Numbers and Operations
This page introduces fundamental mathematical concepts crucial for students to master. It covers methods for calculating the greatest common divisor NWD and least common multiple NWW, as well as divisibility rules for natural numbers.
Definition: NWD Największywspoˊlnydzielnik is the largest number that divides two or more integers without a remainder.
Definition: NWW Najmniejszawspoˊlnawielokrotnosˊcˊ is the smallest positive number that is divisible by two or more numbers.
The page explains how to calculate NWD and NWW using prime factorization. For example, to find the NWD of 8 and 20, we multiply the common factors in their prime factorizations: NWD8,20 = 2 * 2 = 4.
Example: To calculate NWW8,20, multiply the first number by the factors in the second number's factorization that are not in the first: NWW8,20 = 8 * 5 = 40.
The document then presents the divisibility rules for natural numbers, specifically for 2, 3, 5, 9, and 10. These rules provide quick methods to determine if a number is divisible by another without performing the division.
Highlight: A number is divisible by 2 if its last digit is 0, 2, 4, 6, or 8; by 3 if the sum of its digits is divisible by 3; by 5 if its last digit is 0 or 5; by 9 if the sum of its digits is divisible by 9; and by 10 if its last digit is 0.
The page concludes with an introduction to the order of operations, emphasizing the importance of square and cube roots in mathematical calculations.
