Operations with Fractions

This page details the rules and procedures for performing operations with fractions.

Definition: For addition and subtraction of fractions, find the least common multiple (LCM) of denominators first.

Example: When multiplying fractions: 3/4 × 5/7 = (3×5)/(4×7) = 15/28

Highlight: For division of fractions, convert to multiplication by using the reciprocal of the second fraction.

Vocabulary: The reciprocal of a fraction is found by inverting the numerator and denominator.

Monomials

This page introduces monomials and their operations.

Definition: A monomial consists of a numerical coefficient and literal part (variables with exponents).

Example: In 6ab, 6 is the coefficient and ab is the literal part.

Highlight: Similar monomials have identical literal parts and can be added or subtracted.

Vocabulary: The espressioni algebriche esercizi with monomials follow specific rules for multiplication and division, where exponents are added or subtracted respectively.

Least Common Multiple (LCM)

This page explains the process of finding the least common multiple through prime factorization.

Definition: The LCM is found by multiplying the prime factors taken with their highest occurring exponents.

Example: For finding LCM of 18, 84, and 360: 18 = 2×3² 84 = 2²×3×7 360 = 2³×3²×5 LCM = 2³×3²×5×7 = 2520

Highlight: Prime factorization is essential for finding the LCM efficiently.

Vocabulary: Prime factors are the building blocks used to construct the LCM.

Order of Operations and Sign Rules

This page introduces fundamental mathematical concepts focusing on the order of operations and sign rules in expressions.

Definition: The ordine delle operazioni matematiche senza parentesi follows: powers first, then multiplication/division, followed by addition/subtraction.

Highlight: For parentheses, the order is: round brackets first, then square brackets, followed by curly brackets.

Example: The regola dei segni for multiplication:

• Positive × Positive = Positive
• Positive × Negative = Negative
• Negative × Negative = Positive

Vocabulary: In powers (potenze), the number being multiplied by itself is called the base, while the number of times it's multiplied is the exponent.