Multiplying by two-digit and three-digit numbers

When the second factor is not a single digit, it helps to split it by place value and multiply in parts. Two-digit factor. For example,

34 \cdot 23 = 34 \cdot (20+3) = 34 \cdot 20 + 34 \cdot 3

. Compute the smaller products, then add. Three-digit factor — same idea:

156 \cdot 42 = 156 \cdot (40+2) = 156 \cdot 40 + 156 \cdot 2

, or hundreds first, then the tail of two lower places. Column multiplication is a neat way to do the same steps.

a\cdot (b+c)=a\cdot b+a\cdot c

— distributive property

Two-digit factor: tens + ones

Three-digit: hundreds + two-digit tail (or place by place)

Check: estimate the size and use properties of multiplication

Two-digit factor

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