Skill: Multiply by multiples of 10

Explanation and Free Practice Resources

Multiplication by a multiple of 10 can be decomposed using place value and the distributive property: for example, $36 \times 40=(36 \times 4)\times 10=1{,}440$ . The learner connects the nonzero factor to the basic multiplication and then accounts for the factor of ten by shifting each product digit one place left, understanding that the number of zeros depends on the multiple of 10 rather than being appended indiscriminately; this supports efficient multi-digit multiplication and later work with powers of ten.

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Detailed Explanation: Multiply by multiples of 10

To multiply by a multiple of $(10)$ , first multiply by the nonzero part. Then multiply by $(10)$ , which shifts every digit one place to the left.

Example:

36 \times 40

Rewrite $(40)$ as $(4 \times 10)$ :

36 \times 40=36 \times (4 \times 10)

Multiply $(36)$ by $4$ :

36 \times 4=144

Now multiply $(144)$ by $(10)$ . Each digit shifts one place left, so the number becomes $(1{,}440)$ :

144 \times 10=1{,}440

Therefore,

\boxed{36 \times 40=1{,}440}

The one zero in $(40)$ represents one factor of $(10)$ , so the final answer has one place-value shift.

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