3 Calculate: 9 1/2 - 1 2/3. 2.4 In the number 34,756: a) What is the value of the digit 5? b) Write 34,756 in expanded notation using place values. c) Fill in <, >, or =. 0.756 ____ 0.765

$$9\frac{1}{2} = \frac{(9 \times 2) + 1}{2} = \frac{18 + 1}{2} = \frac{19}{2}$$ $$1\frac{2}{3} = \frac{(1 \times 3) + 2}{3} = \frac{3 + 2}{3} = \frac{5}{3}$$

The least common multiple of 2 and 3 is 6.

$$\frac{19}{2} = \frac{19 \times 3}{2 \times 3} = \frac{57}{6}$$ $$\frac{5}{3} = \frac{5 \times 2}{3 \times 2} = \frac{10}{6}$$

$$\frac{47}{6} = 7\frac{5}{6}$$

The simplified answer is $\boxed{\mathbf{7\frac{5}{6}}}$.

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a) The digit 5 in the number 34,756 is in the tens place.
The value of the digit 5 is $5 \times 10 = \boxed{\mathbf{50}}$.

b) To write 34,756 in expanded notation using place values, we break down the number by the value of each digit.

$$34,756 = \boxed{\mathbf{30,000 + 4,000 + 700 + 50 + 6}}$$

c) To fill in $<, >$ or $=$ for $0,756 \_ 0,765$, we compare the digits from left to right.
The first digit after the decimal point is 7 for both numbers.
The second digit after the decimal point is 5 for 0,756 and 6 for 0,765.
Since $5 < 6$, we have $0,756 < 0,765$.
So, the answer is $\boxed{\mathbf{<}}$.