Standard Algorithm: No Regrouping

Core Concepts

Learn the first steps of the standard algorithm for multiplication, without the need to carry numbers.

Standard Algorithm: No Regrouping

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When using the standard algorithm, in which place value do you always begin multiplying?

You always start with the place value farthest to the right: the ones place.

For the problem $231 \times 3$, what is the first step?

Multiply the ones digit of the top number by the bottom number: $1 \times 3 = 3$. Write the $3$ in the ones place of the answer.

For $231 \times 3$, after multiplying the ones, what is the second step?

Multiply the tens digit by the bottom number: $3 \times 3 = 9$. Write the $9$ in the tens place of the answer.

For $231 \times 3$, what is the final multiplication step?

Multiply the hundreds digit by the bottom number: $2 \times 3 = 6$. Write the $6$ in the hundreds place of the answer. The final product is $693$.

Solve using the standard algorithm: $$ 423 \times 2 $$

1. Ones: $3 \times 2 = 6$\ 2. Tens: $2 \times 2 = 4$\ 3. Hundreds: $4 \times 2 = 8$\ Answer: $846$

Solve using the standard algorithm: $$ 1,421 \times 2 $$

1. Ones: $1 \times 2 = 2$\ 2. Tens: $2 \times 2 = 4$\ 3. Hundreds: $4 \times 2 = 8$\ 4. Thousands: $1 \times 2 = 2$\ Answer: $2,842$

What does "no regrouping" mean?

"No regrouping" means that the product in each place value column is less than $10$, so you do not have to carry any numbers over to the next column.

Solve using the standard algorithm: $$ 3,110 \times 3 $$

1. Ones: $0 \times 3 = 0$\ 2. Tens: $1 \times 3 = 3$\ 3. Hundreds: $1 \times 3 = 3$\ 4. Thousands: $3 \times 3 = 9$\ Answer: $9,330$

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