2. Convert: a) \( \frac{44}{9} \) into a mixed number. b) \( 1 \frac{33}{34} \) into an improper fraction.

To convert \( \frac{44}{9} \) into a mixed number, you divide 44 by 9. This gives you 4 as the whole number part (since \( 9 \times 4 = 36 \)) and a remainder of 8. So, \( \frac{44}{9} \) can be expressed as \( 4 \frac{8}{9} \). To convert \( 1 \frac{33}{34} \) into an improper fraction, you multiply the whole number 1 by the denominator (34), which gives you 34, and then add the numerator (33). This results in \( 34 + 33 = 67 \), so the improper fraction is \( \frac{67}{34} \).