Determine whether the numerical inequality is true or false. $\frac { 1 } { 4 } + \frac { 1 } { 5 }

Question

Determine whether the numerical inequality is true or false. $\frac { 1 } { 4 } + \frac { 1 } { 5 } < \frac { 1 } { 5 } + \frac { 1 } { 6 }$
A) False
B) True

Quizplus · Accepted Answer

To determine the truth value of the inequality, we can find the common denominator and simplify:

\begin{align*}
\frac{1}{4} + \frac{1}{5} &< \frac{1}{5} + \frac{1}{6} \
\frac{30}{120} + \frac{24}{120} &< \frac{24}{120} + \frac{20}{120} \
\frac{54}{120} &< \frac{44}{120} \
0.45 &< 0.366666 \ldots \
\end{align*}

Since $0.45$ is not less than $0.366666\ldots$, the inequality is false. The answer is A) False.

Determine Whether the Numerical Inequality Is True or False 14+15<15+16\frac { 1 } { 4 } + \frac { 1 } { 5 } < \frac { 1 } { 5 } + \frac { 1 } { 6 }41​+51​<51​+61​

Determine Whether the Numerical Inequality Is True or False $\frac { 1 } { 4 } + \frac { 1 } { 5 } < \frac { 1 } { 5 } + \frac { 1 } { 6 }$