Question

1. add.

\\(\frac{3}{4} + -6\frac{1}{2} = square\\)

1. add.

\\(6\frac{3}{5} + 3 = square\\)

1. add.

\\(-9\frac{1}{10} + \frac{2}{5} = square\\)

1. add.

\\(9\frac{3}{4} + \frac{1}{2} = square\\)

Explanation:

Step1: Convert mixed numbers to improper fractions

For Q17: $-6\frac{1}{2} = -\frac{13}{2}$; For Q18: $6\frac{3}{5} = \frac{33}{5}$; For Q19: $-9\frac{1}{10} = -\frac{91}{10}$; For Q20: $9\frac{3}{4} = \frac{39}{4}$

Step2: Find common denominators

Q17: $\frac{3}{4} + (-\frac{13}{2}) = \frac{3}{4} - \frac{26}{4}$
Q18: $\frac{33}{5} + 3 = \frac{33}{5} + \frac{15}{5}$
Q19: $-\frac{91}{10} + \frac{2}{5} = -\frac{91}{10} + \frac{4}{10}$
Q20: $\frac{39}{4} + \frac{1}{2} = \frac{39}{4} + \frac{2}{4}$

Step3: Add the fractions

Q17: $\frac{3 - 26}{4} = -\frac{23}{4}$
Q18: $\frac{33 + 15}{5} = \frac{48}{5}$
Q19: $\frac{-91 + 4}{10} = -\frac{87}{10}$
Q20: $\frac{39 + 2}{4} = \frac{41}{4}$

Step4: Convert back to mixed numbers (optional, standard form)

Q17: $-\frac{23}{4} = -5\frac{3}{4}$
Q18: $\frac{48}{5} = 9\frac{3}{5}$
Q19: $-\frac{87}{10} = -8\frac{7}{10}$
Q20: $\frac{41}{4} = 10\frac{1}{4}$

Answer:

1. $-5\frac{3}{4}$ (or $-\frac{23}{4}$)
2. $9\frac{3}{5}$ (or $\frac{48}{5}$)
3. $-8\frac{7}{10}$ (or $-\frac{87}{10}$)
4. $10\frac{1}{4}$ (or $\frac{41}{4}$)