Examples: Example 1: \( 42 \div 2 \) \( =(40+2) \div 2 \) \( =(40 \div 2)+(2 \div 2) \)

Did you know that division is one of the four fundamental operations of arithmetic, alongside addition, subtraction, and multiplication? It dates back to ancient civilizations, where methods for dividing quantities were essential for trade, agriculture, and construction. The division symbol (÷) was popularized by the mathematician Johann Rahn in the 17th century, but ways to express division using fractions like \( a/b \) have been around since ancient Chinese and Indian texts! When tackling division problems, a common mistake is forgetting to properly handle remainders. For instance, when dividing 10 by 3, some might incorrectly say the quotient is 3, neglecting to mention the remainder of 1. One effective tip is to always check your work by multiplying the quotient by the divisor and adding the remainder; this ensures your solution satisfies the original equation!