Calculate three and four-ninths plus four and six-sevenths. Here we
are adding two mixed numbers. A mixed number is a combination of a whole number and a fraction. So in our
example, the three and the four are the whole numbers and the four-ninths and the six-sevenths
are our fractions.
In order to calculate this addition problem, we should add our whole numbers
together and add our fractions together. Our whole numbers again are three and four; so add those together to get seven. And our fractions we’re adding together are four-ninths and six-sevenths. In
order to add these fractions, we need a common denominator. We want nine and seven to be the same denominator. So we need to find a number
that nine and seven both go into. And it should actually be the smallest number that they both
go into. That number would be sixty-three. So if sixty-three is gonna be our common denominator, how did we get from a
denominator of nine to now a denominator of sixty-three? We would need to multiply the nine by
seven. However if you’re gonna multiply the denominator by seven, you would also need to
multiply the numerator by seven. Now looking at six-sevenths, instead of having seven as a denominator, we’re gonna
have sixty-three as a denominator. To get from seven to sixty-three, we would multiply it by
nine. So if we multiply our denominator by nine, we’d multiply our numerator by nine.
Let’s go ahead and simplify. Remember to bring down your seven. And now we need to take the four-ninths times
seven-sevenths. So we multiply the numerators together, four times seven which is twenty-eight,
and our denominators together, nine times seven which is sixty-three. Now we’re gonna take six times nine multiplying our numerators and then take
seven times nine on the bottom, our denominators. Six times nine gives us fifty-four and seven
times nine gives us sixty-three.
Now that our fractions are like — meaning they have the same denominator — we can
add them together by adding our numerators and keeping our common denominator. So twenty-eight
plus fifty-four is eighty-two. So we have seven plus eighty-two sixty-thirds. Now this wouldn’t make a mixed
number because a mixed number is a combination of a whole number, which is seven — which is great
we have that — and a fraction. Well eighty-two sixty-thirds, yes it’s a fraction. But it’s an
improper fraction. An improper fraction is a fraction that’s greater than or equal to one. And eighty-two out of
sixty-three is bigger than one. So we can actually take one out because we can take out
sixty-three sixty-thirds. So if we take sixty-three out of our numerator at eighty-two, we would have
nineteen sixty-thirds left over.
Now let’s simplify. Because sixty-three over sixty-three is one, a whole number,
and we can add that to our seven, we can put together the seven plus one because they’re whole numbers to get
eight and then nineteen sixty-thirds would be our fraction. So our final answer is eight and nineteen sixty-thirds.