Add three-sevenths and six-sevenths; then write the answer in its simplest form.
Let’s sketch some things. Let’s draw our three-sevenths in pink, so there is our three-sevenths. And to those three-sevenths, we want to add six-sevenths; here’s the first one. Okay, I’ve added four-sevenths to the first line, but that’s all that will fit there. I still have two more sevenths that I need to add. So I have to fill in those two-sevenths underneath.
When I added three-sevenths and four-sevenths, they made one whole, but I still need to add two more sevenths. What that shows us is that when we add three-sevenths plus six-sevenths, we get one whole and two-sevenths, but the thing is, we can’t always draw that kind of picture. Sometimes we need to be able to solve these kind of problems without drawing a picture. And in that case, we add our numerators together: three plus six equals nine. Our denominator stays the same, seven.
And now we have the fraction nine over seven, but nine over seven is an improper fraction; its numerator is larger than its denominator, so we break it up into two parts: seven-sevenths plus two-sevenths. Seven out of seven equals one, and we keep the two-sevenths as another piece. Nine over seven in simplest form is one and two-sevenths. Our simplest form answer is one and two-sevenths.