Introduction

We can use the standard algorithm to multiply a three-digit number by a one-digit number. In this case, we might need to carry a digit from the multiplication of the ones and tens.

For instance, let's find the value of

143 \times 7.

We start by writing the problem out as follows:

\begin{align*} %%%%%%%%%% %%% Step 0 %%% %%%%%%%%%% & %%% Long Multiplication %%% \begin{array}{ccccc} & & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \\ & & \!\!\!\! 1 \!\!\!\! & \!\!\!\! 4 \!\!\!\! & \!\!\!\! 3 \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & & \!\!\!\! 7 \!\!\!\! \\ \hline & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! \end{array} &\qquad\qquad&\qquad \phantom{10 \quad\text{and}\quad {\color{blue}2} + 10 = 1200000} \end{align*}

First, we multiply the ones. We have 3\times 7 = {\color{blue}2}{\color{red}1}. We write \color{red}1 in the ones place and carry the {\color{blue}2}.

\begin{align*} %%%%%%%%%% %%% Step 1 %%% %%%%%%%%%% & %%% Long Multiplication %%% \begin{array}{ccccc} & & \!\!\!\! \!\!\!\! & \!\!\!\! \underset{\color{blue}2}{} \!\!\!\! & \\ & & \!\!\!\! 1 \!\!\!\! & \!\!\!\! 4 \!\!\!\! & \!\!\!\! \bbox[2px, lightgray]{3} \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & & \!\!\!\! \bbox[2px, lightgray]{7} \!\!\!\! \\ \hline & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\! \color{red}1 \!\!\!\! \end{array} &\qquad\qquad& %%%% Explanations %%% \begin{array}{l} \bbox[2px, lightgray]{3} \times \bbox[2px, lightgray]{7} = 21\phantom{00000000000000000} \\ \text{Carry:}\: {\color{blue}2} \\ \text{Write:}\: {\color{red}1} \end{array} \end{align*}

Next, we multiply the tens as follows:

  • We have 4\times 7= 28.

  • We add the 2 carried from the previous multiplication to get 2+28 = {\color{blue}3}{\color{red}0}.

  • We write down \color{red}0 and carry {\color{blue}3}.

\begin{align*} %%%%%%%%%% %%% Step 2 %%% %%%%%%%%%% & %%% Long Multiplication %%% \begin{array}{ccccc} & & \!\!\!\! \underset{\color{blue}3}{} \!\!\!\! & \!\!\!\! \underset{\color{blue}2}{} \!\!\!\! & \\ & & \!\!\!\! 1 \!\!\!\! & \!\!\!\!\! \bbox[2px, lightgray]{4} \!\!\!\! & \!\!\!\! 3 \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & & \!\!\!\!\! \bbox[2px, lightgray]{7} \!\!\!\! \\ \hline & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \color{red}0 \!\!\!\! & \!\!\!\! 1 \!\!\!\! \end{array} &\qquad\qquad& %%%% Explanations %%% \begin{array}{l} \bbox[2px, lightgray]{4} \times \bbox[2px, lightgray]{7} = 28 \quad\text{and}\quad {\color{blue}2} + 28 = 30 \\ \text{Carry:}\: {\color{blue}3} \\ \text{Write:}\: {\color{red}0} \end{array} \end{align*}

Finally, we multiply the hundreds as follows:

  • We have 1\times 7 = 7.

  • We add the 3 carried from the previous multiplication to get 3+7= 10.

  • Since this is the final multiplication, we write the entire result, {\color{red}10}.

\begin{align*} %%%%%%%%%% %%% Step 3 %%% %%%%%%%%%% & %%% Long Multiplication %%% \begin{array}{ccccc} & & \!\!\!\! \underset{\color{blue}3}{} \!\!\!\! & \!\!\!\! \underset{\color{blue}2}{} \!\!\!\! & \\ & & \!\!\!\!\! \bbox[2px, lightgray]{1} \!\!\!\! & \!\!\!\! 4 \!\!\!\! & \!\!\!\! 3 \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & & \!\!\!\!\! \bbox[2px, lightgray]{7} \!\!\!\! \\ \hline & \!\!\!\! \color{red}1 \!\!\!\! & \!\!\!\! \color{red}0 \!\!\!\! & \!\!\!\! 0 \!\!\!\! & \!\!\!\! 1 \!\!\!\! \end{array} &\qquad\qquad& %%%% Explanations %%% \begin{array}{l} \bbox[2px, lightgray]{1} \times \bbox[2px, lightgray]{7} = 7 \quad\text{and}\quad {\color{blue}3} + 7 = 10 \\ \text{Carry:}\: {\color{blue}-} \\ \text{Write:}\: {\color{red}10} \end{array} \\[5pt] & \end{align*}

Therefore, 143 \times 7 = 1,001.

FLAG
Example: Multiplying a Three-Digit Number By a One-Digit Number: Finding Missing Digits

From left to right, what are the missing digits in the following multiplication problem?

\begin{array}{ccccc} & & \!\!\!\! 4 \!\!\!\! & \!\!\!\! 7 \!\!\!\! & \!\!\!\! 9 \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & & \!\!\!\! 6 \!\!\!\! \\ \hline & \!\!\!\! 2\!\!\!\! & \!\!\!\!\!\! \fbox{[math]\phantom{i}[/math]} \!\!\!\! & \!\!\!\!\! \fbox{[math]\phantom{i}[/math]} \!\!\!\! & \!\!\!\! 4 \!\!\!\! \end{array}

EXPLANATION

First, we multiply the ones:

\begin{align*} %%%%%%%%%% %%% Step 1 %%% %%%%%%%%%% & %%% Long Multiplication %%% \begin{array}{ccccc} & & \!\!\!\! \!\!\!\! & \!\!\!\! \underset{\color{blue}5}{} \!\!\!\! & \\ & & \!\!\!\! 4 \!\!\!\! & \!\!\!\! 7 \!\!\!\! & \!\!\!\! \bbox[2px, lightgray]{9} \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & & \!\!\!\! \bbox[2px, lightgray]{6} \!\!\!\! \\ \hline & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \color{red}4 \!\!\!\! \end{array} &\qquad\qquad& %%%% Explanations %%% \begin{array}{l} \bbox[2px, lightgray]{9} \times \bbox[2px, lightgray]{6} = 54 \\ \text{Carry:}\: {\color{blue}5} \\ \text{Write:}\: {\color{red}4} \end{array} \end{align*}

Next, we multiply the tens:

\begin{align*} %%%%%%%%%% %%% Step 2 %%% %%%%%%%%%% & %%% Long Multiplication %%% \begin{array}{ccccc} & & \!\!\!\! \underset{\color{blue}4}{} \!\!\!\! & \!\!\!\! \underset{\color{blue}5}{} \!\!\!\! & \\ & & \!\!\!\! 4 \!\!\!\! & \!\!\!\! \bbox[2px, lightgray]{7} \!\!\!\! & \!\!\!\! 9 \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & & \!\!\!\! \bbox[2px, lightgray]{6} \!\!\!\! \\ \hline & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \color{red}7 \!\!\!\! & \!\!\!\! 4 \!\!\!\! \end{array} &\qquad\qquad& %%%% Explanations %%% \begin{array}{l} \bbox[2px, lightgray]{7} \times \bbox[2px, lightgray]{6} = 42 \quad\text{and}\quad {\color{blue}5} + 42 = 47 \\ \text{Carry:}\: {\color{blue}4} \\ \text{Write:}\: {\color{red}7} \end{array} \end{align*}

Finally, we multiply the hundreds:

\begin{align*} %%%%%%%%%% %%% Step 3 %%% %%%%%%%%%% & %%% Long Multiplication %%% \begin{array}{ccccc} & & \!\!\!\! \underset{\color{blue}4}{} \!\!\!\! & \!\!\!\! \underset{\color{blue}5}{} \!\!\!\! & \\ & & \!\!\!\! \bbox[2px, lightgray]{4} \!\!\!\! & \!\!\!\! 7 \!\!\!\! & \!\!\!\! 9 \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & & \!\!\!\! \bbox[2px, lightgray]{6} \!\!\!\! \\ \hline & \!\!\!\! \color{red}2 \!\!\!\! & \!\!\!\! \fbox{[math]\color{red}8[/math]} \!\!\!\! & \!\!\!\! \fbox{7} \!\!\!\! & \!\!\!\! 4 \!\!\!\! \end{array} &\qquad\qquad& %%%% Explanations %%% \begin{array}{l} \bbox[2px, lightgray]{4} \times \bbox[2px, lightgray]{6} = 24 \quad\text{and}\quad {\color{blue}4} + 24 = 28 \\ \text{Carry:}\: {\color{blue}-} \\ \text{Write:}\: {\color{red}28} \end{array} \\[5pt] & \end{align*}

Therefore, the missing digits, from left-to-right, are \bbox[3pt,Gainsboro]{\color{blue}8} and \bbox[3pt,Gainsboro]{\color{blue}7}.

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Practice: Multiplying a Three-Digit Number By a One-Digit Number: Finding Missing Digits

Insert the missing digits in the following multiplication problem:

a
b
c
d
e
Practice: Multiplying a Three-Digit Number By a One-Digit Number: Finding Missing Digits

Insert the missing digits in the following multiplication problem:

a
b
c
d
e
Practice: Multiplying a Three-Digit Number By a One-Digit Number: Finding Missing Digits

Insert the missing digits in the following multiplication problem:

a
b
c
d
e
Example: Multiplying a Three-Digit Number By a One-Digit Number

Find the value of 727 \times 6.

EXPLANATION

We write it this way:

\begin{align*} %%%%%%%%%% %%% Step 0 %%% %%%%%%%%%% & %%% Long Multiplication %%% \begin{array}{ccccc} & & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \\ & & \!\!\!\! 7 \!\!\!\! & \!\!\!\! 2 \!\!\!\! & \!\!\!\! 7 \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & & \!\!\!\! 6 \!\!\!\! \\ \hline & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! \end{array} &\qquad\qquad& \end{align*}

First, we multiply the ones:

\begin{align*} %%%%%%%%%% %%% Step 1 %%% %%%%%%%%%% & %%% Long Multiplication %%% \begin{array}{ccccc} & & \!\!\!\! \!\!\!\! & \!\!\!\! \underset{\color{blue}4}{} \!\!\!\! & \\ & & \!\!\!\! 7 \!\!\!\! & \!\!\!\! 2 \!\!\!\! & \!\!\!\! \bbox[2px, lightgray]{7} \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & & \!\!\!\! \bbox[2px, lightgray]{6} \!\!\!\! \\ \hline & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \color{red}2 \!\!\!\! \end{array} &\qquad\qquad& %%%% Explanations %%% \begin{array}{l} \bbox[2px, lightgray]{7} \times \bbox[2px, lightgray]{6} = 42 \\ \text{Carry:}\: {\color{blue}4} \\ \text{Write:}\: {\color{red}2} \end{array} \end{align*}

Next, we multiply the tens:

\begin{align*} %%%%%%%%%% %%% Step 2 %%% %%%%%%%%%% & %%% Long Multiplication %%% \begin{array}{ccccc} & & \!\!\!\! \underset{\color{blue}1}{} \!\!\!\! & \!\!\!\! \underset{\color{blue}4}{} \!\!\!\! & \\ & & \!\!\!\! 7 \!\!\!\! & \!\!\!\! \bbox[2px, lightgray]{2} \!\!\!\! & \!\!\!\! 7 \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & & \!\!\!\! \bbox[2px, lightgray]{6} \!\!\!\! \\ \hline & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \color{red}6 \!\!\!\! & \!\!\!\! 2 \!\!\!\! \end{array} &\qquad\qquad& %%%% Explanations %%% \begin{array}{l} \bbox[2px, lightgray]{2} \times \bbox[2px, lightgray]{6} = 12 \quad\text{and}\quad {\color{blue}4} + 12 = 16 \\ \text{Carry:}\: {\color{blue}1} \\ \text{Write:}\: {\color{red}6} \end{array} \end{align*}

Finally, we multiply the hundreds:

\begin{align*} %%%%%%%%%% %%% Step 3 %%% %%%%%%%%%% & %%% Long Multiplication %%% \begin{array}{ccccc} & & \!\!\!\! \underset{\color{blue}1}{} \!\!\!\! & \!\!\!\! \underset{\color{blue}4}{} \!\!\!\! & \\ & & \!\!\!\! \bbox[2px, lightgray]{7} \!\!\!\! & \!\!\!\! 2 \!\!\!\! & \!\!\!\! 7 \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & & \!\!\!\! \bbox[2px, lightgray]{6} \!\!\!\! \\ \hline & \!\!\!\! \color{red}4 \!\!\!\! & \!\!\!\! \color{red}3 \!\!\!\! & \!\!\!\! 6 \!\!\!\! & \!\!\!\! 2 \!\!\!\! \end{array} &\qquad\qquad& %%%% Explanations %%% \begin{array}{l} \bbox[2px, lightgray]{7} \times \bbox[2px, lightgray]{6} = 42 \quad\text{and}\quad {\color{blue}1} + 42 = 43 \\ \text{Carry:}\: {\color{blue}-} \\ \text{Write:}\: {\color{red}43} \end{array} \\[5pt] & \end{align*}

Therefore, 727 \times 6 = 4 \, 362.

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Practice: Multiplying a Three-Digit Number By a One-Digit Number

$348 \times 5 =$

a
 $1,604$
b
 $1,392$
c
 $1,407$
d
 $1,740$
e
 $1,470$
Practice: Multiplying a Three-Digit Number By a One-Digit Number

$263 \times 7 =$

a
b
c
d
e
Practice: Multiplying a Three-Digit Number By a One-Digit Number

A supermarket sold $6$ containers of soda cans last weekend. There were $125$ cans of soda in each container. How many cans of soda did the store sell in total?

a
 $720$
b
 $750$
c
 $900$
d
 $620$
e
 $625$
Example: Multiplying a Four-Digit Number By a One-Digit Number: Finding Missing Digits

From left to right, what are the missing digits in the following multiplication problem?

\begin{array}{ccccc} & & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \\ & & \!\!\!\! 1 \!\!\!\! & \!\!\!\! 8 \!\!\!\! & \!\!\!\! 5 \!\!\!\! & \!\!\!\! 2 \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & & & \!\!\!\! 7 \!\!\!\! \\ \hline & \!\!\!\! 1 \!\!\!\!\! & \!\!\!\! \fbox{[math]\phantom{i}[/math]} \!\!\!\! & \!\!\! 9 \!\!\!\! & \!\!\! \fbox{[math]\phantom{i}[/math]}\!\!\! & \!\!\! 4 \!\!\!\! \end{array}

EXPLANATION

First, we multiply the ones:

\begin{align*} %%%%%%%%%% %%% Step 1 %%% %%%%%%%%%% & %%% Long Multiplication %%% \begin{array}{ccccc} & & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \underset{\color{blue}1}{} \!\!\!\! & \\ & & \!\!\!\! 1 \!\!\!\! & \!\!\!\! 8 \!\!\!\! & \!\!\!\! 5 \!\!\!\! & \!\!\!\! \bbox[2px, lightgray]{2} \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & & & \!\!\!\! \bbox[2px, lightgray]{7} \!\!\!\! \\ \hline & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \color{red}4 \!\!\!\! \end{array} &\qquad\qquad& %%%% Explanations %%% \begin{array}{l} \bbox[2px, lightgray]{2} \times \bbox[2px, lightgray]{7} = 14 \\ \text{Carry:}\: {\color{blue}1} \\ \text{Write:}\: {\color{red}4} \end{array} \end{align*}

Next, we multiply the tens:

\begin{align*} %%%%%%%%%% %%% Step 2 %%% %%%%%%%%%% & %%% Long Multiplication %%% \begin{array}{ccccc} & & \!\!\!\! \!\!\!\! & \!\!\!\! \underset{\color{blue}3}{} \!\!\!\! & \!\!\!\! \underset{\color{blue}1}{} \!\!\!\! & \\ & & \!\!\!\! 1 \!\!\!\! & \!\!\!\! 8 \!\!\!\! & \!\!\!\! \bbox[2px, lightgray]{5} \!\!\!\! & \!\!\!\! 2 \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & & & \!\!\!\! \bbox[2px, lightgray]{7} \!\!\!\! \\ \hline & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \color{red}6 \!\!\!\! & \!\!\!\! 4 \!\!\!\! \end{array} &\qquad\qquad& %%%% Explanations %%% \begin{array}{l} \bbox[2px, lightgray]{5} \times \bbox[2px, lightgray]{7} = 35 \quad\text{and}\quad {\color{blue}1} + 35 = 36 \\ \text{Carry:}\: {\color{blue}3} \\ \text{Write:}\: {\color{red}6} \end{array} \end{align*}

Next, we multiply the hundreds:

\begin{align*} %%%%%%%%%% %%% Step 3 %%% %%%%%%%%%% & %%% Long Multiplication %%% \begin{array}{ccccc} & & \!\!\!\! \underset{\color{blue}5}{} \!\!\!\! & \!\!\!\! \underset{\color{blue}3}{} \!\!\!\! & \!\!\!\! \underset{\color{blue}1}{} \!\!\!\! & \\ & & \!\!\!\! 1 \!\!\!\! & \!\!\!\! \bbox[2px, lightgray]{8} \!\!\!\! & \!\!\!\! 5 \!\!\!\! & \!\!\!\! 2 \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & & & \!\!\!\! \bbox[2px, lightgray]{7} \!\!\!\! \\ \hline & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \color{red}9 \!\!\!\! & \!\!\!\! 6 \!\!\!\! & \!\!\!\! 4 \!\!\!\! \end{array} &\qquad\qquad& %%%% Explanations %%% \begin{array}{l} \bbox[2px, lightgray]{8} \times \bbox[2px, lightgray]{7} = 56 \quad\text{and}\quad {\color{blue}3} + 56 = 59 \\ \text{Carry:}\: {\color{blue}5} \\ \text{Write:}\: {\color{red}9} \end{array} \end{align*}

Finally, we multiply the thousands:

\begin{align*} %%%%%%%%%% %%% Step 4 %%% %%%%%%%%%% & %%% Long Multiplication %%% \begin{array}{ccccc} & & \!\!\!\! \underset{\color{blue}5}{} \!\!\!\! & \!\!\!\! \underset{\color{blue}3}{} \!\!\!\! & \!\!\!\! \underset{\color{blue}1}{} \!\!\!\! & \\ & & \!\!\!\! \bbox[2px, lightgray]{1} \!\!\!\! & \!\!\!\! 8 \!\!\!\! & \!\!\!\! 5 \!\!\!\! & \!\!\!\! 2 \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & & & \!\!\!\! \bbox[2px, lightgray]{7} \!\!\!\! \\ \hline & \!\!\!\! \color{red}1 \!\!\!\! & \!\!\!\! \fbox{[math]\color{red}2[/math]} \!\!\!\! & \!\!\! 9 \!\!\!\! & \!\!\!\! \fbox{6} \!\!\!\! & \!\!\! 4 \!\!\!\! \end{array} &\qquad\qquad& %%%% Explanations %%% \begin{array}{l} \bbox[2px, lightgray]{1} \times \bbox[2px, lightgray]{7} = 7 \quad\text{and}\quad {\color{blue}5} + 7 = 12 \\ \text{Carry:}\: {\color{blue}-} \\ \text{Write:}\: {\color{red}12} \end{array} \\[5pt] & \end{align*}

Therefore, the missing digits, from left-to-right, are \bbox[3pt,Gainsboro]{\color{blue}2} and \bbox[3pt,Gainsboro]{\color{blue}6}.

FLAG
Practice: Multiplying a Four-Digit Number By a One-Digit Number: Finding Missing Digits

Insert the missing numbers in the following multiplication problem:

a
b
c
d
e
Practice: Multiplying a Four-Digit Number By a One-Digit Number: Finding Missing Digits

Insert the missing numbers in the following multiplication problem:

a
b
c
d
e
Practice: Multiplying a Four-Digit Number By a One-Digit Number: Finding Missing Digits

Insert the missing numbers in the following multiplication problem:

a
b
c
d
e
Example: Multiplying a Four-Digit Number By a One-Digit Number

A bag of acorn seeds contains 2,162 seeds in total. Mary purchases 4 bags. How many seeds does she have in total?

EXPLANATION

To calculate the total number of seeds, we need to multiply 2,162 by 4 :

\begin{align*} %%%%%%%%%% %%% Step 0 %%% %%%%%%%%%% & %%% Long Multiplication %%% \begin{array}{ccccc} & & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \\ & & \!\!\!\! 2 \!\!\!\! & \!\!\!\! 1 \!\!\!\! & \!\!\!\! 6 \!\!\!\! & \!\!\!\! 2 \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & & & \!\!\!\! 4 \!\!\!\! \\ \hline & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! \end{array} &\qquad\qquad&\qquad \phantom{ 24 \quad\text{and}\quad {\color{blue}1} + 24 = 250000} \end{align*}

First, we multiply the ones. Notice that there is no digit to carry.

\begin{align*} %%%%%%%%%% %%% Step 1 %%% %%%%%%%%%% & %%% Long Multiplication %%% \begin{array}{ccccc} & & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \underset{}{} \!\!\!\! & \\ & & \!\!\!\! 2 \!\!\!\! & \!\!\!\! 1 \!\!\!\! & \!\!\!\! 6 \!\!\!\! & \!\!\!\! \bbox[2px, lightgray]{2} \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & & & \!\!\!\! \bbox[2px, lightgray]{4} \!\!\!\! \\ \hline & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \color{red}8 \!\!\!\! \end{array} &\qquad\qquad& %%%% Explanations %%% \begin{array}{l} \bbox[2px, lightgray]{2} \times \bbox[2px, lightgray]{4} = 8 \phantom{0000000000000000} \\ \text{Carry:}\: - \\ \text{Write:}\: {\color{red}8} \end{array} \end{align*}

Next, we multiply the tens. This time there is a digit to carry, which we should place above the hundreds column.

\begin{align*} %%%%%%%%%% %%% Step 2 %%% %%%%%%%%%% & %%% Long Multiplication %%% \begin{array}{ccccc} & & \!\!\!\! \!\!\!\! & \!\!\!\! \underset{\color{blue}2}{} \!\!\!\! & \!\!\!\! \underset{}{} \!\!\!\! & \\ & & \!\!\!\! 2 \!\!\!\! & \!\!\!\! 1 \!\!\!\! & \!\!\!\! \bbox[2px, lightgray]{6} \!\!\!\! & \!\!\!\! 2 \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & & & \!\!\!\! \bbox[2px, lightgray]{4} \!\!\!\! \\ \hline & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \color{red}4 \!\!\!\! & \!\!\!\! 8 \!\!\!\! \end{array} &\qquad\qquad& %%%% Explanations %%% \begin{array}{l} \bbox[2px, lightgray]{6} \times \bbox[2px, lightgray]{4} = 24 \phantom{0000000000000000} \\ \text{Carry:}\: {\color{blue}2} \\ \text{Write:}\: {\color{red}4} \end{array} \end{align*}

Next, we multiply the hundreds:

\begin{align*} %%%%%%%%%% %%% Step 3 %%% %%%%%%%%%% & %%% Long Multiplication %%% \begin{array}{ccccc} & & \!\!\!\! \!\!\!\! & \!\!\!\! \underset{\color{blue}2}{} \!\!\!\! & \!\!\!\! \!\!\!\! & \\ & & \!\!\!\! 2 \!\!\!\! & \!\!\!\! \bbox[2px, lightgray]{1} \!\!\!\! & \!\!\!\! 6 \!\!\!\! & \!\!\!\! 2 \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & & & \!\!\!\! \bbox[2px, lightgray]{4} \!\!\!\! \\ \hline & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \color{red}6 \!\!\!\! & \!\!\!\! 4 \!\!\!\! & \!\!\!\! 8 \!\!\!\! \end{array} &\qquad\qquad& %%%% Explanations %%% \begin{array}{l} \bbox[2px, lightgray]{1} \times \bbox[2px, lightgray]{4} = 4 \quad\text{and}\quad {\color{blue}2} + 4 = 6 \\ \text{Carry:}\: - \\ \text{Write:}\: {\color{red}6} \end{array} \end{align*}

Finally, we multiply the thousands:

\begin{align*} %%%%%%%%%% %%% Step 4 %%% %%%%%%%%%% & %%% Long Multiplication %%% \begin{array}{ccccc} & & \!\!\!\! \!\!\!\! & \!\!\!\! \underset{\color{blue}2}{} \!\!\!\! & \!\!\!\! \!\!\!\! & \\ & & \!\!\!\! \bbox[2px, lightgray]{2} \!\!\!\! & \!\!\!\! 1 \!\!\!\! & \!\!\!\! 6 \!\!\!\! & \!\!\!\! 2 \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & & & \!\!\!\! \bbox[2px, lightgray]{4} \!\!\!\! \\ \hline & \!\!\!\! \color{red} \!\!\!\! & \!\!\!\! \color{red}8 \!\!\!\! & \!\!\!\! 6 \!\!\!\! & \!\!\!\! 4 \!\!\!\! & \!\!\!\! 8 \!\!\!\! \end{array} &\qquad\qquad& %%%% Explanations %%% \begin{array}{l} \bbox[2px, lightgray]{2} \times \bbox[2px, lightgray]{4} = 8 \phantom{0000000000000000} \\ \text{Carry:}\: {\color{blue}-} \\ \text{Write:}\: {\color{red}8} \end{array} \\[5pt] & \end{align*}

Therefore, 2,162 \times 4 = 8, 648.

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Practice: Multiplying a Four-Digit Number By a One-Digit Number

$1,136 \times 2 =$

a
 $2,273$
b
 $2,272$
c
 $2,372$
d
 $2,742$
e
 $2,527$
Practice: Multiplying a Four-Digit Number By a One-Digit Number

$1,352 \times 6 =$

a
 $8,112$
b
 $6,112$
c
 $8,012$
d
 $8,222$
e
 $7,802$
Practice: Multiplying a Four-Digit Number By a One-Digit Number

In a shipping yard, $7$ containers contain bananas. There are $1,763$ bananas in each container. How many bananas are there in total?

a
 $12,621$
b
 $11,431$
c
 $12,341$
d
 $11,771$
e
 $12,111$
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