Question

How do you write the degree measure over $ 360^\circ $ to find the fraction of the circle given $ 240^\circ $ ?

Answer 1

Hint: Here we will convert the given word statements in the form of the mathematical expressions and then will simplify for the resultant required value. Here, we will frame the frame for the circle, where fraction is the expression in which numerator is placed upon the denominator.

Complete step by step solution:
Given that: the degree measure over $ 360^\circ $ to the fraction of the circle given $ 240^\circ $
Fraction is the term which is defined as the part of the whole, and it is the term expressed as a numerator upon the denominator.
The above statement can be expressed as: $ \dfrac{{240^\circ }}{{360^\circ }} $
Now, find the factors for the terms in the above expression –
 $ \dfrac{{240^\circ }}{{360^\circ }} = \dfrac{{2 \times 120^\circ }}{{3 \times 120^\circ }} $
Common factors from the numerator and the denominator cancel each other and therefore remove $ 120^\circ $ from the numerator and the denominator of the above expression.
 $ \dfrac{{240^\circ }}{{360^\circ }} = \dfrac{2}{3} $
Hence, the degree measure over $ 360^\circ $ to the circle given $ 240^\circ $ is expressed as $ \dfrac{2}{3} $ of the circle.

Note: Always frame the correct mathematical expression and remember the correct representation is important. Whole term is always placed in the denominator and its part is always placed in the numerator part and in case the terms are interchanged the solution will be wrong. Be good in solving the fractions and by getting the values removed by finding the common multiples from the numerator and the denominator. Factorization is done while simplifying, which is to find out the terms when multiplied together to form the original value.