Introduction

In this lesson, we'll get practice at multiplying five-digit and six-digit numbers by one-digit numbers using the standard algorithm.

As before, we multiply each place value by the one-digit number from right to left.

Without further ado, let's dive in!

FLAG
Example: Multiplying Larger Numbers By One-Digit Numbers: Finding Missing Digits

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

\begin{align*} \begin{array}{ccccc} & & \!\!\!\! \underset{\color{blue}5}{} \!\!\!\! & \!\!\!\! \underset{\color{blue}0}{} \!\!\!\! & \!\!\!\! \underset{\color{blue}0}{} \!\!\!\! & \!\!\!\! \underset{\color{blue}3}{} \!\!\!\! & \\ & & \!\!\!\! \bbox[2px, lightgray]{7} \!\!\!\! & \!\!\!\! 9 \!\!\!\! & \!\!\!\! 0 \!\!\!\! & \!\!\!\! 0 \!\!\!\! & \!\!\!\! 6 \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & & & & \!\!\!\! \bbox[2px, lightgray]{6} \!\!\!\! \\ \hline & \!\!\!\! \fbox{[math]\phantom{4}[/math]} \!\!\!\! & \!\!\!\! \fbox{[math]\phantom{7}[/math]} \!\!\!\! & \!\!\! 4 \!\!\!\! & \!\!\!\! \fbox{[math]\phantom{0}[/math]} \!\!\!\! & \!\!\!3 \!\!\!\! & \!\!\!\! 6 \!\!\!\! \end{array} \end{align*}

EXPLANATION

First, we multiply the ones:

\begin{align*} %%%%%%%%%% %%% Step 1 %%% %%%%%%%%%% & %%% Long Multiplication %%% \begin{array}{ccccc} & & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \underset{\color{blue}3}{} \!\!\!\! & \\ & & \!\!\!\! 7 \!\!\!\! & \!\!\!\! 9 \!\!\!\! & \!\!\!\! 0 \!\!\!\! & \!\!\!\! 0 \!\!\!\! & \!\!\!\! \bbox[2px, lightgray]{6} \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & & & & \!\!\!\! \bbox[2px, lightgray]{6} \!\!\!\! \\ \hline & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \color{red}6 \!\!\!\! \end{array} &\qquad\qquad& %%%% Explanations %%% \begin{array}{l} \bbox[2px, lightgray]{6} \times \bbox[2px, lightgray]{6} = 36 \\ \text{Carry:}\: {\color{blue}3} \\ \text{Write:}\: {\color{red}6} \end{array} \end{align*}

Next, we multiply the tens:

\begin{align*} %%%%%%%%%% %%% Step 2 %%% %%%%%%%%%% & %%% Long Multiplication %%% \begin{array}{ccccc} & & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \underset{\color{blue}0}{} \!\!\!\! & \!\!\!\! \underset{\color{blue}3}{} \!\!\!\! & \\ & & \!\!\!\! 7 \!\!\!\! & \!\!\!\! 9 \!\!\!\! & \!\!\!\! 0 \!\!\!\! & \!\!\!\! \bbox[2px, lightgray]{0} \!\!\!\! & \!\!\!\! 6 \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & & & & \!\!\!\! \bbox[2px, lightgray]{6} \!\!\!\! \\ \hline & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \color{red}3 \!\!\!\! & \!\!\!\! 6 \!\!\!\! \end{array} &\qquad\qquad& %%%% Explanations %%% \begin{array}{l} \bbox[2px, lightgray]{0} \times \bbox[2px, lightgray]{6} = 0 \quad\text{and}\quad {\color{blue}3} + 0 = 3 \\ \text{Carry:}\: {\color{blue}0} \\ \text{Write:}\: {\color{red}3} \end{array} \end{align*}

Next, we multiply the hundreds:

\begin{align*} %%%%%%%%%% %%% Step 3 %%% %%%%%%%%%% & %%% Long Multiplication %%% \begin{array}{ccccc} & & \!\!\!\! \!\!\!\! & \!\!\!\! \underset{\color{blue}0}{} \!\!\!\! & \!\!\!\! \underset{\color{blue}0}{} \!\!\!\! & \!\!\!\! \underset{\color{blue}3}{} \!\!\!\! & \\ & & \!\!\!\! 7 \!\!\!\! & \!\!\!\! 9 \!\!\!\! & \!\!\!\! \bbox[2px, lightgray]{0} \!\!\!\! & \!\!\!\! 0 \!\!\!\! & \!\!\!\! 6 \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & & & & \!\!\!\! \bbox[2px, lightgray]{6} \!\!\!\! \\ \hline & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \color{red}0 \!\!\!\! & \!\!\!\! 3 \!\!\!\! & \!\!\!\! 6 \!\!\!\! \end{array} &\qquad\qquad& %%%% Explanations %%% \begin{array}{l} \bbox[2px, lightgray]{0} \times \bbox[2px, lightgray]{6} = 0 \quad\text{and}\quad {\color{blue}0} + 0 = 0 \\ \text{Carry:}\: {\color{blue}0} \\ \text{Write:}\: {\color{red}0} \end{array} \end{align*}

Next, we multiply the thousands:

\begin{align*} %%%%%%%%%% %%% Step 4 %%% %%%%%%%%%% & %%% Long Multiplication %%% \begin{array}{ccccc} & & \!\!\!\! \underset{\color{blue}5}{} \!\!\!\! & \!\!\!\! \underset{\color{blue}0}{} \!\!\!\! & \!\!\!\! \underset{\color{blue}0}{} \!\!\!\! & \!\!\!\! \underset{\color{blue}3}{} \!\!\!\! & \\ & & \!\!\!\! 7 \!\!\!\! & \!\!\!\! \bbox[2px, lightgray]{9} \!\!\!\! & \!\!\!\! 0 \!\!\!\! & \!\!\!\! 0 \!\!\!\! & \!\!\!\! 6 \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & & & & \!\!\!\! \bbox[2px, lightgray]{6} \!\!\!\! \\ \hline & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \color{red}4 \!\!\!\! & \!\!\!\! 0 \!\!\!\! & \!\!\!\! 3 \!\!\!\! & \!\!\!\! 6 \!\!\!\! \end{array} &\qquad\qquad& %%%% Explanations %%% \begin{array}{l} \bbox[2px, lightgray]{9} \times \bbox[2px, lightgray]{6} = 54 \quad\text{and}\quad {\color{blue}0} + 54 = 54 \\ \text{Carry:}\: {\color{blue}5} \\ \text{Write:}\: {\color{red}4} \end{array} \end{align*}

Finally, we multiply the tens of thousands:

\begin{align*} %%%%%%%%%% %%% Step 5 %%% %%%%%%%%%% & %%% Long Multiplication %%% \begin{array}{ccccc} & & \!\!\!\! \underset{\color{blue}5}{} \!\!\!\! & \!\!\!\! \underset{\color{blue}0}{} \!\!\!\! & \!\!\!\! \underset{\color{blue}0}{} \!\!\!\! & \!\!\!\! \underset{\color{blue}3}{} \!\!\!\! & \\ & & \!\!\!\! \bbox[2px, lightgray]{7} \!\!\!\! & \!\!\!\! 9 \!\!\!\! & \!\!\!\! 0 \!\!\!\! & \!\!\!\! 0 \!\!\!\! & \!\!\!\! 6 \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & & & & \!\!\!\! \bbox[2px, lightgray]{6} \!\!\!\! \\ \hline & \!\!\!\! \fbox{[math]\color{red}4[/math]} \!\!\!\! & \!\!\!\! \fbox{[math]\color{red}7[/math]} \!\!\!\! & \!\!\! 4 \!\!\!\! & \!\!\!\! \fbox{0} \!\!\!\! & \!\!\! 3 \!\!\!\! & \!\!\!\! 6 \!\!\!\! \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}-} \\ \text{Write:}\: {\color{red}47} \end{array} \\[5pt] & \end{align*}

Therefore, the missing digits, from left-to-right, are \bbox[3pt,Gainsboro]{\color{blue}4},\bbox[3pt,Gainsboro]{\color{blue}7}, and \bbox[3pt,Gainsboro]{\color{blue}0}.

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Practice: Multiplying Larger Numbers By One-Digit Numbers: Finding Missing Digits

Insert the missing digits in the following multiplication problem:

a
b
c
d
e
Practice: Multiplying Larger Numbers By One-Digit Numbers: Finding Missing Digits

Insert the missing digits in the following multiplication problem:

a
b
c
d
e
Practice: Multiplying Larger Numbers By One-Digit Numbers: Finding Missing Digits

Insert the missing digits in the following multiplication problem:

a
b
c
d
e
Example: Multiplying Larger Numbers By One-Digit Numbers

Calculate the value of 43,532 \times 7.

EXPLANATION

We write it this way:

\begin{align*} %%%%%%%%%% %%% Step 0 %%% %%%%%%%%%% & %%% Long Multiplication %%% \begin{array}{ccccc} & & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \\ & & \!\!\!\! 4 \!\!\!\! & \!\!\!\! 3 \!\!\!\! & \!\!\!\! 5 \!\!\!\! & \!\!\!\! 3 \!\!\!\! & \!\!\!\! 2 \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & & & & \!\!\!\! 7 \!\!\!\! \\ \hline & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! \end{array} &\qquad\qquad&\qquad \phantom{ 24 \quad\text{and}\quad {\color{blue}1} + 24 = 2500000} \end{align*}

First, we multiply the ones:

\begin{align*} %%%%%%%%%% %%% Step 1 %%% %%%%%%%%%% & %%% Long Multiplication %%% \begin{array}{ccccc} & & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \underset{\color{blue}1}{} \!\!\!\! & \\ & & \!\!\!\! 4 \!\!\!\! & \!\!\!\! 3 \!\!\!\! & \!\!\!\! 5 \!\!\!\! & \!\!\!\! 3 \!\!\!\! & \!\!\!\! \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 \phantom{00000000000000000} \\ \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}2}{} \!\!\!\! & \!\!\!\! \underset{\color{blue}1}{} \!\!\!\! & \\ & & \!\!\!\! 4 \!\!\!\! & \!\!\!\! 3 \!\!\!\! & \!\!\!\! 5 \!\!\!\! & \!\!\!\! \bbox[2px, lightgray]{3} \!\!\!\! & \!\!\!\! 2 \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & & & & \!\!\!\! \bbox[2px, lightgray]{7} \!\!\!\! \\ \hline & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \color{red}2 \!\!\!\! & \!\!\!\! 4 \!\!\!\! \end{array} &\qquad\qquad& %%%% Explanations %%% \begin{array}{l} \bbox[2px, lightgray]{3} \times \bbox[2px, lightgray]{7} = 21 \quad\text{and}\quad {\color{blue}1} + 21 = 22 \\ \text{Carry:}\: {\color{blue}2} \\ \text{Write:}\: {\color{red}2} \end{array} \end{align*}

Next, we multiply the hundreds:

\begin{align*} %%%%%%%%%% %%% Step 3 %%% %%%%%%%%%% & %%% Long Multiplication %%% \begin{array}{ccccc} & & \!\!\!\! \!\!\!\! & \!\!\!\! \underset{\color{blue}3}{} \!\!\!\! & \!\!\!\! \underset{\color{blue}2}{} \!\!\!\! & \!\!\!\! \underset{\color{blue}1}{} \!\!\!\! & \\ & & \!\!\!\! 4 \!\!\!\! & \!\!\!\! 3 \!\!\!\! & \!\!\!\! \bbox[2px, lightgray]{5} \!\!\!\! & \!\!\!\! 3 \!\!\!\! & \!\!\!\! 2 \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & & & & \!\!\!\! \bbox[2px, lightgray]{7} \!\!\!\! \\ \hline & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \color{red}7 \!\!\!\! & \!\!\!\! 2 \!\!\!\! & \!\!\!\! 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}2} + 35 = 37 \\ \text{Carry:}\: {\color{blue}3} \\ \text{Write:}\: {\color{red}7} \end{array} \end{align*}

Next, we multiply the thousands:

\begin{align*} %%%%%%%%%% %%% Step 4 %%% %%%%%%%%%% & %%% Long Multiplication %%% \begin{array}{ccccc} & & \!\!\!\! \underset{\color{blue}2}{} \!\!\!\! & \!\!\!\! \underset{\color{blue}3}{} \!\!\!\! & \!\!\!\! \underset{\color{blue}2}{} \!\!\!\! & \!\!\!\! \underset{\color{blue}1}{} \!\!\!\! & \\ & & \!\!\!\! 4 \!\!\!\! & \!\!\!\! \bbox[2px, lightgray]{3} \!\!\!\! & \!\!\!\! 5 \!\!\!\! & \!\!\!\! 3 \!\!\!\! & \!\!\!\! 2 \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & & & & \!\!\!\! \bbox[2px, lightgray]{7} \!\!\!\! \\ \hline & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \color{red}4 \!\!\!\! & \!\!\!\! 7 \!\!\!\! & \!\!\!\! 2 \!\!\!\! & \!\!\!\! 4 \!\!\!\! \end{array} &\qquad\qquad& %%%% Explanations %%% \begin{array}{l} \bbox[2px, lightgray]{3} \times \bbox[2px, lightgray]{7} = 21 \quad\text{and}\quad {\color{blue}3} + 21 = 24 \\ \text{Carry:}\: {\color{blue}2} \\ \text{Write:}\: {\color{red}4} \end{array} \end{align*}

Finally, we multiply the ten thousands:

\begin{align*} %%%%%%%%%% %%% Step 5 %%% %%%%%%%%%% & %%% Long Multiplication %%% \begin{array}{ccccc} & & \!\!\!\! \underset{\color{blue}2}{} \!\!\!\! & \!\!\!\! \underset{\color{blue}3}{} \!\!\!\! & \!\!\!\! \underset{\color{blue}2}{} \!\!\!\! & \!\!\!\! \underset{\color{blue}1}{} \!\!\!\! & \\ & & \!\!\!\! \bbox[2px, lightgray]{4} \!\!\!\! & \!\!\!\! 3 \!\!\!\! & \!\!\!\! 5 \!\!\!\! & \!\!\!\! 3 \!\!\!\! & \!\!\!\! 2 \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & & & & \!\!\!\! \bbox[2px, lightgray]{7} \!\!\!\! \\ \hline & \!\!\!\! \color{red}3 \!\!\!\! & \!\!\!\! \color{red}0 \!\!\!\! & \!\!\!\! 4 \!\!\!\! & \!\!\!\! 7 \!\!\!\! & \!\!\!\! 2 \!\!\!\! & \!\!\!\! 4 \!\!\!\! \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}-} \\ \text{Write:}\: {\color{red}30} \end{array} \\[5pt] & \end{align*}

Therefore, 43,532 \times 7 = 304 , 724.

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Practice: Multiplying Larger Numbers By One-Digit Numbers

$24,258 \times 5 =$

a
 $123,290$
b
 $124,294$
c
 $121,290$
d
 $121,720$
e
 $211,290$
Practice: Multiplying Larger Numbers By One-Digit Numbers

$26,303 \times 8 =$

a
b
c
d
e
Practice: Multiplying Larger Numbers By One-Digit Numbers

$817,916 \times 6 =$

a
 $9,704,946$
b
 $4,907,496$
c
 $4,709,946$
d
 $4,907,946$
e
 $4,709,496$
Example: Word Problems

A factory uses 836\,802 kilowatt-hours of electricity each quarter. How much electricity will it use in a year, if a year contains 4 quarters?

EXPLANATION

To calculate the factory's energy consumption over one year, we need to multiply 836\,802 by 4.

We write it this way:

\begin{align*} %%%%%%%%%% %%% Step 0 %%% %%%%%%%%%% & %%% Long Multiplication %%% \begin{array}{ccccc} & & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \\ & & \!\!\!\! 8 \!\!\!\! & \!\!\!\! 3 \!\!\!\! & \!\!\!\! 6 \!\!\!\! & \!\!\!\! 8 \!\!\!\! & \!\!\!\! 0 \!\!\!\! & \!\!\!\! 2 \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & & & & & \!\!\!\! 4 \!\!\!\! \\ \hline & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! \end{array} &\qquad\qquad& \end{align*}

First, we multiply the ones:

\begin{align*} %%%%%%%%%% %%% Step 1 %%% %%%%%%%%%% & %%% Long Multiplication %%% \begin{array}{ccccc} & & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \underset{\color{blue}0}{} \!\!\!\! & \\ & & \!\!\!\! 8 \!\!\!\! & \!\!\!\! 3 \!\!\!\! & \!\!\!\! 6 \!\!\!\! & \!\!\!\! 8 \!\!\!\! & \!\!\!\! 0 \!\!\!\! & \!\!\!\! \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 \\ \text{Carry:}\: {\color{blue}0} \\ \text{Write:}\: {\color{red}8} \end{array} \end{align*}

Next, we multiply the tens:

\begin{align*} %%%%%%%%%% %%% Step 2 %%% %%%%%%%%%% & %%% Long Multiplication %%% \begin{array}{ccccc} & & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \underset{\color{blue}0}{} \!\!\!\! & \!\!\!\! \underset{\color{blue}0}{} \!\!\!\! & \\ & & \!\!\!\! 8 \!\!\!\! & \!\!\!\! 3 \!\!\!\! & \!\!\!\! 6 \!\!\!\! & \!\!\!\! 8 \!\!\!\! & \!\!\!\! \bbox[2px, lightgray]{0} \!\!\!\! & \!\!\!\! 2 \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & & & & & \!\!\!\! \bbox[2px, lightgray]{4} \!\!\!\! \\ \hline & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \color{red}0 \!\!\!\! & \!\!\!\! 8 \!\!\!\! \end{array} &\qquad\qquad& %%%% Explanations %%% \begin{array}{l} \bbox[2px, lightgray]{0} \times \bbox[2px, lightgray]{4} = 0 \quad\text{and}\quad {\color{blue}0} + 0 = 0 \\ \text{Carry:}\: {\color{blue}0} \\ \text{Write:}\: {\color{red}0} \end{array} \end{align*}

Next, we multiply the hundreds:

\begin{align*} %%%%%%%%%% %%% Step 3 %%% %%%%%%%%%% & %%% Long Multiplication %%% \begin{array}{ccccc} & & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \underset{\color{blue}3}{} \!\!\!\! & \!\!\!\! \underset{\color{blue}0}{} \!\!\!\! & \!\!\!\! \underset{\color{blue}0}{} \!\!\!\! & \\ & & \!\!\!\! 8 \!\!\!\! & \!\!\!\! 3 \!\!\!\! & \!\!\!\! 6 \!\!\!\! & \!\!\!\! \bbox[2px, lightgray]{8} \!\!\!\! & \!\!\!\! 0 \!\!\!\! & \!\!\!\! 2 \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & & & & & \!\!\!\! \bbox[2px, lightgray]{4} \!\!\!\! \\ \hline & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \color{red}2 \!\!\!\! & \!\!\!\! 0 \!\!\!\! & \!\!\!\! 8 \!\!\!\! \end{array} &\qquad\qquad& %%%% Explanations %%% \begin{array}{l} \bbox[2px, lightgray]{8} \times \bbox[2px, lightgray]{4} = 32 \quad\text{and}\quad {\color{blue}0} + 32 = 32 \\ \text{Carry:}\: {\color{blue}3} \\ \text{Write:}\: {\color{red}2} \end{array} \end{align*}

Next, we multiply the thousands:

\begin{align*} %%%%%%%%%% %%% Step 4 %%% %%%%%%%%%% & %%% Long Multiplication %%% \begin{array}{ccccc} & & \!\!\!\! \!\!\!\! & \!\!\!\! \underset{\color{blue}2}{} \!\!\!\! & \!\!\!\! \underset{\color{blue}3}{} \!\!\!\! & \!\!\!\! \underset{\color{blue}0}{} \!\!\!\! & \!\!\!\! \underset{\color{blue}0}{} \!\!\!\! & \\ & & \!\!\!\! 8 \!\!\!\! & \!\!\!\! 3 \!\!\!\! & \!\!\!\! \bbox[2px, lightgray]{6} \!\!\!\! & \!\!\!\! 8 \!\!\!\! & \!\!\!\! 0 \!\!\!\! & \!\!\!\! 2 \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & & & & & \!\!\!\! \bbox[2px, lightgray]{4} \!\!\!\! \\ \hline & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \color{red}7 \!\!\!\! & \!\!\!\! 2 \!\!\!\! & \!\!\!\! 0 \!\!\!\! & \!\!\!\! 8 \!\!\!\! \end{array} &\qquad\qquad& %%%% Explanations %%% \begin{array}{l} \bbox[2px, lightgray]{6} \times \bbox[2px, lightgray]{4} = 24 \quad\text{and}\quad {\color{blue}3} + 24 = 27 \\ \text{Carry:}\: {\color{blue}2} \\ \text{Write:}\: {\color{red}7} \end{array} \end{align*}

Next, we multiply the ten thousands:

\begin{align*} %%%%%%%%%% %%% Step 5 %%% %%%%%%%%%% & %%% Long Multiplication %%% \begin{array}{ccccc} & & \!\!\!\! \underset{\color{blue}1}{} \!\!\!\! & \!\!\!\! \underset{\color{blue}2}{} \!\!\!\! & \!\!\!\! \underset{\color{blue}3}{} \!\!\!\! & \!\!\!\! \underset{\color{blue}0}{} \!\!\!\! & \!\!\!\! \underset{\color{blue}0}{} \!\!\!\! & \\ & & \!\!\!\! 8 \!\!\!\! & \!\!\!\! \bbox[2px, lightgray]{3} \!\!\!\! & \!\!\!\! 6 \!\!\!\! & \!\!\!\! 8 \!\!\!\! & \!\!\!\! 0 \!\!\!\! & \!\!\!\! 2 \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & & & & & \!\!\!\! \bbox[2px, lightgray]{4} \!\!\!\! \\ \hline & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \color{red}4 \!\!\!\! & \!\!\!\! 7 \!\!\!\! & \!\!\!\! 2 \!\!\!\! & \!\!\!\! 0 \!\!\!\! & \!\!\!\! 8 \!\!\!\! \end{array} &\qquad\qquad& %%%% Explanations %%% \begin{array}{l} \bbox[2px, lightgray]{3} \times \bbox[2px, lightgray]{4} = 12 \quad\text{and}\quad {\color{blue}2} + 12 = 14 \\ \text{Carry:}\: {\color{blue}1} \\ \text{Write:}\: {\color{red}4} \end{array} \\[5pt] & \end{align*}

Finally, we multiply the hundred thousands:

\begin{align*} %%%%%%%%%% %%% Step 6 %%% %%%%%%%%%% & %%% Long Multiplication %%% \begin{array}{ccccc} & & \!\!\!\! \underset{\color{blue}1}{} \!\!\!\! & \!\!\!\! \underset{\color{blue}2}{} \!\!\!\! & \!\!\!\! \underset{\color{blue}3}{} \!\!\!\! & \!\!\!\! \underset{\color{blue}0}{} \!\!\!\! & \!\!\!\! \underset{\color{blue}0}{} \!\!\!\! & \\ & & \!\!\!\! \bbox[2px, lightgray]{8} \!\!\!\! & \!\!\!\! 3 \!\!\!\! & \!\!\!\! 6 \!\!\!\! & \!\!\!\! 8 \!\!\!\! & \!\!\!\! 0 \!\!\!\! & \!\!\!\! 2 \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & & & & & \!\!\!\! \bbox[2px, lightgray]{4} \!\!\!\! \\ \hline & \!\!\!\! \color{red}3 \!\!\!\! & \!\!\!\! \color{red}3 \!\!\!\! & \!\!\!\! 4 \!\!\!\! & \!\!\!\! 7 \!\!\!\! & \!\!\!\! 2 \!\!\!\! & \!\!\!\! 0 \!\!\!\! & \!\!\!\! 8 \!\!\!\! \end{array} &\qquad\qquad& %%%% Explanations %%% \begin{array}{l} \bbox[2px, lightgray]{8} \times \bbox[2px, lightgray]{4} = 32 \quad\text{and}\quad {\color{blue}1} + 32 = 33 \\ \text{Carry:}\: {\color{blue}-} \\ \text{Write:}\: {\color{red}33} \end{array} \\[5pt] & \end{align*}

Therefore, 836\,802 \times 4 = 3 \, 347 \, 208.

Therefore, the factory's total energy consumption in a year is 3\,347\,208 kilowatt-hours.

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Practice: Word Problems

A charity aims to distribute $51\,534$ free meals to people in need. If each meal costs $\$5$ to make, the charity will need $\$$

a
b
c
d
e
Practice: Word Problems

A construction company has $4$ plots of land to build on. Each plot cost $\$54,995.$ What is the total value of all the plots?

a
 $\$218,780$
b
 $\$219,980$
c
 $\$217,480$
d
 $\$214,580$
e
 $\$216,880$
Practice: Word Problems

A city consumes $635\,825$ gallons of water every day. How much water does the city consume in a week?

a
 $4\,084\,775$ gallons
b
 $4\,723\,775$ gallons
c
 $4\,374\,775$ gallons
d
 $4\,978\,775$ gallons
e
 $4\,450\,775$ gallons
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