Solve using a diagram: A gallon of paint covers 1 1/4 walls. Shelly paints 2/3 of a wall. How much paint did she use?

Answer 1

Not a straight forward problem for elementary math!

1 wall needs 4/5 of a gallon of paint.

2/3 of a wall needs (2/3)(4/5) or 8/15 of a gallon.

Answer 2

This is a classic ratios problem. As a first step, convert the mixed number to an improper fraction. So, 1 and 1/4 becomes: 5/4.

1 gallon of paint is to 5/4 of a wall as [x] gallons of paint is to 2/3 of a wall. Algebraically:

1 / (5/4) = x / (2/3)

Now, do some cross multiplication.

Multiply the numerator of the left side of the equation by the denominator of the right side of the equation. Like so: 1 times x = x. This will become the left side of our new equation. Then, multiply the denominator of the left side of the equation by the numerator of the right side of the equation. Like so: (5/4) times (2/3) = 10/12 = 6/5. This will become the right side of our new equation.

So now, our new equation looks like this:

x = 6/5.

Look! It's already solved for us!

Answer: Shelly used 6/5 cans of paint.