Inverse Property of Multiplication | Multiplicative Inverse (Reciprocal) | Math with Mr. J

welcome to math with Mr J [Music] in this video I'm going to cover the inverse property of multiplication simply put when we think of the inverse property of multiplication we need to think what can we multiply something by to get one so for the inverse property of multiplication any number multiplied by its multiplicative inverse will equal 1. now a multiplicative inverse is also known as a reciprocal let's jump into number one and take a look at what multiplicative inverses also known as reciprocals are starting with a where we have two now the multiplicative inverse or reciprocal of 2 is going to be what we can multiply 2 by to equal 1. now the first thing that I'm going to do I'm going to rewrite 2 in fractional form now we can write any whole number in fractional form by putting it over one now let's flip that fraction to get the multiplicative inverse or reciprocal meaning let's take the denominator and that's our numerator now and then the numerator will be the denominator so the multiplicative inverse of 2 is one half now let's multiply two by one-half to show that it will equal one so two and I'm going to keep it in fractional form times one half when we multiply fractions we go straight across that's why I kept two in fractional form that way we can multiply the numerators and denominators so top numbers and bottom numbers let's start with the numerators so the top numbers 2 times 1 equals two now for the denominators the bottom numbers one times two that equals 2 as well so we get two over two which is one so the multiplicative inverse or reciprocal of two is one half let's move on to B where we have a fraction one-fourth the multiplicative inverse or reciprocal of 1 4 is well let's flip this fraction so the denominator is now the numerator and the numerator is now the denominator so the multiplicative inverse is four over one which is four now let's multiply to show that this will equal one so we will do one-fourth times four one fourth times 4 and I will keep four in fractional form that way we can multiply straight across let's start with the numerators the top numbers 1 times 4 that equals four now for the denominators the bottom numbers four times one that equals four as well so we get four over four which equals one so the multiplicative inverse or reciprocal of 1 4 is 4. let's move on to number two where we will take a look at a general overview of the inverse property of multiplication we have two parts we have a whole number and a fraction let's start with the whole number so we have a times what equals one now a can be anything so this is an overview of the inverse property of multiplication if we're starting with a whole number let's find the multiplicative inverse or reciprocal of a so let's put a in fractional form by putting it over one then we can flip that fraction we get 1 over a so a times 1 over a equals one let's multiply it to show that that is true so a and I will put it in fractional form that way we can multiply straight across times 1 over a let's start by multiplying the numerators a times 1 equals a the denominators 1 times a equals a as well so we end up with a over a which equals one so the multiplicative inverse or reciprocal of a is one over a and that's the inverse property of multiplication let's move on to the second part of this problem where we have a fraction 1 over a so this is going to be an overview of the inverse property of multiplication when we start with a fraction let's find the multiplicative inverse or reciprocal of 1 over a so 1 over a flip this fraction and we get a over 1 which is just a so the multiplicative inverse or reciprocal of 1 over a is a let's multiply to show that this equals one so one over a times a and I will put a in fractional form that way we can multiply straight across starting with the numerators so 1 times a is a now for the denominators a times 1 equals a as well a over a is just one so the multiplicative inverse or reciprocal of 1 over a is a and that's another example of the inverse property of multiplication let's move on to numbers three four and five and take a look at more examples of the inverse property of multiplication we are going to need to find the multiplicative inverses or reciprocals and multiply by them to get one let's start with number three where we have eight times what equals one we need to find the multiplicative inverse or reciprocal of eight so let's write eight in fractional form and flip that fraction 1 8 is the multiplicative inverse or reciprocal so eight times one eighth equals one now let's multiply to show that that does equal one so eight and I'm writing it in fractional form that way we can go straight across times 1 8. Let's Start by multiplying the numerators so eight times one that equals eight now for the denominators one times eight that equals eight as well so we get eight over eight which equals one let's move on to number four where we have negative five times what equals one so we are starting with a negative let's find the multiplicative inverse or reciprocal of negative five so let's write negative five in fractional form and then we can flip this fraction and we get Negative one-fifth so the multiplicative inverse of negative five is negative one-fifth and it's important that we have that negative there because a negative times a negative gives us a positive and we need a positive one let's multiply and show that this equals a positive one so we have negative five and I will put it in fractional form times negative one one fifth now there are different ways to write negative fractions I'm going to keep the negative signs with the numerators in that multiplication problem just to keep it consistent so now we can multiply straight across and again we have a negative times a negative so this is going to equal a positive let's start with the numerators negative five times negative one that equals a positive five now for the denominators one times five equals five so we get five over five which equals one so negative one-fifth is the multiplicative inverse or reciprocal of negative five we multiply those two to equal one let's move on to number five where we have three tenths times what equals one let's start by finding the multiplicative inverse or reciprocal of three tenths so let's flip this fraction and we get ten thirds so ten over three ten thirds is the multiplicative inverse or reciprocal of three tenths let's multiply to show that these equal one so three tenths times 10 thirds let's multiply straight across starting with the numerators three times ten equals Thirty now for the denominators so ten times three that equals 30 as well so we get 30 over 30 which equals 1. so there you have it there's the inverse property of multiplication and how we find multiplicative inverses also known as reciprocals I hope that helped thanks so much for watching until next time peace foreign