Adding and Subtracting Fractions and Mixed Numbers with Regrouping

A fraction represents a part of a whole and is written as $$\frac{a}{b}$$ , where 'a' is the numerator and 'b' is the denominator.

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

To add fractions with the same denominator, add the numerators and keep the denominator the same. For example, $$\frac{1}{4} + \frac{2}{4} = \frac{3}{4}$$ .

To subtract fractions with the same denominator, subtract the numerators and keep the denominator the same. For example, $$\frac{3}{4} - \frac{1}{4} = \frac{2}{4} = \frac{1}{2}$$ .

The first step is to find a common denominator, which is a multiple of both denominators.

To convert a mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator. For example, 2 $$\frac{3}{4}$$ becomes $$\frac{(2 \times 4) + 3}{4} = \frac{11}{4}$$ .

Regrouping in subtraction involves borrowing from the next higher place value when the top digit is smaller than the bottom digit.

To simplify a fraction, divide the numerator and the denominator by their greatest common divisor (GCD). For example, $$\frac{4}{8} = \frac{4 \div 4}{8 \div 4} = \frac{1}{2}$$ .

The sum is $$\frac{5}{10} = \frac{1}{2}$$ .

A proper fraction has a numerator smaller than the denominator (e.g., $$\frac{3}{4}$$ ), while an improper fraction has a numerator larger than or equal to the denominator (e.g., $$\frac{5}{4}$$ ).