Mixed numbers can be converted to improper fractions by multiplying the whole number by the denominator and adding the numerator. -1 and 2/3 is -5/3, -4 and 5/14 is -61/14, -2/1 is -2, and 5/3 remains unchanged. This method uses intuitive understanding of fractions.
Converting mixed numbers to improper fractions involves multiplying the whole number by the denominator and adding the numerator. To convert -1 and 2/3 to an improper fraction, multiply 1 (the whole number) by 3 (the denominator) and add 2 (the numerator), giving us -5/3. Similarly, to convert -4 and 5/14 to an improper fraction, we multiply 4 by 14 and add 5, resulting in -61/14. The fraction -2/1 is already in improper form, representing -2. Lastly, 5/3 is already an improper fraction and doesn't require conversion.
In conclusion, understanding how to convert mixed numbers to improper fractions can bolster confidence in handling fractions, as it builds on our natural intuition about parts of a whole.