Definition of Fractions

Fractions are mathematical expressions that represent a part of a whole, consisting of a numerator and a denominator

Importance of Fraction Operations

Mastery of fraction operations is essential for accurately manipulating fractions and solving problems involving parts of a whole

Rules and Procedures for Fraction Operations

Fraction operations, including addition, subtraction, multiplication, and division, follow specific rules and procedures that are crucial for solving problems involving fractions

Adding and Subtracting Fractions with Common Denominators

When fractions have the same denominator, one can add or subtract them by combining the numerators while keeping the denominator constant

Finding the Least Common Denominator (LCD)

To add or subtract fractions with different denominators, one must first find the LCD, which is the smallest non-zero common multiple of the denominators

Converting Mixed Numbers to Improper Fractions

Mixed numbers must be converted to improper fractions before adding or subtracting them with other fractions

Rules for Adding and Subtracting Positive and Negative Fractions

To add or subtract negative fractions, one must add their positive equivalents, and to add or subtract positive fractions, one must subtract their positive counterparts

Understanding the Sign of Fractions

It is important to understand the rules for dealing with the signs of fractions to accurately solve problems involving both positive and negative values

Adding and Subtracting Decimal Fractions

Decimal fractions can be added and subtracted by aligning the decimal points and ensuring that all fractions have the same place value

Converting to Equivalent Fractions with a Common Denominator

To add or subtract decimal fractions, one may need to convert them to equivalent fractions with a common denominator, typically the highest power of ten present in the problem