Question

The product of a fraction with the sum of $5\frac{1}{3}$ and $6\frac{1}{3}$ is $3$. what is the fraction.

Answer 1

Given,

The product of a fraction with the sum of $5\frac{1}{3}$ and $6\frac{1}{3}$ is $3$

Step:$1$

Let the fraction is $x$

Here we two mixed fractions convert them into improper fractions.

$5\frac{1}{3}$$=$$\frac{3\times 5+1}{3}$

$$\begin{gathered} =\frac{15+1}{3} \\ =\frac{16}{3} \end{gathered}$$

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

$$\begin{gathered} =\frac{18+1}{3} \\ =\frac{19}{3} \end{gathered}$$

Step:$2$

So, the sum of the given fractions $=$$\frac{16}{3}+\frac{19}{3}$

$$\begin{gathered} =\frac{16+19}{3} \\ =\frac{35}{3} \end{gathered}$$

According to the question,

The product of a fraction with the sum of $5\frac{1}{3}$ and $6\frac{1}{3}$ is $3$

$$\begin{gathered} x\times \left(\frac{35}{3}\right)=3 \\ x\times 35=3\times 3 \\ x=\frac{3\times 3}{35} \\ x=\frac{9}{35} \end{gathered}$$

Therefore, the required fraction $x=\frac{9}{35}$