Divide refers to the mathematical operation of partitioning a quantity or number into equal parts. It is the inverse operation of multiplication and is used to determine how many times one number is contained within another.
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Division is used to find the number of times one quantity is contained in another, and the result is called the quotient.
The dividend is the number being divided, the divisor is the number by which the dividend is being divided, and the quotient is the result of the division.
Dividing a rectangle's area by its length can give its width, and dividing a triangle's area by its base can give its height.
Dividing a three-dimensional shape's volume by its height can give its area, and dividing its surface area by its height can give its perimeter.
Dividing is an essential operation in solving geometry problems involving the properties of rectangles, triangles, trapezoids, volume, and surface area.
Review Questions
How can division be used to determine the width of a rectangle given its area and length?
To find the width of a rectangle given its area and length, you can divide the area by the length. This will give you the width of the rectangle, as the formula for the area of a rectangle is length times width. By dividing the area by the length, you are essentially determining how many times the length is contained within the area, which gives you the width of the rectangle.
Explain how division can be used to find the height of a triangle given its area and base.
The formula for the area of a triangle is $\frac{1}{2} \times \text{base} \times \text{height}$. To find the height of a triangle given its area and base, you can rearrange this formula to solve for the height by dividing the area by $\frac{1}{2}$ and then dividing that result by the base. This allows you to determine the height of the triangle, as division is used to find how many times the base is contained within the area multiplied by 2.
Describe how division can be used to calculate the perimeter of a three-dimensional shape given its surface area and height.
To find the perimeter of a three-dimensional shape given its surface area and height, you can divide the surface area by the height. This will give you the area of the shape's base, which can then be used to calculate the perimeter. By dividing the surface area by the height, you are determining how much of the surface area is attributed to the base, allowing you to then use that information to find the perimeter of the shape.