Question

Han used 1 1/3 gallons of paint to paints 4/7 of a shed. How many gallons of paint will it take to a paint the whole shed. Write a multiplication equation or a division equation to represent this situation, then find the answer. Show your reasoning.

Answer 1

Given that Han used this amount of paint:

`1(1)/(3)gal`

to paint this part of a shed:

`(4)/(7)`

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:

`1(1)/(3)=((1\cdot3)+1)/(3)=(4)/(3)`

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:

`(4)/(7)x=(4)/(3)`

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:

`\begin{gathered} (7)((4)/(7)x)=((4)/(3))(7) \\ \\ 4x=(28)/(3) \end{gathered}`

2. Apply the Division Property of Equality by dividing both sides of the equation by 4:

`\begin{gathered} (4x)/(4)=(28)/(3\cdot4) \\ \\ x=(28)/(12) \\ \\ x=(7)/(3) \end{gathered}`

Hence, the answer is:

- Equation:

`(4)/(7)x=(4)/(3)`

- Solution:

`x=(7)/(3)`