Question

choose all of the sums that are rational.
a $\frac{3}{8} + \frac{3}{7}$
b $0.125 + 5$
c $\frac{1}{2} + 0.375$
d $sqrt{2} + 4$
e $sqrt{4} + \frac{1}{5}$
f $1 + pi$

Explanation:

Step1: Define rational numbers

Rational numbers are numbers that can be written as $\frac{p}{q}$, where $p,q$ are integers and $q
eq0$. Sums of rational numbers are rational; sum of rational + irrational is irrational.

Step2: Evaluate Option A

$\frac{3}{8}$ and $\frac{3}{7}$ are rational.
$\frac{3}{8}+\frac{3}{7}=\frac{21+24}{56}=\frac{45}{56}$

Step3: Evaluate Option B

$0.125=\frac{1}{8}$ and $5=\frac{5}{1}$ are rational.
$0.125+5=5.125=\frac{41}{8}$

Step4: Evaluate Option C

$\frac{1}{2}$ and $0.375=\frac{3}{8}$ are rational.
$\frac{1}{2}+0.375=0.5+0.375=0.875=\frac{7}{8}$

Step5: Evaluate Option D

$\sqrt{2}$ is irrational, $4$ is rational.
$\sqrt{2}+4$ is irrational.

Step6: Evaluate Option E

$\sqrt{4}=2$ (rational), $\frac{1}{5}$ is rational.
$\sqrt{4}+\frac{1}{5}=2+\frac{1}{5}=\frac{11}{5}$

Step7: Evaluate Option F

$\pi$ is irrational, $1$ is rational.
$1+\pi$ is irrational.

Answer:

A. $\frac{3}{8} + \frac{3}{7}$
B. $0.125 + 5$
C. $\frac{1}{2} + 0.375$
E. $\sqrt{4} + \frac{1}{5}$