Dividing Whole Numbers by Unit Fractions Using Models

Ah, breakfast. A time for breaking the overnight fast and satisfying our hunger! But first, let's satisfy your hunger for knowledge and learn about dividing whole numbers by unit fractions using models. You may already know that division is a process of sharing or splitting a number into equal parts, and that a unit fraction is a fraction where the numerator is one. But what happens when you divide whole numbers by unit fractions? Let's say we have one whole pancake and we want to divide this into quarters. The division sentence for this would be one divided by one quarter. We are simply asking how many quarters are there in this whole pancake? This circle represents our pancake. The complete circle is one whole. Since the division sentence asks us to divide the whole by one-quarter, we can split the model into equally sized quarters. Then, to find the answer, we simply count how many quarter pieces there are in this whole. There are four one quarter pieces in this whole, so one divided by one-quarter is four. It is important to remember that anytime you divide a whole number by a unit fraction, your quotient will always be a value greater than the whole number you began with. Now it's your turn! This time, there are three muffins and each one needs to be divided into thirds. Pause the video to solve the problem and press play when you are ready for the solution. First, set up a model for the muffins; we need three whole circles. Then, divide each muffin into thirds, like this. Finally, count all the one third pieces there are in all three muffins. There are nine one third pieces of muffins, so three divided by one third is nine. Now for the final problem! There are four pieces of bacon, which will be divided into one fifth pieces. Pause the video to solve the problem and press play when you are ready for the solution. First, set up a model for the bacon; this time we will use four fraction bars. Then divide each piece into fifths. Finally, count all the one fifth pieces there are in all four pieces of bacon. Four divided by one fifth is twenty. To summarise, when dividing whole numbers by unit fractions, remember you are asking how many of the unit fractions make up the whole. As a result, the quotient will always be a whole number greater than the one you began with. Hopefully todays learning has given you some food for thought!