Question

Write the degree measure over 360 to find the fraction of the circle given ${120}^{\circ }$?

Answer 1

Hint: Here, we need to express the given degree measure as a fraction in the simplest form. We will divide the given degree value by the total degree measure of the circle. After that divide both numerator and denominator by the same number to get the desired result.

Complete step by step answer:
A fraction is a number that represents a part of a group. It is written as ${\displaystyle \frac{a}{b}}$, where a is called the numerator and b is called the denominator. The group is divided into b equal parts.
We have to divide the fraction of the circle given ${120}^{\circ }$ by the degree measure over 360.
$\Rightarrow {\displaystyle \frac{120}{360}}$
We know that a fraction ${\displaystyle \frac{a}{b}}$ is in the simplest form if a and b are co-prime. We will divide the numerator and denominator by the same number till they become co-prime.
We know that 120 is the product of 120 and 1, and 360 is the product of 120 and 3.
Therefore, both the numerator 120 and the denominator 360 are divisible by 120.
Dividing the numerator and denominator by 120, we get
$\Rightarrow {\displaystyle \frac{120}{360}}={\displaystyle \frac{{\displaystyle \frac{120}{120}}}{{\displaystyle \frac{360}{120}}}}$
Cancel out the common factors,
$\Rightarrow {\displaystyle \frac{120}{360}}={\displaystyle \frac{1}{3}}$
Hence, the fraction of the circle given ${120}^{\circ }$ by the degree measure over 360 is ${\displaystyle \frac{1}{3}}$.

Note: We used the term co-prime numbers in the solution. Two numbers are called co-prime numbers if they do not share any common factor other than 1. For example, the factors of 73 are 1 and 73. The factors of 200 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200. Since they have no common factor other than 1, the numbers 73 and 200 are co-prime numbers.