fractions

Definition: A fraction represents a part of a whole or a ratio of two numbers.

• It consists of a numerator and a denominator separated by a horizontal line, called a fraction bar or division bar.
• The numerator represents the number of equal parts being considered, while the denominator represents the total number of equal parts in a whole.

Types of Fractions:

1. Proper Fraction:

   • A proper fraction is a fraction where the numerator is smaller than the denominator. $$ ( \frac{2}{3} ), ( \frac{5}{7} ), ( \frac{1}{4} ) $$

2. Improper Fraction:

   • An improper fraction is a fraction where the numerator is equal to or greater than the denominator. $$ ( \frac{5}{3} ), ( \frac{7}{4} ), ( \frac{11}{5} ) $$

3. Mixed Number:

   • A mixed number is a combination of a whole number and a proper fraction. $$ ( 2 \frac{1}{3} ), ( 3 \frac{2}{5} ), ( 4 \frac{3}{8} ) $$

Properties of Fractions:

1. Equivalent Fractions:

   • Equivalent fractions represent the same value, but they may have different numerators and denominators. $$ ( \frac{1}{2} ) and ( \frac{2}{4} ) $$

2. Addition and Subtraction:

   • To add or subtract fractions, you must have a common denominator. After that, you add or subtract the numerators while keeping the denominator the same. $$ ( \frac{1}{3} + \frac{2}{3} = \frac{3}{3} = 1 ) $$

3. Multiplication:

   • To Understanding multiply fractions, you simply multiply the numerators together to get the new numerator and multiply the denominators together to get the new denominator. $$ ( \frac{1}{2} \times \frac{3}{4} = \frac{3}{8} ) $$

4. Division:

   • To divide fractions, you multiply by the reciprocal of the divisor. $$ ( \frac{1}{2} \div \frac{3}{4} = \frac{1}{2} \times \frac{4}{3} = \frac{2}{3} ) $$