Question

estimate. which sign makes the statement true? 172? 3,344\frac{1}{2} \div 10\frac{1}{2} > <

Explanation:

Step1: Convert mixed numbers to improper fractions

First, convert \( 3344\frac{1}{2} \) to an improper fraction: \( 3344\frac{1}{2}=\frac{3344\times2 + 1}{2}=\frac{6689}{2} \)
Then, convert \( 10\frac{1}{2} \) to an improper fraction: \( 10\frac{1}{2}=\frac{10\times2+1}{2}=\frac{21}{2} \)

Step2: Perform the division

Now, divide the two fractions: \( \frac{6689}{2}\div\frac{21}{2}=\frac{6689}{2}\times\frac{2}{21}=\frac{6689}{21} \)

Step3: Estimate the quotient

Estimate \( \frac{6689}{21} \). Since \( 21\times318 = 6678 \), and \( 6689 - 6678 = 11 \), so \( \frac{6689}{21}\approx318.52 \)

Step4: Compare with 172

Now, compare 172 with 318.52. We can see that \( 172<318.52 \)

Answer:

\( < \)