Adding and Subtracting mixed numbers with unlike denominators

A mixed number is a whole number combined with a proper fraction, such as 2 $$\frac{3}{4}$$ .

1. Convert mixed numbers to improper fractions. 2. Find a common denominator. 3. Add the fractions. 4. Convert back to a mixed number if necessary.

An improper fraction is a fraction where the numerator is greater than or equal to the denominator, such as $$\frac{5}{4}$$ .

A common denominator is a shared multiple of the denominators of two or more fractions, allowing them to be added or subtracted.

1. Convert mixed numbers to improper fractions. 2. Find a common denominator. 3. Subtract the fractions. 4. Convert back to a mixed number if necessary.

Convert both mixed numbers to improper fractions: $$\frac{253}{10} + \frac{41}{8}$$ .

Convert to improper fractions and find a common denominator to get the answer: $$19 \frac{5}{12}$$ .

The least common multiple (LCM) of 10 and 8 is 40, so the common denominator is 40.

Convert to a common denominator: $$\frac{12}{40} + \frac{15}{40} = \frac{27}{40}$$ .

The answer is $$17 \frac{27}{40}$$ .