### Instruction: Of the numbers $\frac{7}{10}, \frac{4}{5}$ and $\frac{3}{4}$, which number is the arithmetic mean of the other two?### Response: To find the arithmetic mean of two numbers, I need to add them and divide by 2.
So I'm looking for a number that satisfies this equation: $\frac{a+b}{2} = c$, where $a$, $b$, and $c$ are the given fractions.
I can rewrite this equation as $a+b = 2c$, which might make it easier to compare the fractions.
I can also convert the fractions to decimals, since I know how to add and multiply decimals more easily than fractions.
So $\frac{7}{10} = 0.7$, $\frac{4}{5} = 0.8$, and $\frac{3}{4} = 0.75$.
Now I can plug in these values into the equation and see if any of them work.
If $a = 0.7$ and $b = 0.8$, then $a+b = 1.5$ and $2c = 1.5$, so $c = 0.75$.
This works, so $\frac{3}{4}$ is the arithmetic mean of $\frac{7}{10}$ and $\frac{4}{5}$.