Big Ideas Math: Modeling Real Life, Grade 7
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Big Ideas Math: Modeling Real Life, Grade 7 View details
1. Circles and Circumference
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Exercise 8 Page 366

The radius of a circle is the distance from the center to any point on the circumference. The diameter is the distance from one side of the circle's circumference, through the center of the circle, to the opposite side.

1 34 inches

Practice makes perfect

We want to find the radius of the circle given its diameter. Let's recall the definitions of radius and diameter.

  • Radius: Distance from the center of the circle to any point on the circumference.
  • Diameter: Distance from one side of the circle's circumference, through the center of the circle, to the opposite side.
We are told that the diameter of this button is 3 12 centimeters. According to the definitions, the radius is half the diameter. Let's divide the diameter by 2! 3 12Ă· 2 Before we evaluate the expression, let's first rewrite the expression so that all of the numbers are fractions.
3 12Ă· 2
3* 2+1/2Ă· 2
3* 2+1/2Ă· 2/1
6+1/2Ă· 2/1
7/2Ă· 2/1
Recall that dividing two fractions is the same as multiplying the first fraction by the reciprocal of the second fraction. 7/2Ă· 2/1 = 7/2* 1/2 When we multiply fractions, we need to remember that the product of two fractions is equal to the product of the numerators divided by the product of the denominators. Let's find the given product!
7/2* 1/2
7* 1/2* 2
7/4
The quotient is 74. This is not the simplest form of this fraction because it is improper. Improper fractions can be written as mixed numbers.
7/4
4+3/4
4/4+3/4
1+3/4
1 34
This means that the radius is 1 34 inches.