Video: Finding the Product of Two Mixed Numbers

James is making a dog house that is 3 1/2 feet long and 2 2/3 feet wide. How many square feet of area will the dog house be?

02:30

Video Transcript

James is making a dog house that is three and a half feet long and two and two-thirds feet wide. How many square feet of area will the dog house be?

We’ve been given the dimensions of James’s dog house: three and a half feet long, two and two-thirds feet wide. If we think about how many square feet of area the dog house will take up, that will be this space. Based on the shape of the dog house, we know that the area will be equal to the length times the width. Both of our measurements are given in feet, which means multiplying these two values together will give us square feet. However, we don’t multiply these mixed numbers together.

In order to do this multiplication, we’ll need to calculate their equivalent improper fractions. To do that, you multiply the whole number value by the denominator, three times two, and then add the numerator of one. And that whole value goes over the denominator of two. Three times two is six plus one is seven. Three and one-half written as an improper fraction is seven-halves. Similarly, we need to multiply two by the denominator of three and add the numerator two, putting that all over three. Two times three is six plus two is eight, which gives us eight-thirds.

To find the area of this dog house, we’ll need to multiply seven-halves by eight-thirds. Before we multiply, we can simplify. Eight and two are both divisible by two. We then have seven times four, which is 28, and one times three in the denominator, which is three. Since the length and width were given as a mixed number, we might want to calculate twenty-eight thirds as a mixed number for the area. And we know that twenty-seven thirds plus one-third equals twenty-eight thirds. But twenty-seven thirds can be simplified. 27 divided by three equals nine, and nine plus one-third written as a mixed number is nine and one-third.

Here, we’re dealing with area, and we need to calculate the units. Both the length and width are given in feet, making the area square feet. The area of this dog house would be nine and one-third square feet.