Question

How many $ \dfrac{1}{3} $ cups do you need to make $ \dfrac{1}{2} $ cup?

Answer 1

Hint:
Cups is a unit of volume popular in English speaking countries. Let's say we have an 'n' number of $ \dfrac{1}{3} $ cups which amount to $ \dfrac{1}{2} $ cups. We can form a linear equation and solve (see Note below) for the value of 'n'. Remember that the total volume of 'n' number of $ \dfrac{1}{3} $ cups will be $ \left( n\times \dfrac{1}{3} \right) $ cups.

Complete Step by step Solution:
Let's say that n cups of size $ \dfrac{1}{3} $ cups amount to a total volume of $ \dfrac{1}{2} $ cups.
We have the following equation:
n × $ \dfrac{1}{3} $ = $ \dfrac{1}{2} $
Multiplying both sides by 3, we get:
⇒ n × $ \dfrac{1}{3} $ × 3 = $ \dfrac{1}{2} $ × 3
⇒ n = $ \dfrac{3}{2} $
Simplifying the RHS by performing the division, we get:
⇒ n = $ 1\dfrac{1}{2} $ = 1.5

Therefore, we need a "1 and a half" or "1.5" number of $ \dfrac{1}{3} $ cups to make $ \dfrac{1}{2} $ cups.

Note:
Remember that we can add / subtract or multiply / divide both sides of the equation by the same number, without affecting the equality. To find the value of the variable, eliminate the terms so as to have all the terms containing the variable on one side and the constants (numbers) on the side of the equality. Since this is a linear equation, there will be a single value of the variable which satisfies the equation.
Both the US liquid and imperial gallon are divided into four quarts (quarter gallons), which in turn are divided into two pints, which in turn are divided into two cups, which in turn are further divided into two gills. Thus, both gallons are equal to four quarts, eight pints, sixteen cups, or thirty-two gills.