Multiplication and Division

WHAT ARE MULTIPLICATION AND DIVISION?

Multiplication and division are fundamental procedures that enable work with numerical expressions and values. We use multiplication and division to express repeated addition or the uniform distribution of numbers. Multiplication means increasing a number by a multiple of another number, while division means splitting a number into equal parts or determining how many times one number contains another. Multiplication and division are interconnected procedures, as any division can also be written as multiplication by the reciprocal of a number.

DEFINITIONS AND NOTATIONS

For multiplication, we use the symbol “×” or “*”. In the expression 7 × 5, the number 7 is the first factor, 5 is the second factor, and the result is the product, which is 35.
For division, we use the symbol “÷” or “/”. In the expression 20 ÷ 4, the number 20 is the dividend, 4 is the divisor, and the result is the quotient, which is 5.

RULES FOR MULTIPLYING AND DIVIDING WITH NEGATIVE NUMBERS

When multiplying and dividing negative numbers, we consider the following:

• If both numbers are negative, the result is positive:
  (-6) × (-3) = 18
  (-12) ÷ (-4) = 3
• If we multiply or divide numbers with different signs, the result is negative:
  (-5) × 4 = -20
  15 ÷ (-3) = -5

CALCULATION EXAMPLE

Let's solve the expression:

(24 ÷ 6) × (-3)

First, we divide:
24 ÷ 6 = 4

Then, we multiply:
4 × (-3) = -12

The result of the expression is -12.

CONCLUSION

Multiplication and division are key procedures when working with different numerical values. By understanding the rules, terms, and the behavior of negative numbers, we can solve expressions involving multiplication and division accurately and without errors. Working with larger expressions becomes simpler if we correctly apply the procedures of multiplication and division and adhere to the order of operations.