Let's take a look at the following addition problem:
132 + 46
In this case, we're adding a two-digit number to a three-digit number. To do this, we use the standard algorithm.
The first step is to write the numbers in the usual way, where ones are aligned over ones, tens over tens, and hundreds over hundreds:
\begin{array}{cccccccc}
& & \!\!\!\! 1 \!\!\!\! & \!\!\!\! 3 \!\!\!\!& \!\!\!\! 2 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & & \!\!\!\! 4 \!\!\!\!& \!\!\!\! 6 \!\!\!\! \\
\hline
& & & &
\end{array}
Next, we proceed by adding the numbers in each place value (from right to left) starting from the ones:
Step 1. Adding the ones, we get
{\color{blue}2} + {\color{blue}6} = {\color{blue}8}{:}
\begin{array}{cccccccc}
& & \!\!\!\! 1 \!\!\!\! & \!\!\!\! 3 \!\!\!\!& \!\!\!\! {\color{blue}2} \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & & \!\!\!\! 4 \!\!\!\!& \!\!\!\! {\color{blue}6} \!\!\!\! \\
\hline
& & & \!\!\!\! \!\!\!\!& \!\!\!\! {\color{blue}8} \!\!\!\!
\end{array}
Step 2. Adding the tens, we get
{\color{blue}3 } + {\color{blue}4} = {\color{blue}7}{:}
\begin{array}{cccccccc}
& & \!\!\!\! 1 \!\!\!\! & \!\!\!\! {\color{blue}3} \!\!\!\!& \!\!\!\! 2 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & & \!\!\!\! {\color{blue}4} \!\!\!\!& \!\!\!\! 6 \!\!\!\! \\
\hline
& & & \!\!\!\! {\color{blue}7} \!\!\!\!& \!\!\!\! 8 \!\!\!\!
\end{array}
Step 3. Notice that
46
\color{red}0
\begin{array}{cccccccc}
& & \!\!\!\! {\color{black}1} \!\!\!\!& \!\!\!\! 3 \!\!\!\!& \!\!\!\! 2 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! {\color{red}0} \!\!\!\! & \!\!\!\! 4 \!\!\!\!& \!\!\!\! 6 \!\!\!\! \\
\hline
& & \!\!\!\! \!\!\!\! & \!\!\!\! 7 \!\!\!\!& \!\!\!\! 8 \!\!\!\!
\end{array}
Then, adding the hundreds, we get
{\color{blue}1} + {\color{blue}0} = {\color{blue}1}{:}
\begin{array}{cccccccc}
& & \!\!\!\! {\color{blue}1} \!\!\!\!& \!\!\!\! 3 \!\!\!\!& \!\!\!\! 2 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! {\color{blue}0} \!\!\!\! & \!\!\!\! 4 \!\!\!\!& \!\!\!\! 6 \!\!\!\! \\
\hline
& & \!\!\!\! {\color{blue}1} \!\!\!\! & \!\!\!\! 7 \!\!\!\!& \!\!\!\! 8 \!\!\!\!
\end{array}
Therefore,
132 + 46 = 178.
Tom and Jerry are running a race that takes place over several days. Tom runs a total of
122
36
To find the number of kilometers Jerry ran, we need to calculate the value of
122 + 36.
First, we line up our numbers (ones over ones , tens over tens , hundreds over hundreds ):
\begin{array}{cccccccc}
& & \!\!\!\! 1 \!\!\!\! & \!\!\!\! 2 \!\!\!\!& \!\!\!\! 2 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & & \!\!\!\! 3 \!\!\!\!& \!\!\!\! 6 \!\!\!\! \\
\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}6} = {\color{blue}8}{:}
\begin{array}{cccccccc}
& & \!\!\!\! 1 \!\!\!\! & \!\!\!\! 2 \!\!\!\!& \!\!\!\! {\color{blue}2} \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & & \!\!\!\! 3 \!\!\!\!& \!\!\!\! {\color{blue}6} \!\!\!\! \\
\hline
& & & \!\!\!\! \!\!\!\!& \!\!\!\! {\color{blue}8} \!\!\!\!
\end{array}
Step 2. Adding the tens,
{\color{blue}2 } + {\color{blue}3} = {\color{blue}5}{:}
\begin{array}{cccccccc}
& & \!\!\!\! 1 \!\!\!\! & \!\!\!\! {\color{blue}2} \!\!\!\!& \!\!\!\! 2 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & & \!\!\!\! {\color{blue}3} \!\!\!\!& \!\!\!\! 6 \!\!\!\! \\
\hline
& & & \!\!\!\! {\color{blue}5} \!\!\!\!& \!\!\!\! 8 \!\!\!\!
\end{array}
Step 3. Adding the hundreds,
{\color{blue}1} + {\color{blue}0} = {\color{blue}1}{:}
\begin{array}{cccccccc}
& & \!\!\!\! {\color{blue}1} \!\!\!\!& \!\!\!\! 2 \!\!\!\!& \!\!\!\! 2 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! {\color{blue}0} \!\!\!\! & \!\!\!\! 3 \!\!\!\!& \!\!\!\! 6 \!\!\!\! \\
\hline
& & \!\!\!\! {\color{blue}1} \!\!\!\! & \!\!\!\! 5 \!\!\!\!& \!\!\!\! 8 \!\!\!\!
\end{array}
Therefore, Jerry ran
158
a
$395$
b
$295$
c
$297$
d
$277$
e
$197$
First, we line up our numbers (ones over ones , tens over tens , hundreds over hundreds ):
\[
\begin{array}{cccccccc}
& & \!\!\!\! 2 \!\!\!\! & \!\!\!\! 7 \!\!\!\!& \!\!\!\! 2 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & & \!\!\!\! 2 \!\!\!\!& \!\!\!\! 5 \!\!\!\! \\
\hline
& & & & &
\end{array}
\]
Next, we proceed by adding the numbers in each place value (from right to left):
Step 1. Adding the ones, ${\color{blue}2} + {\color{blue}5} = {\color{blue}7}{:}$
\[
\begin{array}{cccccccc}
& & \!\!\!\! 2 \!\!\!\!& \!\!\!\! 7 \!\!\!\!& \!\!\!\! {\color{blue}2} \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & & \!\!\!\! 2 \!\!\!\!& \!\!\!\! {\color{blue}5} \!\!\!\! \\
\hline
& & & \!\!\!\! \!\!\!\!& \!\!\!\! {\color{blue}7} \!\!\!\!
\end{array}
\]
Step 2. Adding the tens, ${\color{blue}7} + {\color{blue}2} = {\color{blue}9}{:}$
\[
\begin{array}{cccccccc}
& & \!\!\!\! 2 \!\!\!\!& \!\!\!\! {\color{blue}7} \!\!\!\!& \!\!\!\! 2 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & & \!\!\!\! {\color{blue}2} \!\!\!\!& \!\!\!\! 5 \!\!\!\! \\
\hline
& & & \!\!\!\! {\color{blue}9} \!\!\!\!& \!\!\!\! 7 \!\!\!\!
\end{array}
\]
Step 3. Adding the hundreds, ${\color{blue}2} + {\color{blue}0} = {\color{blue}2}{:}$
\[
\begin{array}{cccccccc}
& & \!\!\!\! {\color{blue}2} \!\!\!\!& \!\!\!\! 7 \!\!\!\!& \!\!\!\! 2 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! {\color{blue}0} \!\!\!\! & \!\!\!\! 2 \!\!\!\!& \!\!\!\! 5 \!\!\!\! \\
\hline
& & \!\!\!\! {\color{blue}2} \!\!\!\! & \!\!\!\! 9 \!\!\!\!& \!\!\!\! 7 \!\!\!\!
\end{array}
\]
Therefore, $272+25 = 297.$
a
$387$
b
$398$
c
$386$
d
$388$
e
$378$
First, we line up our numbers (ones over ones , tens over tens , hundreds over hundreds ):
\[
\begin{array}{cccccccc}
& & & \!\!\!\! 6 \!\!\!\!& \!\!\!\! 5 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 3 \!\!\!\! & \!\!\!\! 2 \!\!\!\!& \!\!\!\! 3 \!\!\!\! \\
\hline
& & & &
\end{array}
\]
Next, we proceed by adding the numbers in each place value (from right to left):
Step 1. Adding the ones, ${\color{blue}5} + {\color{blue}3} = {\color{blue}8}{:}$
\[
\begin{array}{cccccccc}
& & & \!\!\!\! 6 \!\!\!\!& \!\!\!\! {\color{blue}5} \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 3 \!\!\!\! & \!\!\!\! 2 \!\!\!\!& \!\!\!\! {\color{blue}3} \!\!\!\! \\
\hline
& & & \!\!\!\! \!\!\!\!& \!\!\!\! {\color{blue}8} \!\!\!\!
\end{array}
\]
Step 2. Adding the tens, ${\color{blue}6} + {\color{blue}2} = {\color{blue}8}{:}$
\[
\begin{array}{cccccccc}
& & & \!\!\!\! {\color{blue}6} \!\!\!\!& \!\!\!\! 5 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 3 \!\!\!\! & \!\!\!\! {\color{blue}2} \!\!\!\!& \!\!\!\! 3 \!\!\!\! \\
\hline
& & & \!\!\!\! {\color{blue}8} \!\!\!\!& \!\!\!\! 8 \!\!\!\!
\end{array}
\]
Step 3. Adding the hundreds, ${\color{blue}0} + {\color{blue}3} = {\color{blue}3}{:}$
\[
\begin{array}{cccccccc}
& & \!\!\!\! {\color{blue}0} \!\!\!\!& \!\!\!\! 6 \!\!\!\!& \!\!\!\! 5 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! {\color{blue}3} \!\!\!\! & \!\!\!\! 2 \!\!\!\!& \!\!\!\! 3 \!\!\!\! \\
\hline
& & \!\!\!\! {\color{blue}3} \!\!\!\! & \!\!\!\! 8 \!\!\!\!& \!\!\!\! 8 \!\!\!\!
\end{array}
\]
Therefore, $65 + 323 = 388.$
Now, let's calculate the following sum:
119 + 71
To use the standard algorithm, we first line up our numbers (ones over ones , tens over tens , hundreds over hundreds ):
\begin{array}{cccccccc}
& & \!\!\!\! 1 \!\!\!\! & \!\!\!\! 1 \!\!\!\!& \!\!\!\! 9 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & & \!\!\!\! 7 \!\!\!\!& \!\!\!\! 1 \!\!\!\! \\
\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}9} + {\color{blue}1} = {\color{red}1}{\color{blue}0}.
{\color{red}1}{\color{blue}0}
{\color{blue}0}
ones and carry
{\color{red}1}
tens :
\begin{array}{cccccccc}
& & & \!\!\!\! {\color{red}1} \!\!\!\! & \\
& & \!\!\!\! 1 \!\!\!\! & \!\!\!\! 1 \!\!\!\!& \!\!\!\! {\color{blue}9} \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & & \!\!\!\! 7 \!\!\!\!& \!\!\!\! {\color{blue}1} \!\!\!\! \\
\hline
& & & \!\!\!\! \!\!\!\!& \!\!\!\! {\color{blue}0} \!\!\!\!
\end{array}
Step 2. Adding the tens, we get
{\color{blue}1} + {\color{blue}1} + {\color{blue}7} = {\color{blue}9}{:}
\begin{array}{cccccccc}
& & & \!\!\!\! {\color{blue}1} \!\!\!\! & \\
& & \!\!\!\! 1 \!\!\!\! & \!\!\!\! {\color{blue}1} \!\!\!\!& \!\!\!\! 9 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & & \!\!\!\! {\color{blue}7} \!\!\!\!& \!\!\!\! 1 \!\!\!\! \\
\hline
& & & \!\!\!\! {\color{blue}9} \!\!\!\!& \!\!\!\! 0 \!\!\!\!
\end{array}
Step 3. Adding the hundreds, we get
{\color{blue}1} + {\color{blue}0} = {\color{blue}1}{:}
\begin{array}{cccccccc}
& & & \!\!\!\! 1 \!\!\!\! & \\
& & \!\!\!\! {\color{blue}1} \!\!\!\! & \!\!\!\! 1 \!\!\!\!& \!\!\!\! 9 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! {\color{blue}0} \!\!\!\! & \!\!\!\! 7 \!\!\!\!& \!\!\!\! 1 \!\!\!\! \\
\hline
& & \!\!\!\! {\color{blue}1} \!\!\!\! & \!\!\!\! 9 \!\!\!\!& \!\!\!\! 0 \!\!\!\!
\end{array}
Therefore,
119 + 71 = 190.
First, we line up our numbers (ones over ones , tens over tens , hundreds over hundreds ):
\begin{array}{cccccccc}
& & & \!\!\!\! 5 \!\!\!\!& \!\!\!\! 1 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 2 \!\!\!\! & \!\!\!\! 6 \!\!\!\!& \!\!\!\! 7 \!\!\!\! \\
\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}7} = {\color{blue}8}{:}
\begin{array}{cccccccc}
& & & \!\!\!\! 5 \!\!\!\!& \!\!\!\! {\color{blue}1} \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 2 \!\!\!\! & \!\!\!\! 6 \!\!\!\!& \!\!\!\! {\color{blue}7} \!\!\!\! \\
\hline
& & & \!\!\!\! \!\!\!\!& \!\!\!\! {\color{blue}8} \!\!\!\!
\end{array}
Step 2. Adding the tens,
{\color{blue}5} + {\color{blue}6} = {\color{red}1}{\color{blue}1}.
{\color{blue}1}
tens and carry
{\color{red}1}
hundreds :
\begin{array}{cccccccc}
& & \!\!\!\! {\color{red}1} \!\!\!\!& & \\
& & & \!\!\!\! {\color{blue}5} \!\!\!\!& \!\!\!\! 1 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 2 \!\!\!\! & \!\!\!\! {\color{blue}6} \!\!\!\!& \!\!\!\! 7 \!\!\!\! \\
\hline
& & & \!\!\!\! {\color{blue}1} \!\!\!\!& \!\!\!\! 8 \!\!\!\!
\end{array}
Step 3. Adding the hundreds,
{\color{blue}1} + {\color{blue}0} + {\color{blue}2} = {\color{blue}3}{:}
\begin{array}{cccccccc}
& & \!\!\!\! {\color{blue}1} \!\!\!\!& & \\
& & \!\!\!\! {\color{blue}0} \!\!\!\!& \!\!\!\! 5 \!\!\!\!& \!\!\!\! 1 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! {\color{blue}2} \!\!\!\! & \!\!\!\! 6 \!\!\!\!& \!\!\!\! 7 \!\!\!\! \\
\hline
& & \!\!\!\! {\color{blue}3} \!\!\!\! & \!\!\!\! 1 \!\!\!\!& \!\!\!\! 8 \!\!\!\!
\end{array}
Therefore,
51 + 267 = 318.
a
$841$
b
$730$
c
$741$
d
$830$
e
$731$
First, we line up our numbers (ones over ones , tens over tens , hundreds over hundreds ):
\[
\begin{array}{cccccccc}
& & & \!\!\!\! 2 \!\!\!\!& \!\!\!\! 7 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 7 \!\!\!\!& \!\!\!\! 1 \!\!\!\!& \!\!\!\! 4 \!\!\!\! \\
\hline
& & & & &
\end{array}
\]
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 :
\[
\begin{array}{cccccccc}
& & & \!\!\!\! {\color{red}1} \!\!\!\! & \\
& & & \!\!\!\! 2 \!\!\!\!& \!\!\!\! {\color{blue}7} \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 7 \!\!\!\!& \!\!\!\! 1 \!\!\!\!& \!\!\!\! {\color{blue}4} \!\!\!\! \\
\hline
& & & \!\!\!\! \!\!\!\!& \!\!\!\! {\color{blue}1} \!\!\!\!
\end{array}
\]
Step 2. Adding the tens, ${\color{blue}1} + {\color{blue}2} + {\color{blue}1} = {\color{blue}4}{:}$
\[
\begin{array}{cccccccc}
& & & \!\!\!\! {\color{blue}1} \!\!\!\! & \\
& & & \!\!\!\! {\color{blue}2} \!\!\!\!& \!\!\!\! 7 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 7 \!\!\!\!& \!\!\!\! {\color{blue}1} \!\!\!\!& \!\!\!\! 4 \!\!\!\! \\
\hline
& & & \!\!\!\! {\color{blue}4} \!\!\!\!& \!\!\!\! 1 \!\!\!\!
\end{array}
\]
Step 3. Adding the hundreds, ${\color{blue}0} + {\color{blue}7} = {\color{blue}7}{:}$
\[
\begin{array}{cccccccc}
& & & \!\!\!\! 1 \!\!\!\! & \\
& & \!\!\!\! {\color{blue}0} \!\!\!\! & \!\!\!\! 2 \!\!\!\!& \!\!\!\! 7 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! {\color{blue}7} \!\!\!\!& \!\!\!\! 1 \!\!\!\!& \!\!\!\! 4 \!\!\!\! \\
\hline
& & \!\!\!\! {\color{blue}7} \!\!\!\!& \!\!\!\! 4 \!\!\!\!& \!\!\!\! 1 \!\!\!\!
\end{array}
\]
Therefore, $27+714 = 741.$
a
$105$
b
$2,005$
c
$195$
d
$205$
e
$1,105$
First, we line up our numbers (ones over ones , tens over tens , hundreds over hundreds ):
\[
\begin{array}{cccccccc}
& & \!\!\!\! 1 \!\!\!\!& \!\!\!\! 5 \!\!\!\!& \!\!\!\! 2 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & & \!\!\!\! 5 \!\!\!\!& \!\!\!\! 3 \!\!\!\! \\
\hline
& & & & &
\end{array}
\]
Next, we proceed by adding the numbers in each place value (from right to left):
Step 1. Adding the ones, ${\color{blue}2} + {\color{blue}3} = {\color{blue}5}{:}$
\[
\begin{array}{cccccccc}
& & \!\!\!\! 1 \!\!\!\!& \!\!\!\! 5 \!\!\!\!& \!\!\!\! {\color{blue}2} \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & & \!\!\!\! 5 \!\!\!\!& \!\!\!\! {\color{blue}3} \!\!\!\! \\
\hline
& & & \!\!\!\! \!\!\!\!& \!\!\!\! {\color{blue}5} \!\!\!\!
\end{array}
\]
Step 2. Adding the tens, ${\color{blue}5} + {\color{blue}5} = {\color{red}1}{\color{blue}0}.$ We write $\color{blue}0$ below the tens and carry $\color{red}1$ to the hundreds :
\[
\begin{array}{cccccccc}
& & \!\!\!\! {\color{red}1} \!\!\!\!& & \\
& & \!\!\!\! 1 \!\!\!\!& \!\!\!\! {\color{blue}5} \!\!\!\!& \!\!\!\! 2 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & & \!\!\!\! {\color{blue}5} \!\!\!\!& \!\!\!\! 3 \!\!\!\! \\
\hline
& & & \!\!\!\! {\color{blue}0} \!\!\!\!& \!\!\!\! 5 \!\!\!\!
\end{array}
\]
Step 3. Adding the hundreds, ${\color{blue}1}+{\color{blue}1}+{\color{blue}0}={\color{blue}2}{:}$
\[
\begin{array}{cccccccc}
& & \!\!\!\! {\color{blue}1} \!\!\!\! & & \\
& & \!\!\!\! {\color{blue}1} \!\!\!\! & \!\!\!\! 5 \!\!\!\!& \!\!\!\! 2 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! {\color{blue}0} \!\!\!\! & \!\!\!\! 5 \!\!\!\!& \!\!\!\! 3 \!\!\!\! \\
\hline
& & \!\!\!\! {\color{blue}2} \!\!\!\! & \!\!\!\! 0 \!\!\!\! & \!\!\!\! 5 \!\!\!\!
\end{array}
\]
Therefore, $152+53 = 205.$
First, we line up our numbers (ones over ones , tens over tens , hundreds over hundreds ):
\begin{array}{cccccccc}
& & & \!\!\!\! 8 \!\!\!\!& \!\!\!\! 9 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 9 \!\!\!\! & \!\!\!\! 8 \!\!\!\!& \!\!\!\! 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}9} + {\color{blue}2} = {\color{red}1}{\color{blue}1}.
{\color{blue}1}
ones and carry
{\color{red}1}
tens :
\begin{array}{cccccccc}
& & & \!\!\!\! {\color{red}1} \!\!\!\! & \\
& & & \!\!\!\! 8 \!\!\!\!& \!\!\!\! {\color{blue}9} \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 9 \!\!\!\! & \!\!\!\! 8 \!\!\!\!& \!\!\!\! {\color{blue}2} \!\!\!\! \\
\hline
& & & \!\!\!\! \!\!\!\!& \!\!\!\! {\color{blue}1} \!\!\!\!
\end{array}
Step 2. Adding the tens,
{\color{blue}1} + {\color{blue}8 } + {\color{blue}8} = {\color{red}1}{\color{blue}7}.
{\color{blue}7}
tens and carry
{\color{red}1}
hundreds :
\begin{array}{cccccccc}
& & \!\!\!\! {\color{red}1} \!\!\!\! & \!\!\!\! {\color{blue}1} \!\!\!\! & \\
& & & \!\!\!\! {\color{blue}8} \!\!\!\!& \!\!\!\! 9 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 9 \!\!\!\! & \!\!\!\! {\color{blue}8} \!\!\!\!& \!\!\!\! 2 \!\!\!\! \\
\hline
& & & \!\!\!\! {\color{blue}7} \!\!\!\!& \!\!\!\! 1 \!\!\!\!
\end{array}
Step 3. Adding the hundreds,
{\color{blue}1} + {\color{blue}0} + {\color{blue}9} = {\color{red}1}{\color{blue}0}.
{\color{blue}0}
hundreds and carry
{\color{red}1}
thousands :
\begin{array}{cccccccc}
& \!\!\!\! {\color{red}1} \!\!\!\! & \!\!\!\! {\color{blue}1} \!\!\!\! & \!\!\!\! 1 \!\!\!\! & \\
& & \!\!\!\! {\color{blue}0} \!\!\!\! & \!\!\!\! 8 \!\!\!\!& \!\!\!\! 9 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! {\color{blue}9} \!\!\!\! & \!\!\!\! 8 \!\!\!\!& \!\!\!\! 2 \!\!\!\! \\
\hline
& & \!\!\!\! {\color{blue}0} \!\!\!\! & \!\!\!\! 7 \!\!\!\!& \!\!\!\! 1 \!\!\!\!
\end{array}
Step 4. Adding the thousands,
{\color{blue}1}+{\color{blue}0}+{\color{blue}0}={\color{blue}1}{:}
\begin{array}{cccccccc}
& \!\!\!\! {\color{blue}1} \!\!\!\! & \!\!\!\! 1 \!\!\!\! & \!\!\!\! 1 \!\!\!\! & \\
& \!\!\!\! {\color{blue}0} \!\!\!\! & \!\!\!\! 0 \!\!\!\! & \!\!\!\! 8 \!\!\!\!& \!\!\!\! 9 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & \!\!\!\! {\color{blue}0} \!\!\!\! & \!\!\!\! 9 \!\!\!\! & \!\!\!\! 8 \!\!\!\!& \!\!\!\! 2 \!\!\!\! \\
\hline
& \!\!\!\! {\color{blue}1} \!\!\!\! & \!\!\!\! 0 \!\!\!\! & \!\!\!\! 7 \!\!\!\!& \!\!\!\! 1 \!\!\!\!
\end{array}
Therefore,
89 + 982 = 1,071.
a
$442$
b
$352$
c
$342$
d
$412$
e
$452$
First, we line up our numbers (ones over ones , tens over tens , hundreds over hundreds ):
\[
\begin{array}{cccccccc}
& & & \!\!\!\! 6 \!\!\!\!& \!\!\!\! 5 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 3 \!\!\!\!& \!\!\!\! 8 \!\!\!\!& \!\!\!\! 7 \!\!\!\! \\
\hline
& & & & &
\end{array}
\]
Next, we proceed by adding the numbers in each place value (from right to left):
Step 1. Adding the ones, ${\color{blue}5} + {\color{blue}7} = {\color{red}1}{\color{blue}2}.$ We write $\color{blue}2$ below the ones and carry $\color{red}1$ to the tens :
\[
\begin{array}{cccccccc}
& & & \!\!\!\! {\color{red}1} \!\!\!\! & \\
& & & \!\!\!\! 6 \!\!\!\!& \!\!\!\! {\color{blue}5} \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 3 \!\!\!\!& \!\!\!\! 8 \!\!\!\!& \!\!\!\! {\color{blue}7} \!\!\!\! \\
\hline
& & & \!\!\!\! \!\!\!\!& \!\!\!\! {\color{blue}2} \!\!\!\!
\end{array}
\]
Step 2. Adding the tens, ${\color{blue}1} + {\color{blue}6} + {\color{blue}8} = {\color{red}1}{\color{blue}5}.$ We write $\color{blue}5$ below the tens and carry $\color{red}1$ to the hundreds :
\[
\begin{array}{cccccccc}
& & \!\!\!\! {\color{red}1} \!\!\!\! & \!\!\!\! {\color{blue}1} \!\!\!\!& \\
& & & \!\!\!\! {\color{blue}6} \!\!\!\!& \!\!\!\! 5 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! 3 \!\!\!\!& \!\!\!\! {\color{blue}8} \!\!\!\!& \!\!\!\! 7 \!\!\!\! \\
\hline
& & & \!\!\!\! {\color{blue}5} \!\!\!\!& \!\!\!\! 2 \!\!\!\!
\end{array}
\]
Step 3. Adding the hundreds, ${\color{blue}1}+{\color{blue}0}+{\color{blue}3}={\color{blue}4}{:}$
\[
\begin{array}{cccccccc}
& & \!\!\!\! {\color{blue}1} \!\!\!\! & \!\!\!\! 1 \!\!\!\!& \\
& & \!\!\!\! {\color{blue}0} \!\!\!\! & \!\!\!\! 6 \!\!\!\!& \!\!\!\! 5 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! {\color{blue}3} \!\!\!\! & \!\!\!\! 8 \!\!\!\!& \!\!\!\! 7 \!\!\!\! \\
\hline
& & \!\!\!\! {\color{blue}4} \!\!\!\! & \!\!\!\! 5 \!\!\!\! & \!\!\!\! 2 \!\!\!\!
\end{array}
\]
Therefore, $65+387 = 452.$
a
$1,934$
b
$1,034$
c
$1,134$
d
$1,024$
e
$924$
First, we line up our numbers (ones over ones , tens over tens , hundreds over hundreds ):
\[
\begin{array}{cccccccc}
& & \!\!\!\! 9 \!\!\!\!& \!\!\!\! 2 \!\!\!\!& \!\!\!\! 8 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & & \!\!\!\! 9 \!\!\!\!& \!\!\!\! 6 \!\!\!\! \\
\hline
& & & & &
\end{array}
\]
Next, we proceed by adding the numbers in each place value (from right to left):
Step 1. Adding the ones, ${\color{blue}8} + {\color{blue}6} = {\color{red}1}{\color{blue}4}.$ We write $\color{blue}4$ below the ones and carry $\color{red}1$ to the tens :
\[
\begin{array}{cccccccc}
& & & \!\!\!\! {\color{red}1} \!\!\!\! & \\
& & \!\!\!\! 9 \!\!\!\!& \!\!\!\! 2 \!\!\!\!& \!\!\!\! {\color{blue}8} \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & & \!\!\!\! 9 \!\!\!\!& \!\!\!\! {\color{blue}6} \!\!\!\! \\
\hline
& & & \!\!\!\! \!\!\!\!& \!\!\!\! {\color{blue}4} \!\!\!\!
\end{array}
\]
Step 2. Adding the tens, ${\color{blue}1} + {\color{blue}2} + {\color{blue}9} = {\color{red}1}{\color{blue}2}.$ We write $\color{blue}2$ below the tens and carry $\color{red}1$ to the hundreds :
\[
\begin{array}{cccccccc}
& & \!\!\!\! {\color{red}1} \!\!\!\! & \!\!\!\! {\color{blue}1} \!\!\!\!& \\
& & \!\!\!\! 9 \!\!\!\!& \!\!\!\! {\color{blue}2} \!\!\!\!& \!\!\!\! 8 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & & \!\!\!\! {\color{blue}9} \!\!\!\!& \!\!\!\! 6 \!\!\!\! \\
\hline
& & & \!\!\!\! {\color{blue}2} \!\!\!\!& \!\!\!\! 4 \!\!\!\!
\end{array}
\]
Step 3. Adding the hundreds, ${\color{blue}1}+{\color{blue}9}+{\color{blue}0}={\color{red}1}{\color{blue}0}.$ We write $\color{blue}0$ below the hundreds and carry $\color{red}1$ to the thousands :
\[
\begin{array}{cccccccc}
& \!\!\!\! {\color{red}1} \!\!\!\! & \!\!\!\! {\color{blue}1} \!\!\!\! & \!\!\!\! 1 \!\!\!\! & \\
& & \!\!\!\! {\color{blue}9} \!\!\!\! & \!\!\!\! 2 \!\!\!\!& \!\!\!\! 8 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & & \!\!\!\! {\color{blue}0} \!\!\!\! & \!\!\!\! 9 \!\!\!\!& \!\!\!\! 6 \!\!\!\! \\
\hline
& & \!\!\!\! {\color{blue}0} \!\!\!\! & \!\!\!\! 2 \!\!\!\! & \!\!\!\! 4 \!\!\!\!
\end{array}
\]
Step 4. Adding the thousands, ${\color{blue}1}+{\color{blue}0}+{\color{blue}0}={\color{blue}1}{:}$
\[
\begin{array}{cccccccc}
& \!\!\!\! {\color{blue}1} \!\!\!\! & \!\!\!\! 1 \!\!\!\! & \!\!\!\! 1 \!\!\!\! & \\
& \!\!\!\! {\color{blue}0} \!\!\!\! & \!\!\!\! 9 \!\!\!\! & \!\!\!\! 2 \!\!\!\!& \!\!\!\! 8 \!\!\!\! \\
\!\!\!\!+\!\!\!\! & \!\!\!\! {\color{blue}0} \!\!\!\! & \!\!\!\! 0 \!\!\!\! & \!\!\!\! 9 \!\!\!\!& \!\!\!\! 6 \!\!\!\! \\
\hline
& \!\!\!\! {\color{blue}1} \!\!\!\! & \!\!\!\! 0 \!\!\!\! & \!\!\!\! 2 \!\!\!\! & \!\!\!\! 4 \!\!\!\!
\end{array}
\]
Therefore, $928+96 = 1,024.$
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