We can use place value to add two-digit whole numbers easily.
As an example, let's find the following sum:
24+35
First, we line up our numbers (ones over ones and tens over tens ):
tens ones
\color{red}2
\color{blue}4
\color{red}3
\color{blue}5
Next, we proceed by adding the numbers in each place value (from right to left) and writing the results below:
Step 1. Adding the ones, we get
{\color{blue}4} + {\color{blue}5} = {\color{blue}9}{:}
tens ones
\color{red}2
\color{blue}4
\color{red}3
\color{blue}5
\color{blue}9
Step 2. Adding the tens, we get
{\color{red}2} + {\color{red}3} = {\color{red}5}{:}
tens ones
\color{red}2
\color{blue}4
\color{red}3
\color{blue}5
\color{red}5
\color{blue}9
Therefore, we conclude that
24+35 = 59.
Drawing place value charts each time we want to add a pair of numbers isn't very convenient. For this reason, we usually follow a simplified process called the standard algorithm .
Let's once again consider the following sum:
24+35
First, we line up our numbers as follows: (ones over ones, and tens over tens):
\begin{array}{cccccccc}
& & \!\!\!\! 2 \!\!\!\!& \!\!\!\! 4 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 3 \!\!\!\!& \!\!\!\! 5 \!\!\!\! \\
\hline
& & \!\!\!\! \!\!\!\!& \!\!\!\! \!\!\!\!
\end{array}
Notice that we've also drawn a horizontal line. This is where we'll write our answer.
Next, we proceed by adding the numbers in each place value (from right to left):
Step 1. Adding the ones, we get
{\color{blue}4} + {\color{blue}5} = {\color{blue}9}{:}
\begin{array}{cccccccc}
& & \!\!\!\! 2 \!\!\!\!& \!\!\!\! {\color{blue}4} \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 3 \!\!\!\!& \!\!\!\! {\color{blue}5} \!\!\!\! \\
\hline
& & \!\!\!\! \!\!\!\!& \!\!\!\! {\color{blue}9} \!\!\!\!
\end{array}
Step 2. Adding the tens, we get
{\color{blue}2} + {\color{blue}3} = {\color{blue}5}{:}
\begin{array}{cccccccc}
& & \!\!\!\! {\color{blue}2} \!\!\!\!& \!\!\!\! 4 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! {\color{blue}3} \!\!\!\!& \!\!\!\! 5 \!\!\!\! \\
\hline
& & \!\!\!\! {\color{blue}5} \!\!\!\!& \!\!\!\! 9 \!\!\!\!
\end{array}
Therefore,
24 + 35 = 59.
Robert weighs
37
41
To find the combined weight, we need to calculate the value of
37+41.
First, we line up our numbers (ones over ones and tens over tens ):
\begin{array}{cccccccc}
& & \!\!\!\! 3 \!\!\!\!& \!\!\!\! 7 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 4 \!\!\!\!& \!\!\!\! 1 \!\!\!\! \\
\hline
& & \!\!\!\! \!\!\!\!& \!\!\!\! \!\!\!\!
\end{array}
Next, we proceed by adding the numbers in each place value (from right to left):
Step 1. Adding the ones,
{\color{blue}7} + {\color{blue}1} = {\color{blue}8}{:}
\begin{array}{cccccccc}
& & \!\!\!\! 3 \!\!\!\!& \!\!\!\! {\color{blue}7} \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 4 \!\!\!\!& \!\!\!\! {\color{blue}1} \!\!\!\! \\
\hline
& & \!\!\!\! \!\!\!\!& \!\!\!\! {\color{blue}8} \!\!\!\!
\end{array}
Step 2. Adding the tens,
{\color{blue}3 } + {\color{blue}4} = {\color{blue}7}{:}
\begin{array}{cccccccc}
& & \!\!\!\! {\color{blue}3} \!\!\!\!& \!\!\!\! 7 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! {\color{blue}4} \!\!\!\!& \!\!\!\! 1 \!\!\!\! \\
\hline
& & \!\!\!\! {\color{blue}7} \!\!\!\!& \!\!\!\! 8 \!\!\!\!
\end{array}
Therefore,
37 + 41 = 78.
So, the combined weight of the children is
78
a
$70$
b
$92$
c
$76$
d
$80$
e
$86$
First, we line up our numbers (ones over ones and tens over tens ):
\[
\begin{array}{cccccccc}
& & \!\!\!\! 4 \!\!\!\!& \!\!\!\! 1 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 3 \!\!\!\!& \!\!\!\! 5 \!\!\!\! \\
\hline
& & & &
\end{array}
\]
Next, we proceed by adding the numbers in each place value (from right to left):
Step 1. Adding the ones, ${\color{blue}1} + {\color{blue}5} = {\color{blue}6}{:}$
\[
\begin{array}{cccccccc}
& & \!\!\!\! 4 \!\!\!\!& \!\!\!\! {\color{blue}1} \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 3 \!\!\!\!& \!\!\!\! {\color{blue}5} \!\!\!\! \\
\hline
& & \!\!\!\! \!\!\!\!& \!\!\!\! {\color{blue}6} \!\!\!\!
\end{array}
\]
Step 2. Adding the tens, ${\color{blue}4 } + {\color{blue}3} = {\color{blue}7}{:}$
\[
\begin{array}{cccccccc}
& & \!\!\!\! {\color{blue}4} \!\!\!\!& \!\!\!\! 1 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! {\color{blue}3} \!\!\!\!& \!\!\!\! 5 \!\!\!\! \\
\hline
& & \!\!\!\! {\color{blue}7} \!\!\!\!& \!\!\!\! 6 \!\!\!\!
\end{array}
\]
Therefore, $41 + 35 = 76.$
First, we line up our numbers (ones over ones and tens over tens ):
\[
\begin{array}{cccccccc}
& & \!\!\!\! 2 \!\!\!\!& \!\!\!\! 6 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 6 \!\!\!\!& \!\!\!\! 2 \!\!\!\! \\
\hline
& & & &
\end{array}
\]
Next, we proceed by adding the numbers in each place value (from right to left):
Step 1. Adding the ones, ${\color{blue}6} + {\color{blue}2} = {\color{blue}8}{:}$
\[
\begin{array}{cccccccc}
& & \!\!\!\! 2 \!\!\!\!& \!\!\!\! {\color{blue}6} \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 6 \!\!\!\!& \!\!\!\! {\color{blue}2} \!\!\!\! \\
\hline
& & \!\!\!\! \!\!\!\!& \!\!\!\! {\color{blue}8} \!\!\!\!
\end{array}
\]
Step 2. Adding the tens, ${\color{blue}2 } + {\color{blue}6} = {\color{blue}8}{:}$
\[
\begin{array}{cccccccc}
& & \!\!\!\! {\color{blue}2} \!\!\!\!& \!\!\!\! 6 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! {\color{blue}6} \!\!\!\!& \!\!\!\! 2 \!\!\!\! \\
\hline
& & \!\!\!\! {\color{blue}8} \!\!\!\!& \!\!\!\! 8 \!\!\!\!
\end{array}
\]
Therefore, $26 + 62 = \bbox[3pt,Gainsboro]{\color{blue}88}.$
Mary bought some candy for her daughter's birthday party. She bought $35$ mint candies and $41$ chocolate candies.
How many candies did she buy altogether?
a
$76$ candies
b
$126$ candies
c
$66$ candies
d
$46$ candies
e
$74$ candies
To find the number of candies Mary bought, we need to calculate the value of
\[
35 + 41.
\]
First, we line up our numbers (ones over ones and tens over tens ):
\[
\begin{array}{cccccccc}
& & \!\!\!\! 3 \!\!\!\!& \!\!\!\! 5 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 4 \!\!\!\!& \!\!\!\! 1 \!\!\!\! \\
\hline
& & & &
\end{array}
\]
Next, we proceed by adding the numbers in each place value (from right to left):
Step 1. Adding the ones, ${\color{blue}5} + {\color{blue}1} = {\color{blue}6}{:}$
\[
\begin{array}{cccccccc}
& & \!\!\!\! 3 \!\!\!\!& \!\!\!\! {\color{blue}5} \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 4 \!\!\!\!& \!\!\!\! {\color{blue}1} \!\!\!\! \\
\hline
& & \!\!\!\! \!\!\!\!& \!\!\!\! {\color{blue}6} \!\!\!\!
\end{array}
\]
Step 2. Adding the tens, ${\color{blue}3} + {\color{blue}4} = {\color{blue}7}{:}$
\[
\begin{array}{cccccccc}
& & \!\!\!\! {\color{blue}3} \!\!\!\!& \!\!\!\! 5 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! {\color{blue}4} \!\!\!\!& \!\!\!\! 1 \!\!\!\! \\
\hline
& & \!\!\!\! {\color{blue}7} \!\!\!\!& \!\!\!\! 6 \!\!\!\!
\end{array}
\]
So, $35+41 = 76.$
Therefore, Mary bought a total of $76$ candies.
Let's now calculate the following sum using place value charts:
37+26
First, we line up our numbers (ones over ones, and tens over tens), as before:
tens ones
\color{red}3
\color{blue}7
\color{red}2
\color{blue}6
Next, we proceed by adding the numbers in each place value (from right to left):
Step 1. Adding the ones, we get
{\color{blue}7} + {\color{blue}6} = {\color{red}1}{\color{blue}3}.
Now, notice that
{\color{red}1}{\color{blue}3} = \textrm{[math]\color{red}1[/math] ten} + \textrm{[math]\color{blue}3[/math] ones}.
So, we write
\color{blue}3
ones and carry
\color{red}1
tens . Let's write this additional
\color{red}1
tens column.
\color{red}1
tens ones
\color{red}3
\color{blue}7
\color{red}2
\color{blue}6
\color{blue}3
Step 2. Adding the tens, we get
{\color{red}1} + {\color{red}3} + {\color{red}2} = {\color{red}6}
\color{red}1
\color{red}1
tens ones
\color{red}3
\color{blue}7
\color{red}2
\color{blue}6
\color{red}6
\color{blue}3
Therefore,
37+26 = 63.
Let's now solve the same problem using the standard algorithm.
Once again, we consider the following sum:
37+26
To use the standard algorithm, we first line up our numbers (ones over ones, and tens over tens):
\begin{array}{cccccccc}
& & \!\!\!\! 3 \!\!\!\!& \!\!\!\! 7 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 2 \!\!\!\!& \!\!\!\! 6 \!\!\!\! \\
\hline
& & \!\!\!\! \!\!\!\!& \!\!\!\! \!\!\!\!
\end{array}
Next, we proceed by adding the numbers in each place value (from right to left):
Step 1. Adding the ones, we get
{\color{blue}7} + {\color{blue}6} = {\color{red}1}{\color{blue}3}.
{\color{blue}3}
ones and carry
{\color{red}1}
tens :
\begin{array}{cccccccc}
& & \!\!\!\! {\color{red}1} \!\!\!\! & \\
& & \!\!\!\! 3 \!\!\!\!& \!\!\!\! {\color{blue}7} \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 2 \!\!\!\!& \!\!\!\! {\color{blue}6} \!\!\!\! \\
\hline
& & \!\!\!\! \!\!\!\!& \!\!\!\! {\color{blue}3} \!\!\!\!
\end{array}
Step 2. Adding the tens, we get
{\color{blue}1} + {\color{blue}3} + {\color{blue}2} = {\color{blue}6}{:}
\begin{array}{cccccccc}
& & \!\!\!\! {\color{blue}1} \!\!\!\! & \\
& & \!\!\!\! {\color{blue}3} \!\!\!\!& \!\!\!\! 7 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! {\color{blue}2} \!\!\!\!& \!\!\!\! 6 \!\!\!\! \\
\hline
& & \!\!\!\! {\color{blue}6} \!\!\!\!& \!\!\!\! 3 \!\!\!\!
\end{array}
Therefore,
37 + 26 = 63.
The regular time of a particular soccer game lasted
92
33
To find the combined time, we need to calculate the value of
92 + 33.
First, we line up our numbers (ones over ones and tens over tens ):
\begin{array}{cccccccc}
& & \!\!\!\! 9 \!\!\!\!& \!\!\!\! 2 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 3 \!\!\!\!& \!\!\!\! 3 \!\!\!\! \\
\hline
& & \!\!\!\! \!\!\!\!& \!\!\!\! \!\!\!\!
\end{array}
Next, we proceed by adding the numbers in each place value (from right to left):
Step 1. Adding the ones,
{\color{blue}2} + {\color{blue}3} = {\color{blue}5}{:}
\begin{array}{cccccccc}
& & \!\!\!\! 9 \!\!\!\!& \!\!\!\! {\color{blue}2} \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 3 \!\!\!\!& \!\!\!\! {\color{blue}3} \!\!\!\! \\
\hline
& & \!\!\!\! \!\!\!\!& \!\!\!\! {\color{blue}5} \!\!\!\!
\end{array}
Step 2. Adding the tens,
{\color{blue}9} + {\color{blue}3} = {\color{red}1}{\color{blue}2}.
{\color{blue}2}
tens and carry
{\color{red}1}
hundreds :
\begin{array}{cccccccc}
& \!\!\!\! {\color{red}1} \!\!\!\! & & \\
& & \!\!\!\! {\color{blue}9} \!\!\!\!& \!\!\!\! 2 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! {\color{blue}3} \!\!\!\!& \!\!\!\! 3 \!\!\!\! \\
\hline
& & \!\!\!\! {\color{blue}2} \!\!\!\!& \!\!\!\! 5 \!\!\!\!
\end{array}
Step 3. Adding the hundreds,
{\color{blue}1}+{\color{blue}0}+{\color{blue}0}={\color{blue}1}{:}
\begin{array}{cccccccc}
& \!\!\!\! {\color{blue}1} \!\!\!\! & & \\
& \!\!\!\! {\color{blue}0} \!\!\!\! & \!\!\!\! 9 \!\!\!\!& \!\!\!\! 2 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & \!\!\!\! {\color{blue}0} \!\!\!\! & \!\!\!\! 3 \!\!\!\!& \!\!\!\! 3 \!\!\!\! \\
\hline
& \!\!\!\! {\color{blue}1} \!\!\!\!& \!\!\!\! 2 \!\!\!\!& \!\!\!\! 5 \!\!\!\!
\end{array}
Therefore, the game lasted
125
First, we line up our numbers (ones over ones and tens over tens ):
\[
\begin{array}{cccccccc}
& & \!\!\!\! 4 \!\!\!\!& \!\!\!\! 7 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 2 \!\!\!\!& \!\!\!\! 9 \!\!\!\! \\
\hline
& & & &
\end{array}
\]
Next, we proceed by adding the numbers in each place value (from right to left):
Step 1. Adding the ones, ${\color{blue}7} + {\color{blue}9} = {\color{red}1}{\color{blue}6}.$ We write ${\color{blue}6}$ below the ones and carry ${\color{red}1}$ to the tens :
\[
\begin{array}{cccccccc}
& & \!\!\!\! {\color{red}1} \!\!\!\! & \\
& & \!\!\!\! 4 \!\!\!\!& \!\!\!\! {\color{blue}7} \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 2 \!\!\!\!& \!\!\!\! {\color{blue}9} \!\!\!\! \\
\hline
& & \!\!\!\! \!\!\!\!& \!\!\!\! {\color{blue}6} \!\!\!\!
\end{array}
\]
Step 2. Adding the tens, ${\color{blue}1} + {\color{blue}4} + {\color{blue}2} = {\color{blue}7}{:}$
\[
\begin{array}{cccccccc}
& & \!\!\!\! {\color{blue}1} \!\!\!\! & \\
& & \!\!\!\! {\color{blue}4} \!\!\!\!& \!\!\!\! 7 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! {\color{blue}2} \!\!\!\!& \!\!\!\! 9 \!\!\!\! \\
\hline
& & \!\!\!\! {\color{blue}7} \!\!\!\!& \!\!\!\! 6 \!\!\!\!
\end{array}
\]
Therefore, $47 + 29 = \bbox[3pt,Gainsboro]{\color{blue}76}.$
First, we line up our numbers (ones over ones and tens over tens ):
\[
\begin{array}{cccccccc}
& & \!\!\!\! 9 \!\!\!\!& \!\!\!\! 3 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 7 \!\!\!\!& \!\!\!\! 4 \!\!\!\! \\
\hline
& & & &
\end{array}
\]
Next, we proceed by adding the numbers in each place value (from right to left):
Step 1. Adding the ones, ${\color{blue}3} + {\color{blue}4} = {\color{blue}7}{:}$
\[
\begin{array}{cccccccc}
& & \!\!\!\! 9 \!\!\!\!& \!\!\!\! {\color{blue}3} \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 7 \!\!\!\!& \!\!\!\! {\color{blue}4} \!\!\!\! \\
\hline
& & \!\!\!\! \!\!\!\!& \!\!\!\! {\color{blue}7} \!\!\!\!
\end{array}
\]
Step 2. Adding the tens, ${\color{blue}9} + {\color{blue}7} = {\color{red}1}{\color{blue}6}.$ We write ${\color{blue}6}$ below the tens and carry ${\color{red}1}$ to the hundreds :
\[
\begin{array}{cccccccc}
& \!\!\!\! {\color{red}1} \!\!\!\! & & \\
& & \!\!\!\! {\color{blue}9} \!\!\!\!& \!\!\!\! 3 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! {\color{blue}7} \!\!\!\!& \!\!\!\! 4 \!\!\!\! \\
\hline
& & \!\!\!\! {\color{blue}6} \!\!\!\!& \!\!\!\! 7 \!\!\!\!
\end{array}
\]
Step 3. Adding the hundreds, ${\color{blue}1}+{\color{blue}0}+{\color{blue}0}={\color{blue}1}{:}$
\[
\begin{array}{cccccccc}
& \!\!\!\! {\color{blue}1} \!\!\!\! & & \\
& \!\!\!\! {\color{blue}0} \!\!\!\! & \!\!\!\! 9 \!\!\!\!& \!\!\!\! 3 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & \!\!\!\! {\color{blue}0} \!\!\!\! & \!\!\!\! 7 \!\!\!\!& \!\!\!\! 4 \!\!\!\! \\
\hline
& \!\!\!\! {\color{blue}1} \!\!\!\!& \!\!\!\! 6 \!\!\!\!& \!\!\!\! 7 \!\!\!\!
\end{array}
\]
Therefore, $93 + 74 = \bbox[3pt,Gainsboro]{\color{blue}167}.$
Peter has $18$ lemon candies while Angela has $25$ strawberry candies. Therefore, they have
To find out how many candies Peter and Angela have in total, we need to calculate the value of
\[
11 + 19.
\]
First, we line up our numbers (ones over ones and tens over tens ):
\[
\begin{array}{cccccccc}
& & \!\!\!\! 1 \!\!\!\!& \!\!\!\! 8 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 2 \!\!\!\!& \!\!\!\! 5 \!\!\!\! \\
\hline
& & & &
\end{array}
\]
Next, we proceed by adding the numbers in each place value (from right to left):
Step 1. Adding the ones, ${\color{blue}8} + {\color{blue}5} = {\color{red}1}{\color{blue}3}.$ We write ${\color{blue}3}$ below the ones and carry ${\color{red}1}$ to the tens :
\[
\begin{array}{cccccccc}
& & \!\!\!\! {\color{red}1} \!\!\!\! & \\
& & \!\!\!\! 1 \!\!\!\!& \!\!\!\! {\color{blue}8} \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 2 \!\!\!\!& \!\!\!\! {\color{blue}5} \!\!\!\! \\
\hline
& & \!\!\!\! \!\!\!\!& \!\!\!\! {\color{blue}3} \!\!\!\!
\end{array}
\]
Step 2. Adding the tens, ${\color{blue}1} + {\color{blue}1} + {\color{blue}2} = {\color{blue}4}{:}$
\[
\begin{array}{cccccccc}
& & \!\!\!\! {\color{blue}1} \!\!\!\! & \\
& & \!\!\!\! {\color{blue}1} \!\!\!\!& \!\!\!\! 8 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! {\color{blue}2} \!\!\!\!& \!\!\!\! 5 \!\!\!\! \\
\hline
& & \!\!\!\! {\color{blue}4} \!\!\!\!& \!\!\!\! 3 \!\!\!\!
\end{array}
\]
Therefore, $18 + 25 =43.$
So, Peter and Angela have a total of $\bbox[3pt,Gainsboro]{\color{blue}43}$ candies.
First, we line up our numbers (ones over ones and tens over tens ):
\begin{array}{cccccccc}
& & \!\!\!\! 5 \!\!\!\!& \!\!\!\! 8 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 5 \!\!\!\!& \!\!\!\! 5 \!\!\!\! \\
\hline
& & \!\!\!\! \!\!\!\!& \!\!\!\! \!\!\!\!
\end{array}
Next, we proceed by adding the numbers in each place value (from right to left):
Step 1. Adding the ones,
{\color{blue}8} + {\color{blue}5} = {\color{red}1}{\color{blue}3}.
{\color{blue}3}
ones and carry
{\color{red}1}
tens :
\begin{array}{cccccccc}
& & \!\!\!\! {\color{red}1} \!\!\!\! & \\
& & \!\!\!\! 5 \!\!\!\!& \!\!\!\! {\color{blue}8} \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 5 \!\!\!\!& \!\!\!\! {\color{blue}5} \!\!\!\! \\
\hline
& & \!\!\!\! \!\!\!\!& \!\!\!\! {\color{blue}3} \!\!\!\!
\end{array}
Step 2. Adding the tens,
{\color{blue}1} + {\color{blue}5} + {\color{blue}5} = {\color{red}1}{\color{blue}1}.
{\color{blue}1}
tens and carry
{\color{red}1}
hundreds :
\begin{array}{cccccccc}
& \!\!\!\! {\color{red}1} \!\!\!\! & \!\!\!\! {\color{blue}1} \!\!\!\! & \\
& & \!\!\!\! {\color{blue}5} \!\!\!\!& \!\!\!\! 8 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! {\color{blue}5} \!\!\!\!& \!\!\!\! 5 \!\!\!\! \\
\hline
& & \!\!\!\! {\color{blue}1} \!\!\!\!& \!\!\!\! 3 \!\!\!\!
\end{array}
Step 3. Notice that neither
58
55
\color{red}0
\begin{array}{cccccccc}
& \!\!\!\! 1 \!\!\!\! & \!\!\!\! 1 \!\!\!\! & \\
& \!\!\!\! {\color{red}0} \!\!\!\! & \!\!\!\! 5 \!\!\!\!& \!\!\!\! 8 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & \!\!\!\! {\color{red}0} \!\!\!\! & \!\!\!\! 5 \!\!\!\!& \!\!\!\! 5 \!\!\!\! \\
\hline
& \!\!\!\! \!\!\!\!& \!\!\!\! 1 \!\!\!\!& \!\!\!\! 3 \!\!\!\!
\end{array}
Then, adding the hundreds, we get
{\color{blue}1}+{\color{blue}0}+{\color{blue}0}={\color{blue}1}{:}
\begin{array}{cccccccc}
& \!\!\!\! {\color{blue}1} \!\!\!\! & \!\!\!\! 1 \!\!\!\! & \\
& \!\!\!\! {\color{blue}0} \!\!\!\! & \!\!\!\! 5 \!\!\!\!& \!\!\!\! 8 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & \!\!\!\! {\color{blue}0} \!\!\!\! & \!\!\!\! 5 \!\!\!\!& \!\!\!\! 5 \!\!\!\! \\
\hline
& \!\!\!\! {\color{blue}1} \!\!\!\!& \!\!\!\! 1 \!\!\!\!& \!\!\!\! 3 \!\!\!\!
\end{array}
Therefore,
58 + 55 = 113.
First, we line up our numbers (ones over ones and tens over tens ):
\[
\begin{array}{cccccccc}
& & \!\!\!\! 9 \!\!\!\!& \!\!\!\! 4 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 4 \!\!\!\!& \!\!\!\! 8 \!\!\!\! \\
\hline
& & & &
\end{array}
\]
Next, we proceed by adding the numbers in each place value (from right to left):
Step 1. Adding the ones, ${\color{blue}4} + {\color{blue}8} = {\color{red}1}{\color{blue}2}.$ We write ${\color{blue}2}$ below the ones and carry ${\color{red}1}$ to the tens :
\[
\begin{array}{cccccccc}
& & \!\!\!\! {\color{red}1} \!\!\!\! & \\
& & \!\!\!\! 9 \!\!\!\!& \!\!\!\! {\color{blue}4} \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 4 \!\!\!\!& \!\!\!\! {\color{blue}8} \!\!\!\! \\
\hline
& & \!\!\!\! \!\!\!\!& \!\!\!\! {\color{blue}2} \!\!\!\!
\end{array}
\]
Step 2. Adding the tens, ${\color{blue}1} + {\color{blue}9} + {\color{blue}4} = {\color{red}1}{\color{blue}4}.$ We write ${\color{blue}4}$ below the tens and carry ${\color{red}1}$ to the hundreds :
\[
\begin{array}{cccccccc}
& \!\!\!\! {\color{red}1} \!\!\!\! & \!\!\!\! {\color{blue}1} \!\!\!\! & \\
& & \!\!\!\! {\color{blue}9} \!\!\!\!& \!\!\!\! 4 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! {\color{blue}4} \!\!\!\!& \!\!\!\! 8 \!\!\!\! \\
\hline
& & \!\!\!\! {\color{blue}4} \!\!\!\!& \!\!\!\! 2 \!\!\!\!
\end{array}
\]
Step 3. Adding the hundreds, ${\color{blue}1}+{\color{blue}0}+{\color{blue}0}={\color{blue}1}{:}$
\[
\begin{array}{cccccccc}
& \!\!\!\! {\color{blue}1} \!\!\!\! & \!\!\!\! {\color{black}1} \!\!\!\! & \\
& \!\!\!\! {\color{blue}0} \!\!\!\! & \!\!\!\! 9 \!\!\!\!& \!\!\!\! 4 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & \!\!\!\! {\color{blue}0} \!\!\!\! & \!\!\!\! 4 \!\!\!\!& \!\!\!\! 8 \!\!\!\! \\
\hline
& \!\!\!\! {\color{blue}1} \!\!\!\!& \!\!\!\! 4 \!\!\!\!& \!\!\!\! 2 \!\!\!\!
\end{array}
\]
Therefore, $94 + 48 = \bbox[3pt,Gainsboro]{\color{blue}142}.$
First, we line up our numbers (ones over ones and tens over tens ):
\[
\begin{array}{cccccccc}
& & \!\!\!\! 1 \!\!\!\!& \!\!\!\! 7 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 9 \!\!\!\!& \!\!\!\! 4 \!\!\!\! \\
\hline
& & & &
\end{array}
\]
Next, we proceed by adding the numbers in each place value (from right to left):
Step 1. Adding the ones, ${\color{blue}7} + {\color{blue}4} = {\color{red}1}{\color{blue}1}.$ We write ${\color{blue}1}$ below the ones and carry ${\color{red}1}$ to the tens :
\[
\begin{array}{cccccccc}
& & \!\!\!\! {\color{red}1} \!\!\!\! & \\
& & \!\!\!\! 1 \!\!\!\!& \!\!\!\! {\color{blue}7} \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 9 \!\!\!\!& \!\!\!\! {\color{blue}4} \!\!\!\! \\
\hline
& & \!\!\!\! \!\!\!\!& \!\!\!\! {\color{blue}1} \!\!\!\!
\end{array}
\]
Step 2. Adding the tens, ${\color{blue}1} + {\color{blue}1} + {\color{blue}9} = {\color{red}1}{\color{blue}1}.$ We write ${\color{blue}1}$ below the tens and carry ${\color{red}1}$ to the hundreds :
\[
\begin{array}{cccccccc}
& \!\!\!\! {\color{red}1} \!\!\!\! & \!\!\!\! {\color{blue}1} \!\!\!\! & \\
& & \!\!\!\! {\color{blue}1} \!\!\!\!& \!\!\!\! 7 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! {\color{blue}9} \!\!\!\!& \!\!\!\! 4 \!\!\!\! \\
\hline
& & \!\!\!\! {\color{blue}1} \!\!\!\!& \!\!\!\! 1 \!\!\!\!
\end{array}
\]
Step 3. Adding the hundreds, ${\color{blue}1}+{\color{blue}0}+{\color{blue}0}={\color{blue}1}{:}$
\[
\begin{array}{cccccccc}
& \!\!\!\! {\color{blue}1} \!\!\!\! & \!\!\!\! {\color{black}1} \!\!\!\! & \\
& \!\!\!\! {\color{blue}0} \!\!\!\! & \!\!\!\! 1 \!\!\!\!& \!\!\!\! 7 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & \!\!\!\! {\color{blue}0} \!\!\!\! & \!\!\!\! 9 \!\!\!\!& \!\!\!\! 4 \!\!\!\! \\
\hline
& \!\!\!\! {\color{blue}1} \!\!\!\!& \!\!\!\! 1 \!\!\!\!& \!\!\!\! 1 \!\!\!\!
\end{array}
\]
Therefore, $17 + 94 = \bbox[3pt,Gainsboro]{\color{blue}111}.$
Dominic and his sister Margaret travel together to visit their parents. Dominic drives the car for $88$ miles, and then Margaret drives the remaining $79$ miles. Therefore, they drove a total of
To find the number of miles Dominic and Margaret drove in total, we need to calculate the value of
\[
88 + 79.
\]
First, we line up our numbers (ones over ones and tens over tens ):
\[
\begin{array}{cccccccc}
& & \!\!\!\! 8 \!\!\!\!& \!\!\!\! 8 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 7 \!\!\!\!& \!\!\!\! 9 \!\!\!\! \\
\hline
& & & &
\end{array}
\]
Next, we proceed by adding the numbers in each place value (from right to left):
Step 1. Adding the ones, ${\color{blue}8} + {\color{blue}9} = {\color{red}1}{\color{blue}7}.$ We write ${\color{blue}7}$ below the ones and carry ${\color{red}1}$ to the tens :
\[
\begin{array}{cccccccc}
& & \!\!\!\! {\color{red}1} \!\!\!\! & \\
& & \!\!\!\! 8 \!\!\!\!& \!\!\!\! {\color{blue}8} \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 7 \!\!\!\!& \!\!\!\! {\color{blue}9} \!\!\!\! \\
\hline
& & \!\!\!\! \!\!\!\!& \!\!\!\! {\color{blue}7} \!\!\!\!
\end{array}
\]
Step 2. Adding the tens, ${\color{blue}1} + {\color{blue}8} + {\color{blue}7} = {\color{red}1}{\color{blue}6}.$ We write ${\color{blue}6}$ below the tens and carry ${\color{red}1}$ to the hundreds :
\[
\begin{array}{cccccccc}
& \!\!\!\! {\color{red}1} \!\!\!\! & \!\!\!\! {\color{blue}1} \!\!\!\! & \\
& & \!\!\!\! {\color{blue}8} \!\!\!\!& \!\!\!\! 8 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! {\color{blue}7} \!\!\!\!& \!\!\!\! 9 \!\!\!\! \\
\hline
& & \!\!\!\! {\color{blue}6} \!\!\!\!& \!\!\!\! 7 \!\!\!\!
\end{array}
\]
Step 3. Adding the hundreds, ${\color{blue}1}+{\color{blue}0}+{\color{blue}0}={\color{blue}1}{:}$
\[
\begin{array}{cccccccc}
& \!\!\!\! {\color{blue}1} \!\!\!\! & \!\!\!\! {\color{black}1} \!\!\!\! & \\
& \!\!\!\! {\color{blue}0} \!\!\!\! & \!\!\!\! 8 \!\!\!\!& \!\!\!\! 8 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & \!\!\!\! {\color{blue}0} \!\!\!\! & \!\!\!\! 7 \!\!\!\!& \!\!\!\! 9 \!\!\!\! \\
\hline
& \!\!\!\! {\color{blue}1} \!\!\!\!& \!\!\!\! 6 \!\!\!\!& \!\!\!\! 7 \!\!\!\!
\end{array}
\]
Therefore, $88 + 79 = 167.$
So, Dominic and Margaret drove $\bbox[3pt,Gainsboro]{\color{blue}167}$ miles in total.
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