Convert fifth to cup
Learn how to convert
1
fifth to
cup
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(fifth\right)={\color{rgb(20,165,174)} x}\left(cup\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(cubic \text{ } meter\right)\)
\(\text{Left side: 1.0 } \left(fifth\right) = {\color{rgb(89,182,91)} 7.570823568 \times 10^{-4}\left(cubic \text{ } meter\right)} = {\color{rgb(89,182,91)} 7.570823568 \times 10^{-4}\left(m^{3}\right)}\)
\(\text{Right side: 1.0 } \left(cup\right) = {\color{rgb(125,164,120)} 2.273045 \times 10^{-4}\left(cubic \text{ } meter\right)} = {\color{rgb(125,164,120)} 2.273045 \times 10^{-4}\left(m^{3}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(fifth\right)={\color{rgb(20,165,174)} x}\left(cup\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 7.570823568 \times 10^{-4}} \times {\color{rgb(89,182,91)} \left(cubic \text{ } meter\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 2.273045 \times 10^{-4}}} \times {\color{rgb(125,164,120)} \left(cubic \text{ } meter\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 7.570823568 \times 10^{-4}} \cdot {\color{rgb(89,182,91)} \left(m^{3}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 2.273045 \times 10^{-4}} \cdot {\color{rgb(125,164,120)} \left(m^{3}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 7.570823568 \times 10^{-4}} \cdot {\color{rgb(89,182,91)} \cancel{\left(m^{3}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 2.273045 \times 10^{-4}} \times {\color{rgb(125,164,120)} \cancel{\left(m^{3}\right)}}\)
\(\text{Conversion Equation}\)
\(7.570823568 \times 10^{-4} = {\color{rgb(20,165,174)} x} \times 2.273045 \times 10^{-4}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(7.570823568 \times {\color{rgb(255,204,153)} \cancel{10^{-4}}} = {\color{rgb(20,165,174)} x} \times 2.273045 \times {\color{rgb(255,204,153)} \cancel{10^{-4}}}\)
\(\text{Simplify}\)
\(7.570823568 = {\color{rgb(20,165,174)} x} \times 2.273045\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 2.273045 = 7.570823568\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{2.273045}\right)\)
\({\color{rgb(20,165,174)} x} \times 2.273045 \times \dfrac{1.0}{2.273045} = 7.570823568 \times \dfrac{1.0}{2.273045}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{2.273045}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{2.273045}}} = 7.570823568 \times \dfrac{1.0}{2.273045}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{7.570823568}{2.273045}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx3.3306967385\approx3.3307\)
\(\text{Conversion Equation}\)
\(1.0\left(fifth\right)\approx{\color{rgb(20,165,174)} 3.3307}\left(cup\right)\)
