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How can multiplication be understood as repeated addition?

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arithmetic A page from a first-grade workbook typical of “new math” might state: “Draw connecting lines from triangles in the first set to triangles in the second set. Are the two sets equivalent in number?”

In arithmetic, multiplication can be understood as a shorthand for repeated addition. When you have a repeated sum of the same number, such as 5 + 5 + 5, the operation is independent of how the summands are grouped. This allows the expression to be written as 3 × 5, where 5 is the multiplicand and 3 is the multiplier, representing the number of times the multiplicand is added to itself.1

This relationship is further illustrated through arrays. For example, arranging 15 dots into three rows of five creates a visual representation of 3 × 5. Because the total number of dots remains the same regardless of whether they are viewed as three rows of five or five rows of three, this demonstrates the commutative law of multiplication, showing that the order of the multiplicands does not affect the product.1