Operations & Algebraic Thinking
Understanding Multiplication
Multiplication as groups of equal size.
Groups of Equal Size
In Grade 2, you used repeated addition to find the total in an array — adding the same number over and over, once for each row. Multiplication is a faster way to write exactly that kind of repeated addition, once every group in the problem is the same size.
Definition — Multiplication
The expression 4 × 3 means 4 groups of 3, and it stands for 3 + 3 + 3 + 3 — adding 3 four times. Multiplication doesn't replace repeated addition; it's a shorthand for it, useful whenever the groups being added are all the exact same size.
Worked Example — Multiplication as Repeated Addition
Worked Example — Reading a Multiplication Expression
Tip
Common Mistakes
Mixing up which number tells the size of each group and which tells the number of groups, such as writing 5 groups of 3 as '3 × 5 means 3 groups of 5' when the problem actually described the opposite.
Read the problem carefully: the number of groups comes first in the story, and the size of each group comes second, even though the product comes out the same either way.
Adding the two factors together instead of multiplying, such as solving 4 × 3 as 4 + 3 = 7.
Multiplication means repeating one factor as many times as the other factor says — 4 × 3 means adding 3 four times, not adding 4 and 3 once.
Key Takeaways
- Multiplication combines equal-size groups into a total, and is a shortcut for repeated addition.
- The two numbers multiplied are called factors; the answer is called the product.
- Multiplying factors in either order gives the same product.
Summary
Multiplication combines equal groups into a total in one fast step. The next lesson looks at the reverse question — splitting a total back into equal groups — which is called division.
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