To solve the equation \( 4 ÷ ? = 1 \), we are looking for a number that when 4 is divided by that number gives us 1. According to the properties of division, if you divide a number by itself, the result is 1. Therefore, the number we are looking for is 4 itself.
So, 4 divided by 4 equals 1:
\[ 4 ÷ 4 = 1 \]
Now, regarding your paint mixing scenario, if you want to go from 4 quarts of red paint to 1 quart of red paint, you would divide 4 by 4, so the answer for the blank is 4.
Now, regarding the additional information involving white paint:
You have:
- 4 quarts of red paint with 3 quarts of white paint, and
- 1 quart of red paint with an unknown amount of white paint.
To maintain the same proportion of red to white paint as in the first case, we can set up a ratio.
In the first scenario, you have:
\[ \text{Ratio of Red to White} = \frac{4 \text{ (Red)}}{3 \text{ (White)}} \]
The ratio can also be expressed as \( \frac{4}{3} \).
In the second scenario, with 1 quart of red paint, we want to find how much white paint (let's call that \( x \)) is needed to maintain the same ratio:
\[ \frac{1}{x} = \frac{4}{3} \]
Cross-multiply to solve for \( x \):
\[ 4x = 3 \ x = \frac{3}{4} \]
Thus, when you have 1 quart of red paint, you would need \( \frac{3}{4} \) (or 0.75) quarts of white paint to maintain the same ratio.
So, the answer to the unknown amount of white paint is \( \frac{3}{4} \) quarts.