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Core Connections: Course 2

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Core Connections: Course 2 View details

Chapter Closure

Exercise 135 Page 124

When multiplying real numbers, the product will be positive if the signs are the same and it will be negative if the signs are different.

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We want to calculate the given product using the given rectangle diagram. 2/3* 1/2 Before we do that, recall that a generic rectangle is a diagram that can help us visualize multiplying expressions. Each side of the rectangle represents one expression we want to multiply. The product of the expressions is the sum of the areas of the smaller rectangles. Let's take a look at an example.

Keeping this in mind, let's go back to our rectangle.

Notice that the area of each rectangle can correspond to 12 square units. This means that each rectangle has the length of 1 and the width of 12 units.

Finally, we can split both rectangles into two other shapes in a way where one part has the length of 23 and the other part has the length of 13.

Finally, we can calculate the product. We can recall that when multiplying real numbers, the product will be positive if the signs are the same and it will be negative if the signs are different. cc Same Sign & Different Signs (+)(+)=(+) & (+)(-)=(-) (-)(-)=(+) & (-)(+)=(-) In our case both numbers are positive, so the product will be positive.

2/3* 1/2

Multiply fractions

2* 1/3* 2

Multiply

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a/b=.a /3./.b /3.

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We can verify this using a calculator.

We can also mark the regions with an area of 13 square units on our rectangle diagram.

We can see that our rectangle consists of three rectangles with an area of 13 square units.

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