Multiplying with Zeros

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Learn the special rules and avoid common mistakes when multiplying numbers that contain zeros.

Multiplying with Zeros

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What is the product of any number multiplied by zero?

The product is always zero. This is the Zero Property of Multiplication. $9 \times 0 = 0$ and $587 \times 0 = 0$.

When solving $305 \times 4$, what is the first step?

Multiply the ones: $5 \times 4 = 20$. Write down the $0$ in the ones place and regroup the $2$ to the tens place.

In $305 \times 4$, after regrouping the $2$, what is the step for the tens place?

First, multiply the digit in the tens place by $4$: $0 \times 4 = 0$. Then, add the regrouped $2$: $0 + 2 = 2$. Write $2$ in the tens place of the answer.

What is the final step and answer for $305 \times 4$?

Multiply the hundreds place: $3 \times 4 = 12$. Write $12$ in front of the other digits. The final answer is $1,220$.

What is a common mistake when solving a problem like $305 \times 4$?

A common mistake is to forget to add the regrouped number after multiplying by zero. Students might write $0$ in the tens place instead of $2$.

Solve using the standard algorithm: $$ 609 \times 7 $$

1. Ones: $9 \times 7 = 63$. Write $3$, regroup $6$. 2. Tens: $0 \times 7 = 0$. Add regrouped $6$: $0 + 6 = 6$. Write $6$. 3. Hundreds: $6 \times 7 = 42$. Write $42$. Answer: $4,263$

How do you solve a problem with a zero at the end, like $240 \times 5$?

You can use a shortcut. Multiply $24 \times 5$ to get $120$, and then add the zero from $240$ back on at the end. The answer is $1,200$.

Solve $1,080 \times 6$ using the shortcut method.

Ignore the zero at the end for a moment. Solve $108 \times 6$. $8 \times 6 = 48$. Write $8$, regroup $4$. $0 \times 6 = 0$, $0+4=4$. Write $4$. $1 \times 6 = 6$. Write $6$. This gives $648$. Now, add the zero back on. Answer: $6,480$.

Solve using the standard algorithm: $$ 2,007 \times 3 $$

1. Ones: $7 \times 3 = 21$. Write $1$, regroup $2$. 2. Tens: $0 \times 3 = 0$. $0+2=2$. Write $2$. 3. Hundreds: $0 \times 3 = 0$. Write $0$. 4. Thousands: $2 \times 3 = 6$. Write $6$. Answer: $6,021$

Why is it important to pay close attention to place value when zeros are involved?

Zeros act as placeholders. Forgetting a zero or misplacing it can drastically change the value of the number and lead to a wrong answer (e.g., $120$ is very different from $12$).

Multiplying with Zeros

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