# Fractions

What is a Fraction?

A fraction is a way to represent a part of a whole or a division of a quantity into equal parts. It consists of two main parts:

Numerator: The numerator is the number on the top of the fraction. It represents the number of equal parts you have.

Denominator: The denominator is the number on the bottom of the fraction. It represents the total number of equal parts that make up the whole.

Types of Fractions:

Proper Fractions: The numerator is smaller than the denominator in proper fractions. For example, 1/2, 3/4, and 5/8 are proper fractions.

Improper Fractions: In improper fractions, the numerator is equal to or greater than the denominator. For example, 7/4, 5/5, and 12/3 are improper fractions.

Mixed Numbers: Mixed numbers combine a whole number and a proper fraction. For example, 2 1/2, 3 3/4, and 1 5/8 are mixed numbers.

Equivalent Fractions: Equivalent fractions represent the same value, even though they may look different. You can multiply or divide the numerator and denominator by the same number to find equivalent fractions. For example, 1/2 and 2/4 are equivalent because if you multiply the numerator and denominator of 1/2 by 2, you get 2/4.

Adding and Subtracting Fractions: They must have the same denominator to add or subtract fractions. If they don't, you need to find a common denominator. Once you have the same denominator, you can add or subtract the numerators while keeping the denominator the same. For example, to add 1/4 and 2/3, you need to find a common denominator, which is 12. So, 1/4 becomes 3/12, and 2/3 becomes 8/12. Now you can add them: 3/12 + 8/12 = 11/12.

Multiplying Fractions: To multiply fractions, multiply the numerators together to get the new numerator, and multiply the denominators to get the new denominator. For example, to multiply 2/3 and 3/4, you get (2 * 3) / (3 * 4) = 6/12 = 1/2.

Dividing Fractions: To divide fractions, flip the second fraction (the divisor) and then multiply. For example, to divide 1/2 by 3/4, you flip 3/4 to get 4/3, and then multiply: (1/2) * (1/4) = 4/2 = 2/1 = 2.

Simplifying Fractions: To simplify a fraction, find the greatest common factor (GCF) of the numerator and denominator and divide both by it. For example, to simplify 8/12, the GCF is 4, so you get (8/4) / (12/4) = 2/3.

Practical Uses of Fractions: Fractions are used in various real-life situations, such as cooking (measuring ingredients), construction (calculating measurements), and finances (calculating interest rates).

Fractions are a fundamental concept in mathematics, and understanding how to work with them is essential for many mathematical and practical applications. Practice and applying these concepts will help you become proficient in using fractions.