91Ó°ÊÓ

The given expression is:

$3\frac{2}{3}+4+5\frac{1}{3}$

The substitution property for multiplication, addition, and subtraction is:

$\begin{array}{c}aâ‹\dots b=c\\ a÷b=c\\ aÂ\pm b=c\end{array}$

The Associative property is:

$a+\left(b+c\right)=\left(a+b\right)+c$

Also, to add or subtract the fraction, the denominator must be the same.

$\begin{array}{c}3\frac{2}{3}=\frac{11}{3}\\ 5\frac{1}{3}=\frac{16}{3}\end{array}$

The expression $3\frac{2}{3}+4+5\frac{1}{3}$ can be written as in below:

$3\frac{2}{3}+4+5\frac{1}{3}=\frac{11}{3}+4+\frac{16}{3}$

Then,

$\begin{array}{l}\frac{11}{3}+4+\frac{16}{3}=\left(\frac{11}{3}+\frac{16}{3}\right)+4\text{ â¶Ä„â¶Ä„â¶Ä„â¶Ä„â¶Ä„â¶Ä„â¶Ä„â¶Ä„â¶Ä„â¶Ä„â¶Ä„â¶Ä„â¶Ä„â¶Ä„â¶Ä‹}\left(\text{´¡²õ²õ´Ç³¦¾±²¹³Ù¾±±¹±ð â¶Ä‰P°ù´Ç±è±ð°ù³Ù²â}\right)\\ =\left(\frac{27}{3}\right)+4\text{ â¶Ä„â¶Ä„â¶Ä„â¶Ä„â¶Ä„â¶Ä„â¶Ä„â¶Ä„â¶Ä„â¶Ä„â¶Ä„â¶Ä„â¶Ä„â¶Ä„â¶Ä‹}\left(\text{³§³Ü²ú²õ³Ù¾±³Ù³Ü³Ù¾±´Ç²Ô â¶Ä‰P°ù´Ç±è±ð°ù³Ù²â}\right)\end{array}$

Since, $\left(\frac{27}{3}\right)+4\text{ }=\frac{27}{3}+\frac{4}{1}\text{ }$. So,

$\begin{array}{l}\frac{11}{3}+4+\frac{16}{3}=\frac{27×1}{3×1}+\frac{4×3}{1×3}\\ =\frac{27}{3}+\frac{12}{3}\text{ â¶Ä„â¶Ä„â¶Ä„â¶Ä„â¶Ä„â¶Ä„â¶Ä„â¶Ä„â¶Ä„â¶Ä„â¶Ä„â¶Ä„â¶Ä„â¶Ä„â¶Ä‹}\left(\text{³§³Ü²ú²õ³Ù¾±³Ù³Ü³Ù¾±´Ç²Ô â¶Ä‰P°ù´Ç±è±ð°ù³Ù²â}\right)\\ =\frac{39}{3}\text{ â¶Ä„â¶Ä„â¶Ä„â¶Ä„â¶Ä„â¶Ä„â¶Ä„â¶Ä„â¶Ä„â¶Ä„â¶Ä„â¶Ä„â¶Ä„â¶Ä„â¶Ä‹}\left(\text{³§³Ü²ú²õ³Ù¾±³Ù³Ü³Ù¾±´Ç²Ô â¶Ä‰P°ù´Ç±è±ð°ù³Ù²â}\right)\\ =\frac{3×13}{3}\\ =13\end{array}$