We can extend our understanding of place value to multiply three-digit numbers by one-digit numbers.

As an example, let's consider the following multiplication problem:

145 \times {\color{red}{4}}

First, let's write the three-digit number (145) in expanded form:

145 = {\color{blue}{100}} + {\color{blue}{40}} + {\color{blue}{5}}

We now multiply all numbers in our expanded form by {\color{red}{4}}\mathbin{:}

\begin{align*} {\color{blue}{100}} \times {\color{red}{4}} &= 400 \\[5pt] {\color{blue}{40}} \times {\color{red}{4}} &= 160 \\[5pt] {\color{blue}{5}} \times {\color{red}{4}} &= 20 \end{align*}

Let's now add these results:

\begin{array}{cccccccc} & \!\!\!\! \!\!\!\! & \!\!\!\! 4 \!\!\!\! & \!\!\!\! 0 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\ \!\!\!\!+\!\!\!\! & & \!\!\!\! 1 \!\!\!\! & \!\!\!\! 6 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\ \!\!\!\!+\!\!\!\! & & \!\!\!\! \!\!\!\! & \!\!\!\! 2 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\ \hline & \!\!\!\! \!\!\!\! & \!\!\!\! 5 \!\!\!\!& \!\!\!\! 8 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \end{array}

Therefore,

145 \times 4 = 580.

FLAG

Mary wishes to find the value of 4\times748. She proceeds as follows:

\begin{align*} 4\times 700 &= \fbox{[math]\phantom{0000}[/math]}\\[5pt] 4\times 40 &= \fbox{[math]\phantom{000}[/math]}\\[5pt] 4\times 8 &= \fbox{[math]\phantom{00}[/math]}\\[5pt] \end{align*}

Find the missing numbers, and use your answers to find the value of 4\times748.

EXPLANATION

Notice that 748 in expanded form is 748 = 700+40+8. So, we can compute 4\times 748 by filling in the missing numbers and adding the results.

First, let's find the missing values:

\begin{align*} 4 \times 700 &= \fbox{[math]\,2,800\,[/math]} \\[5pt] 4 \times 40 &= \fbox{[math]\,160\,[/math]} \\[5pt] 4 \times 8 &= \fbox{[math]\,32\,[/math]} \end{align*}

Let's now add these results:

\begin{array}{cccccccc} & \!\!\!\! 2 \!\!\!\! & \!\!\!\! 8 \!\!\!\! & \!\!\!\! 0 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\ \!\!\!\!+\!\!\!\! & & \!\!\!\! 1 \!\!\!\! & \!\!\!\! 6 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\ \!\!\!\!+\!\!\!\! & & \!\!\!\! \!\!\!\! & \!\!\!\! 3 \!\!\!\!& \!\!\!\! 2 \!\!\!\! \\ \hline & \!\!\!\! 2 \!\!\!\! & \!\!\!\! 9 \!\!\!\!& \!\!\!\! 9 \!\!\!\!& \!\!\!\! 2 \!\!\!\! \end{array}

Therefore,

4\times748 = 2,992.

FLAG

Yeliz wishes to find the value of $6\times354.$ She proceeds as follows:

\begin{align*} 6\times 300 &= \fbox{$\phantom{0000}$}\\[5pt] 6\times 50 &= \fbox{$\phantom{000}$}\\[5pt] 6\times 4 &= \fbox{$\phantom{00}$}\\[5pt] \end{align*}

Find the missing numbers, and use your answers to find the value of $6\times354.$

a
$1,768$
b
$2,124$
c
$1,124$
d
$2,118$
e
$2,354$

Ali wishes to find the value of $875\times9.$ He proceeds as follows:

\begin{align*} 800\times 9 &= \fbox{$\phantom{0000}$}\\[5pt] 70\times 9 &= \fbox{$\phantom{000}$}\\[5pt] 5\times 9 &= \fbox{$\phantom{00}$}\\[5pt] \end{align*}

Find the missing numbers, and use your answers to find the value of $875\times9.$

a
$7,875$
b
$7,265$
c
$7,945$
d
$7,925$
e
$7,245$

What is the value of 745 \times 8?

EXPLANATION

First, let's write the three-digit number (745) in expanded form:

745 = {\color{blue}{700}} + {\color{blue}{40}} + {\color{blue}{5}}.

We now multiply all numbers in our expanded form by {\color{red}{8}}\mathbin{:}

\begin{align*} {\color{blue}{700}} \times {\color{red}{8}} &= 5,600 \\[5pt] {\color{blue}{40}} \times {\color{red}{8}} &= 320 \\[5pt] {\color{blue}{5}} \times {\color{red}{8}} &= 40 \end{align*}

Let's now add these results:

\begin{array}{cccccccc} & \!\!\!\! 5 \!\!\!\! & \!\!\!\! 6 \!\!\!\! & \!\!\!\! 0 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\ \!\!\!\!+\!\!\!\! & & \!\!\!\! 3 \!\!\!\! & \!\!\!\! 2 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\ \!\!\!\!+\!\!\!\! & & \!\!\!\! \!\!\!\! & \!\!\!\! 4 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\ \hline & \!\!\!\! 5 \!\!\!\! & \!\!\!\! 9 \!\!\!\!& \!\!\!\! 6 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \end{array}

Therefore,

745 \times 8 = 5,960.

FLAG

$4 \times 217 =$

a
$918$
b
$868$
c
$928$
d
$828$
e
$842$

$628 \times 7 =$

a
$496$
b
$4,396$
c
$1,456$
d
$4,456$
e
$4,256$

An adhesive tape has a length of 164 feet. What is the total length of 6 adhesive tapes?

EXPLANATION

To figure out the total length of 6 tapes, we need to compute the value of

{\color{red}{6}} \times 164.

First, let's write the three-digit number (164) in expanded form:

164 = {\color{blue}{100}} + {\color{blue}{60}} + {\color{blue}{4}}

We now multiply all numbers in our expanded form by {\color{red}{6}}\mathbin{:}

\begin{align*} {\color{red}{6}} \times {\color{blue}{100}} &= 600 \\[5pt] {\color{red}{6}} \times {\color{blue}{60}} &= 360 \\[5pt] {\color{red}{6}} \times {\color{blue}{4}} &= 24 \end{align*}

Let's now add these results:

\begin{array}{cccccccc} & \!\!\!\! \!\!\!\! & \!\!\!\! 6 \!\!\!\! & \!\!\!\! 0 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\ \!\!\!\!+\!\!\!\! & & \!\!\!\! 3 \!\!\!\! & \!\!\!\! 6 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\ \!\!\!\!+\!\!\!\! & & \!\!\!\! \!\!\!\! & \!\!\!\! 2 \!\!\!\!& \!\!\!\! 4 \!\!\!\! \\ \hline & \!\!\!\! \!\!\!\! & \!\!\!\! 9 \!\!\!\!& \!\!\!\! 8 \!\!\!\!& \!\!\!\! 4 \!\!\!\! \end{array}

Therefore, six tapes cover 984 feet.

FLAG

Ross has $3$ packs of candy, each containing $239$ jelly beans. How many jelly beans does Ross have in total?

a
$749$
b
$827$
c
$697$
d
$727$
e
$717$

During a particular hour, nine trains departed from a train station. If each train was carrying $987$ tons of grain, how many tons of grain were transported from the station during that hour?

a
$8,883$
b
$8,775$
c
$8,664$
d
$9,201$
e
$9,102$
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