How To Add Fractions Without Lcd

here we want to add the fractions and make sure that our sums in simplest form. the most important thing to remember about adding fractions as we have to obtain a common denominator. so looking at our first examplewe have three fifth plus one sixth. so looking at the denominator of fiveand the denominator of six

How To Add Fractions Without Lcd, the least common denominator is goingto be the least common multiple of five and six. which in this case would be 30. so we need to rewrite each of thesefractions with the denominator of 30. have to multiply the numeratordenominator of three fifth by six.

and multiply the numeratordenominator of one sixth by five. notice how on both cases weremultiplying by a fraction has a value of one. therefore we're just changing the form of the fraction but they will be equivalent fractions. so we multiply these two fractionswere going to have eighteen thirtieth. we multiply here we're going to have five thirtieth. now our denominator is the same. we can add the fractions. denominator is going to stay the same.

and then we add the numerator.so 18 plus five is equal to 23. in our second example we havetwelve twenty seventh plus two ninth. so the first step is to determineour least common denominator. which is going to be the leastcommon multiple of nine and 27. so this question is a little bit more challenging. so what we can do is use theprime factorization of denominators to help us determine the least common denominator. so what we're going to do isrewrite this first fraction as 12. over the prime factorization of 27.

which would be three, times three, times three. plus two over the prime factorizationof nine which is three times three. now keeping in mind that order to add thesefractions the denominators must be the same. notice how this fraction herehad an extra factor of three. the denominators would be the same. so we can multiply by a factor of three here. as long as we do the same to the numerator. so by using the prime factorization of denominators.

we can identify the lcd by determining which factors we must multiply by to make the denominators the same. now let's go and rewrite thesewith our common denominator. this is going to be twelve twenty seventh the original fraction. this fraction here is now going to be six twenty seventh. denominator stays the same.

add the numerator. 12 plus six is equal to 18. now we can't forget to simplify here. we saw above the prime factorization of 27 would be three, times three, times three. and the prime factorization of 18 would be two, times three, times three. so this simplifies. three over three simplifies to one. here and here.

so the final sum here is two third. we'll take a look at one more example in the next video.