Answer
Flat-out lie is the response given least often.
240 respondents answered flat-out lie.
$\frac{5}{12}$ responded flat-out lie or total fabrication.
Work Step by Step
Find the smallest fraction by writing each fraction using the same denominator. The least common multiple of the denominators is 60.
$\frac{1}{3}=\frac{1\times20}{3\times20}=\frac{20}{60}$
$\frac{1}{4}=\frac{1\times15}{4\times15}=\frac{15}{60}$
$\frac{1}{5}=\frac{1\times12}{5\times12}=\frac{12}{60}$
$\frac{13}{60}$
12 is the smallest numerator, so $\frac{12}{60}$ or $\frac{1}{5}$ is the smallest fraction making flat-out lie, the section marked as $\frac{1}{5}$, the response given least often.
Find $\frac{1}{5}$ of the total respondents to find how many said flat-out-lie.
$\frac{1}{5} \times 1200$ = $\frac{1200}{5}$ = 240
Add $\frac{12}{60} + \frac{13}{60}$ to find the fraction who said flat-out lie or total fabrication.
$\frac{12}{60} + \frac{13}{60}$ = $\frac{25}{60}$ = $\frac{25 \div 5}{60 \div 5}$ = $\frac{5}{12}$
