# 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 $${\color{rgb(20,165,174)} x}$$
$${\color{rgb(20,165,174)} x}\approx3.3306967385\approx3.3307$$
$$\text{Conversion Equation}$$
$$1.0\left(fifth\right)\approx{\color{rgb(20,165,174)} 3.3307}\left(cup\right)$$