Add the following mixed numbers: a) 7 rac14 + 3 rac310

a)

Step 1: Convert the mixed numbers to improper fractions.

$$7 \frac{1}{4} = \frac{7 \times 4 + 1}{4} = \frac{29}{4}$$ $$3 \frac{3}{10} = \frac{3 \times 10 + 3}{10} = \frac{33}{10}$$

The expression becomes $\frac{29}{4} + \frac{33}{10}$.

Step 2: Find a common denominator, which is 20.

$$\frac{29}{4} = \frac{29 \times 5}{4 \times 5} = \frac{145}{20}$$ $$\frac{33}{10} = \frac{33 \times 2}{10 \times 2} = \frac{66}{20}$$

The expression becomes $\frac{145}{20} + \frac{66}{20}$.

Step 3: Add the fractions.

$$\frac{145}{20} + \frac{66}{20} = \frac{145+66}{20} = \frac{211}{20}$$

Step 4: Convert the improper fraction to a mixed number.

$$\frac{211}{20} = \boxed{10 \frac{11}{20}}$$

b)

Step 1: Convert the mixed numbers to improper fractions.

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