Introduction

We can also use repeated subtraction to multiply large numbers.

For example, suppose we have the following multiplication problem:

80 \times 5 = {\color{blue}{400}}

Let's use repeated subtraction to generate some more multiplication facts:

  • We can find 79\times 5 by subtracting 5 from this result: 79 \times 5 = {\color{blue}{400}} - 5 ={\color{red}{395}}

  • We can find 78\times 5 by subtracting 5 from the previous result: 78 \times 5 = {\color{red}{395}} - 5 ={\color{purple}{390}}

  • We can find 77\times 5 by subtracting 5 from the previous result: 77 \times 5 = {\color{purple}{390}} - 5 ={\color{magenta}385}

And so on.

We can visualize this process using the following number line diagram.

Note that {\color{blue}{400}}, 395, 390, 385, , etc., are all multiples of 5.

FLAG
Example: Multiplying Two-Digit Numbers by One-Digit Numbers

You're given the following multiplication problem:

50\times 6 = 300

Use this to find the value of 46\times 6.

EXPLANATION

We start with the given multiplication problem:

50\times 6 = {\color{blue}{300}}

We can find the correct answer for 46\times 6 using repeated subtraction:

\begin{align*} 49\times 6 &= {\color{blue}{300}} -6 ={\color{red}{294}}\\[10pt] 48\times 6 &= {\color{red}{294}} -6 ={\color{purple}{288}} \\[10pt] 47\times 6 &= {\color{purple}{288}} -6 ={\color{magenta}282} \\[10pt] 46\times 6 &= {\color{magenta}282} - 6 = 276 \end{align*}

Therefore, 46\times 6 = 276.

FLAG
Practice: Multiplying Two-Digit Numbers by One-Digit Numbers

You're given the following multiplication problem:

\[ 30\times 6 = 180 \]

Use this to find the value of $28\times 6.$

a
 $162$
b
 $168$
c
 $154$
d
 $158$
e
 $160$
Practice: Multiplying Two-Digit Numbers by One-Digit Numbers

You're given the following multiplication problem:

\[ 30\times 3 = 90 \]

Use this to find the value of $27\times 3.$

a
 $24$
b
 $81$
c
 $80$
d
 $82$
e
 $83$
Example: Multiplying Three-Digit Numbers by One-Digit Numbers

You're given the following multiplication problem:

110\times 6 = 660

Use this to find the value of 107\times 6.

EXPLANATION

We start with the given multiplication problem:

110\times 6 = {\color{blue}{660}}

We can find the correct answer for 107\times 6 using repeated subtraction:

\begin{align*} 109\times 6 &= {\color{blue}{660}} - 6 ={\color{red}{654}}\\[10pt] 108\times 6 &= {\color{red}{654}} - 6 ={\color{purple}{648}} \\[10pt] 107\times 6 &= {\color{purple}{648}} - 6 =642 \\[10pt] \end{align*}

Therefore, 107\times 6 = 642.

FLAG
Practice: Multiplying Three-Digit Numbers by One-Digit Numbers

You're given the following multiplication problem:

\[ 300\times 9 = 2,700 \]

Use this to find the value of $298\times 9.$

a
 $2,684$
b
 $2,668$
c
 $2,676$
d
 $2,682$
e
 $2,678$
Practice: Multiplying Three-Digit Numbers by One-Digit Numbers

You're given the following multiplication problem:

\[ 200\times 7 = 1,400 \]

Use this to find the value of $197\times 7.$

a
 $1,387$
b
 $1,382$
c
 $1,384$
d
 $1,379$
e
 $1,374$
Example: Multiplying Four-Digit Numbers by One-Digit Numbers

You're given the following multiplication problem:

1,200\times 4 = 4,800

Use this to find the value of 1,196\times 4.

EXPLANATION

We start with the given multiplication problem:

1,200\times 4 = {\color{blue}{4,800}}

We can find the correct answer for 1,196\times 4 using repeated subtraction:

\begin{align*} 1,199\times 4 &= {\color{blue}{4,800}} - 4 ={\color{red}{4,796}}\\[10pt] 1,198\times 4 &= {\color{red}{4,796}} - 4 ={\color{purple}{4,792}} \\[10pt] 1,197\times 4 &= {\color{purple}{4,792}} - 4 ={\color{magenta}4,788} \\[10pt] 1,196\times 4 &= {\color{magenta}4,788} - 4 = 4,784 \end{align*}

Therefore, 1,196\times 4= 4,784.

FLAG
Practice: Multiplying Four-Digit Numbers by One-Digit Numbers

You're given the following multiplication problem:

\[ 5,000\times 6 = 30,000 \]

Use this to find the value of $4,998\times 6.$

a
 $29,988$
b
 $29,984$
c
 $29,974$
d
 $29,978$
e
 $29,982$
Practice: Multiplying Four-Digit Numbers by One-Digit Numbers

You're given the following multiplication problem:

\[ 1,100\times 6 = 6,600 \]

Use this to find the value of $1,097\times 6.$

a
 $6,578$
b
 $6,586$
c
 $6,580$
d
 $6,584$
e
 $6,582$
Flag Content
Did you notice an error, or do you simply believe that something could be improved? Please explain below.
SUBMIT
CANCEL