(2 votes)

- It's called a reciprocal, right?(2 votes)
- That's right. The multiplicative inverse of a number is the reciprocal of that number.

a/b x b/a = 1 whatever a and b are.

a/b and b/a are reciprocals of one another.(2 votes)

- Ok, where did the 1/5 come from this does not make sense...(2 votes)
- the 1/5 is the reciprocal of 5. 5/5 is the same as 5/(5/1) which equals 5*1/5(2 votes)

## Video transcript

Let's say that I have five lemons so that's [counting to five] ... five lemons and I were to ask you: what do I have to multiply times five to get one? or in this case: what do I have to multiply times five lemons to get one lemon? and so, another question you might ask because really multiplication and division are two sides of the same coin is what do I have to divide five by to get to one lemon or yellow circle, or whatever I have drawn right over here Well, if you have five things and you divide by five, you're gonna have five groups of one so if you divide by five, you're gonna have [counting to five] ... five groups So you could say five divided by five is equal to one take five things and divide it into five groups then each group is going to have one in them or you could say five times one fifth is equal to one (and I use the dot for multiplication) I could also say five times one fifth is equal to one these are all really saying the same thing Maybe what's kind of interesting here (although it's not some huge learning) it's really just another way of writing what you already probably know, is this idea that if I have a number and I multiply times it's multiplicative inverse (and most of the time when people talk about inverses in mathematics they are talking about the multiplicative inverse) then I'm going to get one so five time one fifth is equal to one but that's just because five times one fifth is the same thing as five divided by five if you were to actually multiply this out you actually take five times one fifth this is equal to five-over-one times one-over-five you multiply the numerators: five times one is five multiply the denominators: one times five is five so you have five fifths, and five fifths is the exact same thing as one So if someone where to ask you a question, they say "Hey, I have the number 217 and I want to multiply it by something, and I want to get one after multiplying it by that something" Well then you say - Well look, If I took 217 and divided it by 217 that would get me to one and dividing by 217 is the exact same thing as multiplying by one-over-217 multiplying by its multiplicative inverse which is, once again, a word that is fancier than the actual concept you are just multiplying by the inverse of this number Another way to think about it is if I have five things and I take one fifth of those things, how many things do I have? Well, if I take one fifth of five things I have exactly one thing right over here But the general idea is super-duper-duper simple if I have some crazy number ... 8,345 that's actually not so crazy, let's turn it to something in the millions ... and 271 ... so 8,345,271 And I say, what do I have to multiply by (and now I use this multiplication symbol right now) what do I have to multiply that by in order to get one? I just have to multiply it by the inverse of this the multiplicative inverse of this so one-over-8,345,271