Mixed Operations - Fractions

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

To multiply a fraction by a whole number, multiply the numerator by the whole number and keep the denominator the same. For example, $$\frac{5}{7} \times 4 = \frac{5 \times 4}{7} = \frac{20}{7}$$ .

To simplify a fraction, divide both the numerator and the denominator by their greatest common divisor (GCD).

To find a common denominator, identify the least common multiple (LCM) of the denominators. For example, for $$\frac{1}{2}$$ and $$\frac{2}{5}$$ , the LCM of 2 and 5 is 10.

To find the difference between two fractions, convert them to have a common denominator, then subtract the numerators. For example, $$\frac{1}{2} - \frac{2}{5} = \frac{5}{10} - \frac{4}{10} = \frac{1}{10}$$ .

To divide a fraction by a whole number, multiply the denominator by the whole number. For example, $$\frac{2}{3} \div 4 = \frac{2}{3 \times 4} = \frac{2}{12} = \frac{1}{6}$$ .

To divide a whole number by a fraction, multiply the whole number by the reciprocal of the fraction. For example, $$2 \div \frac{1}{4} = 2 \times 4 = 8$$ .

To add fractions with different denominators, first find a common denominator, convert the fractions, and then add the numerators.

A mixed number is a whole number combined with a fraction, such as $$2\frac{1}{3}$$ .

To convert an improper fraction to a mixed number, divide the numerator by the denominator. The quotient is the whole number, and the remainder is the new numerator.