Area of Rectangles with Mixed Number Side Lengths | Math with Mr. J

[00:00:00]Welcome to Math with Mr. J.

[00:00:04]In this video, I'm going to cover how to find the area of a rectangle with mixed number side lengths. Now, remember, area is the amount of surface a shape covers.

[00:00:16]In other words, it's the amount of space inside a shape. Let's jump into our example and find the area of that rectangle. And remember, for rectangles, we use the formula area equals length * width. So, we'll start by writing out that formula. So, area equals length * width. Now, I used a cursive L for length, so it doesn't look like a one.

[00:00:47]Not a big deal either way though, as long as you know it's an L in the formula. Now, let's plug in the length and width. I'm going to use the longer side for the length. So, 4 and 2/3 m, and then I'll use the shorter side, 2 and 1/2 m, for the width. So, area equals 4 and 2/3 m * 2 and 1/2 m. Keep in mind though, if we switched those and did 2 and 1/2 * 4 and 2/3, we'd still get the same area. So, either way works. Just make sure to multiply the two different side lengths, and you'll get the correct area. Now, we can multiply. But before we multiply, we need to convert both of these mixed numbers to improper fractions. That way, we can multiply straight across. So, let's convert both of these, and we'll start with 4 and 2/3. Now, when converting a mixed number to an improper fraction, we start at the bottom and work our way to the top. We multiply and then add. So, we do 3 * 4, which gives us 12 + 2 gives us 14. That's our numerator.

[00:02:23]And then we keep that denominator of 3 the same. Times, and now let's convert 2 and 1/2.

[00:02:32]So, we start at the bottom and work our way to the top. We multiply and then add. So, 2 * 2 gives us 4 + 1 gives us 5. That's our numerator. And then we keep that denominator of 2 the same. So, 4 and 2/3 converts to 14/3 and then 2 and 1/2 converts to 5/2. Now, after converting those two improper fractions, we can multiply straight across. Remember, when we multiply fractions, we multiply straight across.

[00:03:12]So, numerator * numerator and denominator * denominator. Let's start with the numerators. So, we have 14 * 5.

[00:03:21]That gives us 70 over and now for the denominators. 3 * 2 gives us 6. And we end up with 70/6, 70/6, which is an improper fraction. So, let's convert this to a mixed number. And we do this by dividing our numerator, 70, by our denominator, 6. So, 70 / 6. How many groups of six in 70? How many sixes in 70? 10 sixes gets us to 60. 11 sixes gets us to 66, and then 12 sixes gets us to 72. So, 12 is too many. It's going to be 11. Again, 11 sixes, 11 groups of six gets us to 66.

[00:04:18]That's going to be our whole number of our mixed number. Now, since 11 sixes got us to 66, we have a remainder of four. That's our numerator of our mixed number. And then we keep that denominator of six the same. So, we end up with 11 and 4/6, which is correct, but we can simplify that fractional part of the mixed number. We can simplify 4/6. We have a greatest common factor of two that we can divide our numerator and denominator by. So, we get 11, and then 4 / 2 gives us a numerator of two, and then 6 / 2 gives us a denominator of three. So, we get 11 and 2/3. Now, 2/3 is in simplest form. The only common factor between two and three is one. So, we are done here.

[00:05:28]Our area equals 11 and 2/3, and then this is meters. And since we're working with area here, area is always in square units. So, this is square meters. So, our final simplified area here equals 11 and 2/3 square meters. So, there you have it. There's how to find the area of rectangles with mixed number side lengths.

[00:06:02]I hope that helped.

[00:06:04]Thanks so much for watching.

[00:06:06]Until next time, peace.