Introduction

To multiply a two-digit number by a one-digit number, we can use the standard algorithm.

For example, to multiply 23 by 3, we write the two-digit number above the one-digit number, lining up the place values:

\begin{align*} %%%%%%%%%% %%% Step 0 %%% %%%%%%%%%% %%% Long Multiplication %%% \begin{array}{ccccc} & & \!\!\!\! \!\!\!\! & \\ & & \!\!\!\! 2 \!\!\!\! & \!\!\!\! 3 \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & \!\!\!\! 3 \!\!\!\! \\ \hline & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! \end{array} &\qquad\qquad&\qquad \phantom{48 + 720 = {\color{red}768} 00000000} \end{align*}

First, we multiply the ones, placing the answer in the ones column under the line:

\begin{align*} %%%%%%%%%% %%% Step 1 %%% %%%%%%%%%% & %%% Long Multiplication %%% \begin{array}{ccccc} & & \!\!\!\! \underset{\color{blue}\phantom{0}}{} \!\!\!\! & \\ & & \!\!\!\! 2 \!\!\!\! & \!\!\!\! \bbox[2px, lightgray]{3} \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & \!\!\!\! \bbox[2px, lightgray]{3} \!\!\!\! \\ \hline & & \!\!\!\! \!\!\!\! & \!\!\! \color{red}9 \!\!\!\! \end{array} &\qquad\qquad& %%%% Explanations %%% \begin{array}{l} \bbox[2px, lightgray]{3} \times \bbox[2px, lightgray]{3} = 9\phantom{0000000000000000} \\ \text{Write:}\: {\color{red}9} \end{array} \end{align*}

Then, we multiply by the value in the tens place, putting the answer in the tens column under the line:

\begin{align*} %%%%%%%%%% %%% Step 2 %%% %%%%%%%%%% & %%% Long Multiplication %%% \begin{array}{ccccc} & & \!\!\! \underset{\color{blue}\phantom{0}}{} \!\!\!\! & \\ & & \!\!\!\! \bbox[2px, lightgray]{2} \!\!\!\! & \!\!\! 3 \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & \!\!\!\! \bbox[2px, lightgray]{3} \!\!\!\! \\ \hline & \!\!\!\! \color{red} \!\!\!\! & \!\!\! \color{red}6 \!\!\!\! & \!\!\! 9 \!\!\!\! \end{array} &\qquad\qquad& %%%% Explanations %%% \begin{array}{l} \bbox[2px, lightgray]{2} \times \bbox[2px, lightgray]{3} = 6\phantom{0000000000000000}\\ \text{Write:}\: {\color{red}6} \end{array} \\[5pt] & \end{align*}

Therefore, 23 \times 3 = 69.

FLAG
Example: Two-Digit by One-Digit Multiplication

What is 4 multiplied by 21?

EXPLANATION

We write our multiplication this way:

\begin{align*} %%%%%%%%%% %%% Step 0 %%% %%%%%%%%%% %%% Long Multiplication %%% \begin{array}{ccccc} & & \!\!\!\! \!\!\!\! & \\ & & \!\!\!\! 2 \!\!\!\! & \!\!\!\! 1 \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & \!\!\!\! 4 \!\!\!\! \\ \hline & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! \end{array} &\qquad\qquad&\qquad \phantom{48 + 720 = {\color{red}768} 00000000} \end{align*}

First, we multiply the ones:

\begin{align*} %%%%%%%%%% %%% Step 1 %%% %%%%%%%%%% & %%% Long Multiplication %%% \begin{array}{ccccc} & & \!\!\!\! \underset{\color{blue}\phantom{0}}{} \!\!\!\! & \\ & & \!\!\!\! 2 \!\!\!\! & \!\!\!\! \bbox[2px, lightgray]{1} \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & \!\!\!\! \bbox[2px, lightgray]{4} \!\!\!\! \\ \hline & & \!\!\!\! \!\!\!\! & \!\!\! \color{red}4 \!\!\!\! \end{array} &\qquad\qquad& %%%% Explanations %%% \begin{array}{l} \bbox[2px, lightgray]{1} \times \bbox[2px, lightgray]{4} = 4\phantom{0000000000000000} \\ \text{Write:}\: {\color{red}4} \end{array} \end{align*}

Finally, we multiply the tens:

\begin{align*} %%%%%%%%%% %%% Step 2 %%% %%%%%%%%%% & %%% Long Multiplication %%% \begin{array}{ccccc} & & \!\!\! \underset{\color{blue}\phantom{0}}{} \!\!\!\! & \\ & & \!\!\!\! \bbox[2px, lightgray]{2} \!\!\!\! & \!\!\! 1 \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & \!\!\!\! \bbox[2px, lightgray]{4} \!\!\!\! \\ \hline & \!\!\!\! \color{red} \!\!\!\! & \!\!\! \color{red}8 \!\!\!\! & \!\!\! 4 \!\!\!\! \end{array} &\qquad\qquad& %%%% Explanations %%% \begin{array}{l} \bbox[2px, lightgray]{2} \times \bbox[2px, lightgray]{4} = 8\phantom{0000000000000000}\\ \text{Write:}\: {\color{red}8} \end{array} \\[5pt] & \end{align*}

Therefore, 21 \times 4 = 84.

FLAG
Practice: Two-Digit by One-Digit Multiplication

$43\times 2=$

a
 $84$
b
 $82$
c
 $78$
d
 $86$
e
 $88$
Practice: Two-Digit by One-Digit Multiplication

$71\times 8=$

a
b
c
d
e
Practice: Two-Digit by One-Digit Multiplication

$61\times 6=$

a
 $386$
b
 $286$
c
 $366$
d
 $376$
e
 $316$
Multiplying Two-Digit Numbers By One-Digit Numbers With Carries

Sometimes when multiplying the ones, the result is two digits long.

In this case, we write down the digit in the ones place, and we carry the digit in the tens place. We then add the carried digit to the result of the multiplication of the tens.

For example, let's multiply 26 by 6.

\begin{align*} %%%%%%%%%% %%% Step 0 %%% %%%%%%%%%% %%% Long Multiplication %%% \begin{array}{ccccc} & & \!\!\!\! \!\!\!\! & \\ & & \!\!\!\! 2 \!\!\!\! & \!\!\!\! 6 \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & \!\!\!\! 6 \!\!\!\! \\ \hline & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! \end{array} &\qquad\qquad&\qquad \phantom{ 14 \quad\text{and}\quad {\color{blue}3} + 14 = 170000} \end{align*}

First, we multiply the ones. We have 6\times6= {\color{blue}3}{\color{red}6} , so we write the ones place value, \color{red}6 , and carry the tens place value, {\color{blue}3}\mathbin{:}

\begin{align*} %%%%%%%%%% %%% Step 1 %%% %%%%%%%%%% & %%% Long Multiplication %%% \begin{array}{ccccc} & & \!\!\!\! \underset{\color{blue}3}{} \!\!\!\! & \\ & & \!\!\!\! 2 \!\!\!\! & \!\!\!\! \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\phantom{00000000000000000} \\ \text{Carry:}\: {\color{blue}3} \\ \text{Write:}\: {\color{red}6} \end{array} \end{align*}

Finally, we multiply the tens. We have 2\times 6 = 12 , to which we add the carry of {\color{blue}3}\mathbin{:}

\begin{align*} %%%%%%%%%% %%% Step 2 %%% %%%%%%%%%% & %%% Long Multiplication %%% \begin{array}{ccccc} & & \!\!\! \underset{\color{blue}3}{} \!\!\!\! & \\ & & \!\!\!\! \bbox[2px, lightgray]{2} \!\!\!\! & \!\!\!\! 6 \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & \!\!\!\!\! \bbox[2px, lightgray]{6} \!\!\!\! \\ \hline & \!\!\!\! \color{red}1 \!\!\!\! & \!\!\!\! \color{red}5 \!\!\!\! & \!\!\!\! 6 \!\!\!\! \end{array} &\qquad\qquad& %%%% Explanations %%% \begin{array}{l} \bbox[2px, lightgray]{2} \times \bbox[2px, lightgray]{6} = 12 \quad\text{and}\quad {\color{blue}3} + 12 = 15 \\ \text{Carry:}\: {\color{blue}-} \\ \text{Write:}\: {\color{red}15} \end{array} \\[5pt] & \end{align*}

When we reach the tens multiplication, we do not carry anything. Instead, we write down the complete result.

Therefore, 26 \times 6 = 156.

FLAG
Example: Two-Digit by One-Digit Multiplication With Carries

Calculate 37\times 4.

EXPLANATION

We write it this way:

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

First, we multiply the ones:

\begin{align*} %%%%%%%%%% %%% Step 1 %%% %%%%%%%%%% & %%% Long Multiplication %%% \begin{array}{ccccc} & & \!\!\!\! \underset{\color{blue}2}{} \!\!\!\! & \\ & & \!\!\!\! 3 \!\!\!\! & \!\!\!\! \bbox[2px, lightgray]{7} \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & \!\!\!\! \bbox[2px, lightgray]{4} \!\!\!\! \\ \hline & & \!\!\!\! \!\!\!\! & \!\!\!\! \color{red}8 \!\!\!\! \end{array} &\qquad\qquad& %%%% Explanations %%% \begin{array}{l} \bbox[2px, lightgray]{7} \times \bbox[2px, lightgray]{4} = 28 \phantom{\quad\text{and}\quad {\color{blue}2} + 12 = 14}\\ \text{Carry:}\: {\color{blue}2} \\ \text{Write:}\: {\color{red}8} \end{array} \end{align*}

Finally, we multiply the tens:

\begin{align*} %%%%%%%%%% %%% Step 2 %%% %%%%%%%%%% & %%% Long Multiplication %%% \begin{array}{ccccc} & & \!\!\!\! \underset{\color{blue}2}{} \!\!\!\! & \\ & & \!\!\!\! \bbox[2px, lightgray]{3} \!\!\!\! & \!\!\!\! 7 \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & \!\!\!\! \bbox[2px, lightgray]{4} \!\!\!\! \\ \hline & \!\!\!\! \color{red}1 \!\!\!\! & \!\!\!\! \color{red}4 \!\!\!\! & \!\!\!\! 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}-} \\ \text{Write:}\: {\color{red}14} \end{array} \\[5pt] & \end{align*}

Therefore, 37 \times 4 = 148.

FLAG
Practice: Two-Digit by One-Digit Multiplication With Carries

$68\times 2=$

a
b
c
d
e
Practice: Two-Digit by One-Digit Multiplication With Carries

$25 \times 4=$

a
 $10$
b
 $75$
c
 $105$
d
 $100$
e
 $125$
Practice: Two-Digit by One-Digit Multiplication With Carries

$36\times 9=$

a
b
c
d
e
Example: Word Problems

As part of a school assignment, 7 students in the same class must interview 25 people about their sports preferences. How many interviews will they need to conduct in total?

EXPLANATION

To calculate the total number of interviews, we need to multiply 25 by 7.

\begin{align*} %%%%%%%%%% %%% Step 0 %%% %%%%%%%%%% %%% Long Multiplication %%% \begin{array}{ccccc} & & \!\!\!\! \!\!\!\! & \\ & & \!\!\!\! 2 \!\!\!\! & \!\!\!\! 5 \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & \!\!\!\! 7 \!\!\!\! \\ \hline & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! \end{array} &\qquad\qquad&\qquad \phantom{ 14 \quad\text{and}\quad {\color{blue}3} + 14 = 170000} \end{align*}

First, we multiply the ones:

\begin{align*} %%%%%%%%%% %%% Step 1 %%% %%%%%%%%%% & %%% Long Multiplication %%% \begin{array}{ccccc} & & \!\!\!\! \underset{\color{blue}3}{} \!\!\!\! & \\ & & \!\!\!\! 2 \!\!\!\! & \!\!\!\! \bbox[2px, lightgray]{5} \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & \!\!\!\! \bbox[2px, lightgray]{7} \!\!\!\! \\ \hline & & \!\!\!\! \!\!\!\! & \!\!\!\! \color{red}5 \!\!\!\! \end{array} &\qquad\qquad& %%%% Explanations %%% \begin{array}{l} \bbox[2px, lightgray]{5} \times \bbox[2px, lightgray]{7} = 35\phantom{00000000000000000} \\ \text{Carry:}\: {\color{blue}3} \\ \text{Write:}\: {\color{red}5} \end{array} \end{align*}

Finally, we multiply the tens:

\begin{align*} %%%%%%%%%% %%% Step 2 %%% %%%%%%%%%% & %%% Long Multiplication %%% \begin{array}{ccccc} & & \!\!\! \underset{\color{blue}3}{} \!\!\!\! & \\ & & \!\!\!\! \bbox[2px, lightgray]{2} \!\!\!\! & \!\!\!\! 5 \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & \!\!\!\!\! \bbox[2px, lightgray]{7} \!\!\!\! \\ \hline & \!\!\!\! \color{red}1 \!\!\!\! & \!\!\!\! \color{red}7 \!\!\!\! & \!\!\!\! 5 \!\!\!\! \end{array} &\qquad\qquad& %%%% Explanations %%% \begin{array}{l} \bbox[2px, lightgray]{2} \times \bbox[2px, lightgray]{7} = 14 \quad\text{and}\quad {\color{blue}3} + 14 = 17 \\ \text{Carry:}\: {\color{blue}-} \\ \text{Write:}\: {\color{red}17} \end{array} \\[5pt] & \end{align*}

Therefore, there will be a total of 175 interviews.

FLAG
Practice: Word Problems

Carla delivered $27$ candies to each one of her five friends. How many candies did Carla deliver in total?

a
 $162$
b
 $108$
c
 $119$
d
 $135$
e
 $126$
Practice: Word Problems

A box contains $8$ packs of pencils, each pack containing $26$ pencils. How many pencils are in the box in total?

a
b
c
d
e
Practice: Word Problems

An office building has $26$ floors, each with $9$ offices. How many offices are in the building in total?

a
b
c
d
e
Flag Content
Did you notice an error, or do you simply believe that something could be improved? Please explain below.
SUBMIT
CANCEL