Question

Select the correct statement for the given mixed numbers.
$A=1\frac{1}{3},B=1\frac{4}{6},D=1,\text{and}C=2\frac{2}{3}$

Statement 1: The sum of A and B is $3$.
Statement 2: The sum of A and C is $4$.

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

Answer 1

The correct option is A Both statements are true.


Detailed step-by-step solution:

For Statement $1$:
$1\frac{1}{3}+1\frac{4}{6}$

$=(1+1)+(\frac{1}{3}+\frac{4}{6})$

Fractions $\frac{1}{3}\text{and}\frac{4}{6}$ are unlike fractions.

The equivalent fraction of $\frac{1}{3}$ with $6$ as the denominator.

$\frac{1}{3}=\frac{1\times 2}{3\times 2}=\frac{2}{6}$

Now, $\frac{2}{6}\text{and}\frac{4}{6}$ are like fractions. So, add the numerators, and keep the denominators the same.

$=2+(\frac{2}{6}+\frac{4}{6})$

$=2+\frac{6}{6}$

$=2+1=3$

Hence, Statement $1$ is true.

For Statement $2$:
$1\frac{1}{3}+2\frac{2}{3}$

$=(1+2)+(\frac{1}{3}+\frac{2}{3})$

Now, $\frac{1}{3}\text{and}\frac{2}{3}$ are like fractions. So, add the numerators, and keep the denominators the same.

$=3+(\frac{1}{3}+\frac{2}{3})$

$=3+\frac{3}{3}$

$=3+1=4$
Hence, Statement $2$ is true.

So, both statements are correct.

Hence, Option B is correct.