1.2 Add whole numbers (Page 3/6)

Prealgebra Page 3 / 6

When the sum in a place value column is greater than $9,$ we carry over to the next column to the left. Carrying is the same as regrouping by exchanging. For example, $10$ ones for $1$ ten or $10$ tens for $1$ hundred.

Add whole numbers.

Write the numbers so each place value lines up vertically.
Add the digits in each place value. Work from right to left starting with the ones place. If a sum in a place value is more than $9,$ carry to the next place value.
Continue adding each place value from right to left, adding each place value and carrying if needed.

Add: $43 + 69 .$

Solution

Write the numbers so the digits line up vertically.	$\begin{matrix} 43 \\ \underset{____}{+ 69} \end{matrix}$
Add the digits in each place. Add the ones: $3 + 9 = 12$
Write the $2$ in the ones place in the sum. Add the $1$ ten to the tens place.	$\begin{matrix} \overset{1}{4} 3 \\ \underset{____}{+ 69} \\ 2 \end{matrix}$
Now add the tens: $1 + 4 + 6 = 11$ Write the 11 in the sum.	$\begin{matrix} \overset{1}{4} 3 \\ \underset{____}{+ 69} \\ 112 \end{matrix}$

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Add: $35 + 98 .$

$35 + 98 = 133$

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Add: $72 + 89 .$

$72 + 89 = 161$

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Add: $324 + 586 .$

Solution

Write the numbers so the digits line up vertically.
Add the digits in each place value. Add the ones: $4 + 6 = 10$ Write the $0$ in the ones place in the sum and carry the $1$ ten to the tens place.
Add the tens: $1 + 2 + 8 = 11$ Write the $1$ in the tens place in the sum and carry the $1$ hundred to the hundreds
Add the hundreds: $1 + 3 + 5 = 9$ Write the $9$ in the hundreds place.

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Add: $456 + 376 .$

$456 + 376 = 832$

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Add: $269 + 578 .$

$269 + 578 = 847$

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Add: $1,683 + 479 .$

Solution

Write the numbers so the digits line up vertically.	$\begin{matrix} 1,683 \\ \underset{______}{+ 479} \end{matrix}$
Add the digits in each place value.
Add the ones: $3 + 9 = 12.$ Write the $2$ in the ones place of the sum and carry the $1$ ten to the tens place.	$\begin{matrix} 1,6 \overset{1}{8} 3 \\ \underset{______}{+ 479} \\ 2 \end{matrix}$
Add the tens: $1 + 7 + 8 = 16$ Write the $6$ in the tens place and carry the $1$ hundred to the hundreds place.	$\begin{matrix} 1, \overset{1}{6} \overset{1}{8} 3 \\ \underset{______}{+ 479} \\ 62 \end{matrix}$
Add the hundreds: $1 + 6 + 4 = 11$ Write the $1$ in the hundreds place and carry the $1$ thousand to the thousands place.	$\begin{matrix} 1, \overset{1}{6} \overset{1}{8} 3 \\ \underset{______}{+ 479} \\ 162 \end{matrix}$
Add the thousands $1 + 1 = 2$ . Write the $2$ in the thousands place of the sum.	$\begin{matrix} 1, \overset{1}{6} \overset{1}{8} 3 \\ \underset{______}{+ 479} \\ 2,162 \end{matrix}$

When the addends have different numbers of digits, be careful to line up the corresponding place values starting with the ones and moving toward the left.

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Add: $4,597 + 685 .$

$4,597 + 685 = 5,282$

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Add: $5,837 + 695 .$

$5,837 + 695 = 6,532$

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Add: $21,357 + 861 + 8,596 .$

Solution

Write the numbers so the place values line up vertically.	$\begin{matrix} 21,357 \\ 861 \\ \underset{_______}{+ 8,596} \end{matrix}$
Add the digits in each place value.
Add the ones: $7 + 1 + 6 = 14$ Write the $4$ in the ones place of the sum and carry the $1$ to the tens place.	$\begin{matrix} 21,3 \overset{1}{5} 7 \\ 861 \\ \underset{_______}{+ 8,596} \\ 4 \end{matrix}$
Add the tens: $1 + 5 + 6 + 9 = 21$ Write the $1$ in the tens place and carry the $2$ to the hundreds place.	$\begin{matrix} 21, \overset{2}{3} \overset{1}{5} 7 \\ 861 \\ \underset{_______}{+ 8,596} \\ 14 \end{matrix}$
Add the hundreds: $2 + 3 + 8 + 5 = 18$ Write the $8$ in the hundreds place and carry the $1$ to the thousands place.	$\begin{matrix} 2 \overset{1}{1,} \overset{2}{3} \overset{1}{5} 7 \\ 861 \\ \underset{_______}{+ 8,596} \\ 814 \end{matrix}$
Add the thousands $1 + 1 + 8 = 10$ . Write the $0$ in the thousands place and carry the $1$ to the ten thousands place.	$\begin{matrix} \overset{1}{2} \overset{1}{1,} \overset{2}{3} \overset{1}{5} 7 \\ 861 \\ \underset{_______}{+ 8,596} \\ 0814 \end{matrix}$
Add the ten-thousands $1 + 2 = 3$ . Write the $3$ in the ten thousands place in the sum.	$\begin{matrix} \overset{1}{2} \overset{1}{1,} \overset{2}{3} \overset{1}{5} 7 \\ 861 \\ \underset{_______}{+ 8,596} \\ 30,814 \end{matrix}$

This example had three addends. We can add any number of addends using the same process as long as we are careful to line up the place values correctly.

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Add: $46,195 + 397 + 6,281 .$

$46,195 + 397 + 6,281 = 52,873$

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Add: $53,762 + 196 + 7,458 .$

$53,762 + 196 + 7,458 = 61,416$

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Translate word phrases to math notation

Earlier in this section, we translated math notation into words. Now we’ll reverse the process. We’ll translate word phrases into math notation. Some of the word phrases that indicate addition are listed in [link] .

Questions & Answers

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Source: OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9

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