How To Add Fractions With Same Denominators

now we'll look at two examples of addingfractions with like denominators. when addingfractions with like denominators or the samedenominator, we keep the denominator the same and add the numerators. so for two-sevenths plus three-sevenths

How To Add Fractions With Same Denominators, the denominator is going to stay seven and the numberator will be two plus three which is equal to five. so our sum is five-sevenths. if we take a look at a model for thisaddition problem, we can see why the denominator should not change.

if this large rectangle represents one,this would be the model for two-sevenths, this would be the model for three-sevenths and because the denominator is the same, we're adding pieces of the same size. notice how we have a total of fivepieces where each piece represents one-seventh, therefore the sum is equal to five-sevenths as we found above. once we find the sum we need to check to see if this fractionwill simplify, but since five and seven don't share any common factors other than one, this does not simplify. looking at ournext example

we have two-ninths plus one-ninth, so again we have like denominators so the denominator is going to stay the same, and then we add the numerators. well, two plus one is equal to three sothe sum is equal to three ninths, but three and nine do share a commonfactor of three. to show this week could write threeas one times three and nine is three times three. in thisform we can see the common factor of three, three over three simplifies to one,therefore the sum is equal to one-third. again if we take a look atthe model for this here's the model for two-ninths,

here's the model for one-ninth , again because the denominator is the same we are adding pieces of the same size, so we'd have a total of three pieces where each piece represents one-ninth so we have a total of three-ninths. but notice how if we were to divide this large rectangle which equals one intothree equal parts here and here, we can see that thiswould simplify to one-third which we found above. okay, i hope this helps.