decimal to fractions When being asked how to solve the Arithmetic Means of $8, 7, 7, 5, 3, 2,$ and $2$, I understand that adding these numbers then dividing by $7$ (the amount of numbers) gives me the decimal $4.85714...$ But when being asked to change this number into a fraction, I do not understand where the $\frac{6}{7}$ comes from in the answer of $4\frac{6}{7}$. Can someone please help me understand?



Arithmetic mean $= \frac{8+7+7+5+3+2+2}{7} = \frac{34}{7}$


Now, we calculate $\frac{34}{7}$ by using long division and soon we will get a remainder of $6$, the quotient as $4$, and the divisor as $7$ ($x\frac{y}{z}$ ---- $y$ as the remainder, $x$ as the quotient, and $z$ as the divisor). As the result, we will get: $4\frac{6}{7}$
We can also cross-check this division by converting mixed number to improper fraction: $$4\frac{6}{7} =\frac{(4\times 7)+6}{7} = \frac{28+6}{7}= \frac{34}{7}$$
