Question

Tyler used 1 1/4 gallons of paint to paint 5/7 of a fence. How many gallons will it take to paint the whole fence? Explain or show your reasoning.

Answer 1

For this case we have missing $\frac {2} {7}$of fence to be painted.

To paint $\frac {5} {7}$ of fence we used:

$1 \frac {1} {4} = \frac {4 * 1 + 1} {4} = \frac {5} {4}$gallons of paint. So, we make a rule of three:

$\frac {5} {4} ------------> \frac {5} {7}\\x --------------------------> \frac {2} {7}$

Where the variable "x" represents the gallons of paint needed to paint the missing fence

$x = \frac {\frac {2} {7} * \frac {5} {4}} {\frac {5} {7}}\\x = \frac {70} {140} = \frac {1} {2} = 0.5$

Thus, 0.5 gallons of paint is missing for the missing fence.

Answer

0.5 gallons