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

Step 1: Convert the mixed numbers to improper fractions. $9\frac{1}{2} = \frac{(9 \times 2) + 1}{2} = \frac{18 + 1}{2} = \frac{19}{2}$ $1\frac{2}{3} = \frac{(1 \times 3) + 2}{3} = \frac{3 + 2}{3} = \frac{5}{3}$

Step 2: Find a common denominator for the fractions. The least common multiple of 2 and 3 is 6. $\frac{19}{2} = \frac{19 \times 3}{2 \times 3} = \frac{57}{6}$ $\frac{5}{3} = \frac{5 \times 2}{3 \times 2} = \frac{10}{6}$

Step 3: Subtract the fractions. $\frac{57}{6} - \frac{10}{6} = \frac{57 - 10}{6} = \frac{47}{6}$

Step 4: Convert the improper fraction back to a mixed number. $\frac{47}{6} = 7\frac{5}{6}$ The simplified answer is \boxed{7\frac{5{6}}}.

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

b) To write 34,756 in expanded notation using place values, we break down the number by the value of each digit. $34,756 = \mathbf{30,000 + 4,000 + 700 + 50 + 6}$

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 $\boxed{<}$.

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