Question

Which of the following statements about the given mixed numbers is true?
$A=2\frac{1}{3},B=2\frac{2}{3},C=3\frac{1}{3},D=3,$
Statement 1: The sum of $A$ and $B$ is $5$.
Statement 2: The sum of $C$ and $D$ is $6$.

• A. Statement 1 is true and statement 2 is false.
• B. Both statements are false.
• C. Both statements are true.
• D. Statement 1 is false and statement 2 is true.

Answer 1

The correct option is A Statement 1 is true and statement 2 is false.

For statement 1,
$A=2\frac{1}{3}$
$=2+\frac{1}{3}$
$=\frac{2\times 3}{1\times 3}+\frac{1}{3}$
$=\frac{6}{3}+\frac{1}{3}$
$=\frac{7}{3}$

$B=2\frac{2}{3}$
$=2+\frac{2}{3}$
$=\frac{2\times 3}{1\times 3}+\frac{2}{3}$
$=\frac{6}{3}+\frac{2}{3}$
$=\frac{8}{3}$

Sum of A and B $=2\frac{1}{3}+2\frac{2}{3}$
$=\frac{7}{3}+\frac{8}{3}$
$\frac{7}{3}$ and $\frac{8}{3}$ are like fractions.
Adding the numerators and keeping the denominators the same,
$=\frac{7}{3}+\frac{8}{3}$
$=\frac{7+8}{3}$
$=\frac{15}{3}$
$=5$
Hence, statement $1$ is true.

$C=3\frac{1}{3}$
$=3+\frac{1}{3}$
$=\frac{3\times 3}{1\times 3}+\frac{1}{3}$
$=\frac{9}{3}+\frac{1}{3}$
$=\frac{10}{3}$

$D=3$

Sum of C and D $=\frac{3}{1}+\frac{10}{3}$
Since the denominator of both the fractions are not the same, let’s multiply $\frac{3}{1}$ by $\frac{3}{3}$.
$=\frac{3\times 3}{1\times 3}+\frac{10}{3}$
$=\frac{9}{3}+\frac{10}{3}$
$=\frac{19}{3}$
So, $\frac{19}{3}$ is not equal to $6.$
Hence, statement $2$ is false.