Calculate two-thirds divided by three. Give your answer in its simplest form.
In this question, we’re being asked to divide a fraction by a whole number. Two-thirds is a fraction, and three is a whole number. We could write this as two-thirds divided by three over one. That way, both of the numbers are written as fractions. Three over one is an improper fraction. It’s a fraction which is greater than one. The numerator, the number on top, is larger than the denominator, the number on the bottom.
This model represents our proper fraction, two-thirds. We’ve divided the square into three equal parts, and two out of three parts are shaded. Now we have to divide these two-thirds by three. One, two, three. We divided by three. Now each of our parts contains two squares out of a possible nine squares. So two-thirds divided by three equals two-ninths.
We could also calculate the answer using a written method. Dividing two-thirds by three is the same as multiplying two-thirds by one over three or a third. Instead of dividing, we’re multiplying. And we’ve changed the order of the numbers. We’ve switched them around. Three over one is now one over three. Now all we need to do is calculate. Starting with the numerator, two times one is two and three times three is nine.
We used a model and a written method to calculate our answer. Two-thirds divided by three is equal to two-ninths. We were asked to give our answer in its simplest form. Two-ninths is in its simplest form. Two-thirds divided by three is equal to two-ninths.