Multiplication
Multiplication is a fast way to add the same number many times. Instead of adding 4 + 4 + 4, we write 3 × 4 = 12.
Multiplication Formula
Factor × Factor = Product
Multiplication is repeated addition: 4 × 3 = 4 + 4 + 4 = 12.
Concept Explanation
Multiplication combines equal groups. The two numbers being multiplied are called factors, and the result is the product.
Like addition, multiplication is commutative: 3 × 5 = 5 × 3 = 15. It is also associative: (2 × 3) × 4 = 2 × (3 × 4).
Multiplying any number by 0 gives 0. Multiplying any number by 1 gives the number itself. These are the Zero and Identity Properties.
Word problems use multiplication when you see clue words like: "times," "each," "per," "groups of," "total of equal groups," "product," or "at this rate."
Worked Examples
Recall the fact
7 × 8 is a multiplication fact.
Think of it as repeated addition
8 + 8 + 8 + 8 + 8 + 8 + 8 = 56.
Answer
7 × 8 = 56.
Answer: 56
Key Terms
Factor
A number being multiplied. In 4 × 3, both 4 and 3 are factors.
Product
The result of multiplication. 4 × 3 = 12, so 12 is the product.
Array
Objects arranged in rows and columns to show multiplication. 3 rows of 4 = 12.
Commutative Property
The order of factors does not change the product. 6 × 7 = 7 × 6.
Distributive Property
Breaking a factor into parts: 6 × 13 = 6 × 10 + 6 × 3 = 60 + 18 = 78.
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Multiplication