we want to add or subtract the fractions and write the answer in simplified form the most important thing to remember about adding or subtracting fractions is that we must obtain a common denominator before we add or subtract hopefully we can find the least common denominator but we must have at least a common denominator because by doing this we're adding or subtracting pieces or partitions of the same size let's look at a model before we begin let's consider one-half plus 1 4. notice how here the least common denominator would be four which means you'd have to multiply one half by two over two to obtain an equivalent fraction with a denominator of four so instead of one half plus one fourth we have 2 4 plus 1 4. so notice how because our denominators are the same we'll be adding pieces of the same size notice here's the model for 2 4 and here's a model for 1 4. now because the partitions or pieces are the same size we can see we'll have a total of three pieces where each piece is one-fourth giving us a sum of three-fourths so by determining a common denominator we're making sure that we add or subtract pieces of the same size now let's also look at a common error a common error when adding fractions would be to add the numerators and add the denominators using our models we can see why this does not make sense here's our model for one half here's our model for one fourth if we add these two pieces together there's no way we can have two pieces each the size of one sixth giving us a sum of 2 6. this method does not work we must obtain a common denominator before we add or subtract fractions so looking at our first example here we have 1 4 plus 5 8. so ideally we want to find the least common denominator which would be the least common multiple of four and eight which would be eight so we want to write one-fourth as an equivalent fraction with the denominator of eight we can do this by multiplying one-fourth by two over two so now this would be two-eighths plus five-eighths now that our denominator is the same the denominator is going to stay eight and the numerator is going to be two plus five or seven our sum is 7 8 which does not simplify next we have 5 6 minus 5 12. again we're looking for the least common denominator which is the least common multiple of 6 and 12 which would be 12. so we want to write 5 6 as an equivalent fraction with a denominator of 12 so we'll multiply 5 6 by 2 over 2 so this will give us notice 10 12 minus 5 12. notice because we have a common denominator the partitions or pieces are the same size so it'll stay 12 and the numerator is going to be 10 minus 5 which equals 5. this does not simplify and therefore this is our difference 5 12. next we have 5 7 plus 3 5. notice here both 5 and 7 are prime and therefore the least common denominator is going to be their product seven times five equals 35 we're going to write both fractions with a denominator of 35 so we'll multiply 5 7 by 5 over 5. we'll multiply 3 5 by seven over seven so we have 25 35 plus 21 35 so our denominator is going to stay 35 and the numerator is going to be 25 plus 21 which equals 46. so notice here we have an improper fraction it does not simplify because 46 and 25 don't have any common factors other than 1 but notice how we are asked to enter a reduced fraction or mixed number in simplified form so let's also convert this to a mixed number this fraction means 46 divided by 35 so 46 divided by 35 there's 135 and 46 when we subtract we have a remainder of 11 which means 46 35 is equal to one whole and eleven thirty-fifths we have the remainder over the divisor let's go ahead and enter our mixed number one and eleven thirty-fifths and now for our last example we have one-third minus one-fourth so we're looking for the least common multiple of three and four which is our least common denominator which would be twelve so multiply one-third by four over four we'll multiply one-fourth by three over three so we have four twelfths minus three twelfths so our denominator stays 12 and the numerator is four minus three which equals one so our difference is 1 12 and that's going to do it for these examples i hope you found this helpful