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.