What Is Multiplication? Equal Groups Made Easy

What You'll Learn

• Multiplication is a shortcut for adding the SAME number over and over
• 4 x 3 means 4 equal groups with 3 in each group
• The times sign x means "groups of"
• An array is a neat picture of a multiplication: rows and columns
• Order does not change the answer: 4 x 3 = 3 x 4 (this is why the times table is half as big as it looks)

Words to Know

Multiplication

A fast way to add the same number again and again

"4 x 3 beats adding 3 + 3 + 3 + 3."

Equal groups

Groups that all have exactly the same amount

"Four boxes with 3 crayons in each are equal groups."

Array

Things lined up in even rows and columns

"An egg carton is an array: 2 rows of 6."

Product

The answer you get when you multiply

"The product of 4 x 3 is 12."

Times sign (x)

The symbol that means "groups of"

"4 x 3 reads as four groups of three."

Check What You Learned

Fun Facts

• Multiplication means counting equal groups: 5 x 7 is the total in 5 groups of 7 objects each

  Source: CCSS.MATH.CONTENT.3.OA.A.1

• The times sign "x" was first printed in 1631, by English teacher William Oughtred in his book Clavis Mathematicae — it is nearly 400 years old

  Source: Florian Cajori, A History of Mathematical Notations

• The answer to a multiplication is called the product

  Source: NCTM mathematics glossary

• Order does not change a product: 4 x 3 and 3 x 4 both equal 12 — the commutative property of multiplication

  Source: CCSS.MATH.CONTENT.3.OA.B.5

• Because of that, a 10 x 10 times table holds 100 facts but only 55 of them are different — every other one is a repeat with the numbers swapped

  Source: CCSS 3.OA.B.5; 55 = the 45 unordered pairs plus the 10 squares

• Any number times 1 is itself, the identity property: 7 x 1 = 7

  Source: NCTM mathematics glossary