Answer :
Given that Han used this amount of paint:
[tex]1\frac{1}{3}gal[/tex]to paint this part of a shed:
[tex]\frac{4}{7}[/tex]You can convert the Mixed Number to an Improper Fraction as follows:
1. Multiply the whole number part by the denominator of the fraction.
2. Add the Product to the numerator.
3. The denominator does not change.
Then:
[tex]1\frac{1}{3}=\frac{(1\cdot3)+1}{3}=\frac{4}{3}[/tex]Let be "x" the number of gallons of paint that it will take to paint the whole shed.
You can set up the following equation to represent the situation:
[tex]\frac{4}{7}x=\frac{4}{3}[/tex]Now you need to solve for "x" in order to find its value:
1. Apply the Multiplication Property of Equality by multiplying both sides of the equation by 7:
[tex]\begin{gathered} (7)(\frac{4}{7}x)=(\frac{4}{3})(7) \\ \\ 4x=\frac{28}{3} \end{gathered}[/tex]2. Apply the Division Property of Equality by dividing both sides of the equation by 4:
[tex]\begin{gathered} \frac{4x}{4}=\frac{28}{3\cdot4} \\ \\ x=\frac{28}{12} \\ \\ x=\frac{7}{3} \end{gathered}[/tex]Hence, the answer is:
- Equation:
[tex]\frac{4}{7}x=\frac{4}{3}[/tex]- Solution:
[tex]x=\frac{7}{3}[/tex]