### 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 two.
So I want to see if any of these numbers is equal to the sum of the other two divided by two.
I could try plugging in each number and see if it works, but that might take a lot of time and fractions can be tricky to work with.
A better idea is to convert all the fractions to decimals first, because decimals are easier to add and divide.
I know that $\frac{7}{10}$ is 0.7, $\frac{4}{5}$ is 0.8 and $\frac{3}{4}$ is 0.75.
Now I can try each decimal and see if it is the mean of the other two.
If I try 0.7, I get $(0.8 + 0.75) \div 2 = 0.775$, which is not 0.7, so 0.7 is not the mean.
If I try 0.8, I get $(0.7 + 0.75) \div 2 = 0.725$, which is not 0.8, so 0.8 is not the mean either.
If I try 0.75, I get $(0.7 + 0.8) \div 2 = 0.75$, which is exactly 0.75, so 0.75 is the mean.
Therefore, the number that is the arithmetic mean of the other two is $\frac{3}{4}$ or 0.75.