By David Chandler Updated Aug 30, 2022
Multiplication and addition are closely related operations. Repeating the same addition many times yields the same result as multiplying the addend by the number of repetitions – for example, 2 + 2 + 2 = 2 × 3 = 6. These relationships become evident when we examine the associative and commutative properties that both operations share. It’s important to remember that these properties apply only to addition and multiplication; subtraction and division do not share them.
When two numbers are multiplied, swapping their positions does not change the product. This is the commutative property of multiplication. For instance, 3 × 6 = 6 × 3 = 18.
Algebraically:
• a × b = b × a
• ab = ba
When multiplying more than two numbers, the way the numbers are grouped does not affect the final product. For example, (3 × 4) × 2 = 12 × 2 = 24, while 3 × (4 × 2) = 3 × 8 = 24.
Algebraically:
• (a × b) × c = a × (b × c)
Adding two numbers in any order yields the same sum. For example, 2 + 6 = 6 + 2 = 8.
Algebraically:
• a + b = b + a
When adding more than two numbers, the grouping of the addends does not alter the total. For instance, (1 + 2) + 3 = 3 + 3 = 6, and 1 + (2 + 3) = 1 + 5 = 6.
Algebraically:
• (a + b) + c = a + (b + c)
