We can use place value to subtract two-digit whole numbers easily.
As an example, let's find the following difference:
65-42
First, we line up our numbers (ones over ones and tens over tens ):
Tens Ones
\color{red}6
\color{blue}5
\color{red}4
\color{blue}2
Next, we proceed by subtracting the numbers in each place value (from right to left) and writing the results below:
Step 1. Subtracting the ones, we get
{\color{blue}5} - {\color{blue}2} = {\color{blue}3}{:}
Tens Ones
\color{red}6
\color{blue}5
\color{red}4
\color{blue}2
\color{blue}3
Step 2. Subtracting the tens, we get
{\color{red}6} - {\color{red}4} = {\color{red}2}{:}
Tens Ones
\color{red}6
\color{blue}5
\color{red}4
\color{blue}2
\color{red}2
\color{blue}3
Therefore, we conclude that
65-42 = 23.
Drawing place value charts each time we want to subtract 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 difference:
65-42
First, we line up our numbers as follows: (ones over ones, and tens over tens):
\begin{array}{cccccccc}
& & \!\!\!\! 6 \!\!\!\!& \!\!\!\! 5 \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 4 \!\!\!\!& \!\!\!\! 2 \!\!\!\! \\
\hline
& & & &
\end{array}
Next, we proceed by subtracting the numbers in each place value (from right to left):
Step 1. Subtracting the ones, we get
{\color{blue}5} - {\color{blue}2} = {\color{blue}3}{:}
\begin{array}{cccccccc}
& & \!\!\!\! 6 \!\!\!\!& \!\!\!\! {\color{blue}5} \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 4 \!\!\!\!& \!\!\!\! {\color{blue}2} \!\!\!\! \\
\hline
& & \!\!\!\! \!\!\!\!& \!\!\!\! {\color{blue}3} \!\!\!\!
\end{array}
Step 2. Subtracting the tens, we get
{\color{red}6 } - {\color{red}4} = {\color{red}2}{:}
\begin{array}{cccccccc}
& & \!\!\!\! {\color{red}6} \!\!\!\!& \!\!\!\! 5 \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! {\color{red}4} \!\!\!\!& \!\!\!\! 2 \!\!\!\! \\
\hline
& & \!\!\!\! {\color{red}2} \!\!\!\!& \!\!\!\! 3 \!\!\!\!
\end{array}
Therefore,
65 - 42 = 23.
Find the value of
84 - 31.
First, we line up our numbers (ones over ones and tens over tens ):
\begin{array}{cccccccc}
& & \!\!\!\! 8 \!\!\!\!& \!\!\!\! 4 \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 3 \!\!\!\!& \!\!\!\! 1 \!\!\!\! \\
\hline
& & & &
\end{array}
Next, we proceed by subtracting the numbers in each place value (from right to left):
Step 1. Subtracting the ones,
{\color{blue}4} - {\color{blue}1} = {\color{blue}3}{:}
\begin{array}{cccccccc}
& & \!\!\!\! 8 \!\!\!\!& \!\!\!\! {\color{blue}4} \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 3 \!\!\!\!& \!\!\!\! {\color{blue}1} \!\!\!\! \\
\hline
& & \!\!\!\! \!\!\!\!& \!\!\!\! {\color{blue}3} \!\!\!\!
\end{array}
Step 2. Subtracting the tens,
{\color{blue}8 } - {\color{blue}3} = {\color{blue}5}{:}
\begin{array}{cccccccc}
& & \!\!\!\! {\color{blue}8} \!\!\!\!& \!\!\!\! 4 \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! {\color{blue}3} \!\!\!\!& \!\!\!\! 1 \!\!\!\! \\
\hline
& & \!\!\!\! {\color{blue}5} \!\!\!\!& \!\!\!\! 3 \!\!\!\!
\end{array}
Therefore,
84 - 31 = 53.
First, we line up our numbers (ones over ones and tens over tens ):
\[
\begin{array}{cccccccc}
& & \!\!\!\! 2 \!\!\!\! & \!\!\!\! 5 \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 2 \!\!\!\!& \!\!\!\! 2 \!\!\!\! \\
\hline
& & & &
\end{array}
\]
Next, we proceed by subtracting the numbers in each place value (from right to left):
Step 1. Subtracting the ones, ${\color{blue}5} - {\color{blue}2} = {\color{blue}3}{:}$
\[
\begin{array}{cccccccc}
& & \!\!\!\! 2 \!\!\!\!& \!\!\!\! {\color{blue}5} \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 2 \!\!\!\!& \!\!\!\! {\color{blue}2} \!\!\!\! \\
\hline
& & \!\!\!\! \!\!\!\!& \!\!\!\! {\color{blue}3} \!\!\!\! &
\end{array}
\]
Step 2. Subtracting the tens, ${\color{blue}2 } - {\color{blue}2} = {\color{blue}0}{:}$
\[
\begin{array}{cccccccc}
& & \!\!\!\! {\color{blue}2} \!\!\!\!& \!\!\!\! 5 \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! {\color{blue}2} \!\!\!\!& \!\!\!\! 2 \!\!\!\! \\
\hline
& & \!\!\!\! {\color{blue}0} \!\!\!\!& \!\!\!\! 3 \!\!\!\! &
\end{array}
\]
Therefore, $25 - 22 = \bbox[3pt,Gainsboro]{\color{blue}3}.$
a
$13$
b
$27$
c
$23$
d
$17$
e
$7$
First, we line up our numbers (ones over ones and tens over tens ):
\[
\begin{array}{cccccccc}
& & \!\!\!\! 5 \!\!\!\!& \!\!\!\! 8 \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 4 \!\!\!\!& \!\!\!\! 5 \!\!\!\! \\
\hline
& & & &
\end{array}
\]
Next, we proceed by subtracting the numbers in each place value (from right to left):
Step 1. Subtracting the ones, ${\color{blue}8} - {\color{blue}5} = {\color{blue}3}{:}$
\[
\begin{array}{cccccccc}
& & \!\!\!\! 5 \!\!\!\!& \!\!\!\! {\color{blue}8} \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 4 \!\!\!\!& \!\!\!\! {\color{blue}5} \!\!\!\! \\
\hline
& & \!\!\!\! \!\!\!\!& \!\!\!\! {\color{blue}3} \!\!\!\!
\end{array}
\]
Step 2. Subtracting the tens, ${\color{blue}5 } - {\color{blue}4} = {\color{blue}1}{:}$
\[
\begin{array}{cccccccc}
& & \!\!\!\! {\color{blue}5} \!\!\!\!& \!\!\!\! 8 \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! {\color{blue}4} \!\!\!\!& \!\!\!\! 5 \!\!\!\! \\
\hline
& & \!\!\!\! {\color{blue}1} \!\!\!\!& \!\!\!\! 3 \!\!\!\!
\end{array}
\]
Therefore, $58 - 45 = 13.$
a
$11$
b
$21$
c
$19$
d
$29$
e
$12$
First, we line up our numbers (ones over ones and tens over tens ):
\[
\begin{array}{cccccccc}
& & \!\!\!\! 5 \!\!\!\!& \!\!\!\! 5 \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 3 \!\!\!\!& \!\!\!\! 4 \!\!\!\! \\
\hline
& & & &
\end{array}
\]
Next, we proceed by subtracting the numbers in each place value (from right to left):
Step 1. Subtracting the ones, ${\color{blue}5} - {\color{blue}4} = {\color{blue}1}{:}$
\[
\begin{array}{cccccccc}
& & \!\!\!\! 5 \!\!\!\!& \!\!\!\! {\color{blue}5} \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 3 \!\!\!\!& \!\!\!\! {\color{blue}4} \!\!\!\! \\
\hline
& & \!\!\!\! \!\!\!\!& \!\!\!\! {\color{blue}1} \!\!\!\!
\end{array}
\]
Step 2. Subtracting the tens, ${\color{blue}5 } - {\color{blue}3} = {\color{blue}2}{:}$
\[
\begin{array}{cccccccc}
& & \!\!\!\! {\color{blue}5} \!\!\!\!& \!\!\!\! 5 \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! {\color{blue}3} \!\!\!\!& \!\!\!\! 4 \!\!\!\! \\
\hline
& & \!\!\!\! {\color{blue}2} \!\!\!\!& \!\!\!\! 1 \!\!\!\!
\end{array}
\]
Therefore, $55 - 34 = 21.$
Let's consider the following subtraction problem:
45-17
First, we line up our numbers (ones over ones and tens over tens), as before:
Tens Ones
\color{red}4
\color{blue}5
1
7
We have a problem. Since
5
7,
5-7.
The answer is to take the first number
({\color{red}{4}}{\color{blue}{5}}),
\begin{align*}
{\color{red}{4}}\, \textrm{tens} + {\color{blue}{5}}\,\textrm{ones}
&= {\color{red}{3}}\, \textrm{tens} + {\color{blue}{15}}\,\textrm{ones}
\end{align*}
Updating the first row in our table gives the following:
Tens Ones
\color{red}3
\color{blue}15
1
7
Now, we subtract as usual!
Step 1. Subtracting the ones, we get
15-7=8{:}
Tens Ones
\color{red}3
\color{blue}15
1
7
8
Step 1. Subtracting the tens, we get
3-1=2{:}
Tens Ones
\color{red}3
\color{blue}15
1
7
2
8
Therefore, we conclude that
45-17 = 28.
Let's now solve the same problem using the standard algorithm.
Once again, we consider the following difference:
45 - 17
To use the standard algorithm, we first line up our numbers (ones over ones and tens over tens):
\begin{array}{cccccccc}
& & \!\!\!\! 4 \!\!\!\!& \!\!\!\! 5 \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 1 \!\!\!\!& \!\!\!\! 7 \!\!\!\! \\
\hline
& & & &
\end{array}
Step 1. We cannot compute
5-7.
1
tens place. Then we have
4 - 1 = {\color{red}3}
\color{red}15
\require{cancel}
\begin{array}{cccccccc}
& & \!\!\!\! \small{\color{red}3} \!\!\!& \!\!\! \small{\color{red}15} \!\!\!\! \\
& & \!\!\!\! \cancel{4} \!\!\!& \!\!\! \cancel{5} \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 1 \!\!\!& \!\!\! 7 \!\!\!\! \\
\hline
& & \!\!\!\! \!\!\!& \!\!\! \!\!\!\!
\end{array}
Subtracting the ones, we get
{\color{blue}15} - {\color{blue}7} = {\color{blue}8}{:}
\begin{array}{cccccccc}
& & \!\!\!\! \small{3} \!\!\!& \!\!\! \small{\color{blue}15} \!\!\!\! \\
& & \!\!\!\! \cancel{4} \!\!\!& \!\!\! \cancel{5} \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 1 \!\!\!& \!\!\! {\color{blue}7} \!\!\!\! \\
\hline
& & \!\!\!\! \!\!\!& \!\!\! {\color{blue}8} \!\!\!\!
\end{array}
Step 2. Subtracting the tens, we get
{\color{blue}3} - {\color{blue}1} = {\color{blue}2}{:}
\begin{array}{cccccccc}
& & \!\!\!\! \small{\color{blue}3} \!\!\!& \!\!\! \small{15} \!\!\!\! \\
& & \!\!\!\! \cancel{4} \!\!\!& \!\!\! \cancel{5} \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! {\color{blue}1} \!\!\!& \!\!\! 7 \!\!\!\! \\
\hline
& & \!\!\!\! {\color{blue}2} \!\!\!& \!\!\! 8 \!\!\!\!
\end{array}
Therefore,
45 - 17 = 28.
Find the value of
72 - 56.
First, we line up our numbers (ones over ones and tens over tens ):
\begin{array}{cccccccc}
& & \!\!\!\! 7 \!\!\!\!& \!\!\!\! 2 \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 5 \!\!\!\!& \!\!\!\! 6 \!\!\!\! \\
\hline
& & & &
\end{array}
Next, we proceed by subtracting the numbers in each place value (from right to left):
Step 1. We cannot compute
2 - 6.
1
tens place. Then we have
7 - 1 = {\color{red}6}
\color{red}12
\require{cancel}
\begin{array}{cccccccc}
& & \!\!\!\! \small{\color{red}6} \!\!\!& \!\!\! \small{\color{red}12} \!\!\!\! \\
& & \!\!\!\! \cancel{7} \!\!\!& \!\!\! \cancel{2} \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 5 \!\!\!& \!\!\! 6 \!\!\!\! \\
\hline
& & \!\!\!\! \!\!\!& \!\!\! \!\!\!\!
\end{array}
Now, subtracting the ones,
{\color{blue}12} - {\color{blue}6} = {\color{blue}6}{:}
\begin{array}{cccccccc}
& & \!\!\!\! \small{6} \!\!\!& \!\!\! \small{\color{blue}12} \!\!\!\! \\
& & \!\!\!\! \cancel{7} \!\!\!& \!\!\! \cancel{2} \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 5 \!\!\!& \!\!\! {\color{blue}6} \!\!\!\! \\
\hline
& & \!\!\!\! \!\!\!& \!\!\! {\color{blue}6} \!\!\!\!
\end{array}
Step 2. Subtracting the tens,
{\color{blue}6} - {\color{blue}5} = {\color{blue}1}{:}
\begin{array}{cccccccc}
& & \!\!\!\! \small{\color{blue}6} \!\!\!& \!\!\! \small{12} \!\!\!\! \\
& & \!\!\!\! \cancel{7} \!\!\!& \!\!\! \cancel{2} \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! {\color{blue}5} \!\!\!& \!\!\! 6 \!\!\!\! \\
\hline
& & \!\!\!\! {\color{blue}1} \!\!\!& \!\!\! 6 \!\!\!\!
\end{array}
Therefore,
72 - 56 = 16.
First, we line up our numbers (ones over ones and tens over tens ):
\[
\begin{array}{cccccccc}
& & \!\!\!\! 5 \!\!\!\!& \!\!\!\! 6 \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 3 \!\!\!\!& \!\!\!\! 9 \!\!\!\! \\
\hline
& & & &
\end{array}
\]
Next, we proceed by subtracting the numbers in each place value (from right to left):
Step 1. We cannot compute $6 - 9.$ So, we borrow $1$ from the tens place. Then we have $5 - 1 = {\color{red}4}$ tens and $\color{red}16$ ones:
\[
\require{cancel}
\begin{array}{cccccccc}
& & \!\!\!\! \small{\color{red}4} \!\!\!& \!\!\! \small{\color{red}16} \!\!\!\! \\
& & \!\!\!\! \cancel{5} \!\!\!& \!\!\! \cancel{6} \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 3 \!\!\!& \!\!\! 9 \!\!\!\! \\
\hline
& & \!\!\!\! \!\!\!& \!\!\! \!\!\!\! &
\end{array}
\]
Now, subtracting the ones, ${\color{blue}16} - {\color{blue}9} = {\color{blue}7}{:}$
\[
\begin{array}{cccccccc}
& & \!\!\!\! \small{4} \!\!\!& \!\!\! \small{\color{blue}16} \!\!\!\! \\
& & \!\!\!\! \cancel{5} \!\!\!& \!\!\! \cancel{6} \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 3 \!\!\!& \!\!\! {\color{blue}9} \!\!\!\! \\
\hline
& & \!\!\!\! \!\!\!& \!\!\! {\color{blue}7} \!\!\!\! &
\end{array}
\]
Step 2. Subtracting the tens, ${\color{blue}4} - {\color{blue}3} = {\color{blue}1}{:}$
\[
\begin{array}{cccccccc}
& & \!\!\!\! \small{\color{blue}4} \!\!\!& \!\!\! \small{16} \!\!\!\! \\
& & \!\!\!\! \cancel{5} \!\!\!& \!\!\! \cancel{6} \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! {\color{blue}3} \!\!\!& \!\!\! 9 \!\!\!\! \\
\hline
& & \!\!\!\! {\color{blue}1} \!\!\!& \!\!\! 7 \!\!\!\! &
\end{array}
\]
Therefore, $56 - 39 = \bbox[3pt,Gainsboro]{\color{blue}17}.$
a
$37$
b
$23$
c
$33$
d
$17$
e
$13$
First, we line up our numbers (ones over ones and tens over tens ):
\[
\begin{array}{cccccccc}
& & \!\!\!\! 8 \!\!\!\!& \!\!\!\! 6 \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 6 \!\!\!\!& \!\!\!\! 9 \!\!\!\! \\
\hline
& & & &
\end{array}
\]
Next, we proceed by subtracting the numbers in each place value (from right to left):
Step 1. We cannot compute $6 - 9.$ So, we borrow $1$ from the tens place. Then we have $8 - 1 = {\color{red}7}$ tens and $\color{red}16$ ones:
\[
\require{cancel}
\begin{array}{cccccccc}
& & \!\!\!\! \small{\color{red}7} \!\!\!& \!\!\! \small{\color{red}16} \!\!\!\! \\
& & \!\!\!\! \cancel{8} \!\!\!& \!\!\! \cancel{6} \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 6 \!\!\!& \!\!\! 9 \!\!\!\! \\
\hline
& & \!\!\!\! \!\!\!& \!\!\! \!\!\!\!
\end{array}
\]
Now, subtracting the ones, ${\color{blue}16} - {\color{blue}9} = {\color{blue}7}{:}$
\[
\begin{array}{cccccccc}
& & \!\!\!\! \small{7} \!\!\!& \!\!\! \small{\color{blue}16} \!\!\!\! \\
& & \!\!\!\! \cancel{8} \!\!\!& \!\!\! \cancel{6} \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 6 \!\!\!& \!\!\! {\color{blue}9} \!\!\!\! \\
\hline
& & \!\!\!\! \!\!\!& \!\!\! {\color{blue}7} \!\!\!\!
\end{array}
\]
Step 2. Subtracting the tens, ${\color{blue}7} - {\color{blue}6} = {\color{blue}1}{:}$
\[
\begin{array}{cccccccc}
& & \!\!\!\! \small{\color{blue}7} \!\!\!& \!\!\! \small{16} \!\!\!\! \\
& & \!\!\!\! \cancel{8} \!\!\!& \!\!\! \cancel{6} \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! {\color{blue}6} \!\!\!& \!\!\! 9 \!\!\!\! \\
\hline
& & \!\!\!\! {\color{blue}1} \!\!\!& \!\!\! 7 \!\!\!\!
\end{array}
\]
Therefore, $86 - 69 = 17.$
First, we line up our numbers (ones over ones and tens over tens ):
\[
\begin{array}{cccccccc}
& & \!\!\!\! 9 \!\!\!\!& \!\!\!\! 4 \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 3 \!\!\!\!& \!\!\!\! 5 \!\!\!\! \\
\hline
& & & &
\end{array}
\]
Next, we proceed by subtracting the numbers in each place value (from right to left):
Step 1. We cannot compute $4 - 5.$ So, we borrow $1$ from the tens place. Then we have $9 - 1 = {\color{red}8}$ tens and $\color{red}14$ ones:
\[
\require{cancel}
\begin{array}{cccccccc}
& & \!\!\!\! \small{\color{red}8} \!\!\!& \!\!\! \small{\color{red}14} \!\!\!\! \\
& & \!\!\!\! \cancel{9} \!\!\!& \!\!\! \cancel{4} \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 3 \!\!\!& \!\!\! 5 \!\!\!\! \\
\hline
& & \!\!\!\! \!\!\!& \!\!\! \!\!\!\! &
\end{array}
\]
Now, subtracting the ones, ${\color{blue}14} - {\color{blue}5} = {\color{blue}9}{:}$
\[
\begin{array}{cccccccc}
& & \!\!\!\! \small{8} \!\!\!& \!\!\! \small{\color{blue}14} \!\!\!\! \\
& & \!\!\!\! \cancel{9} \!\!\!& \!\!\! \cancel{4} \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 3 \!\!\!& \!\!\! {\color{blue}5} \!\!\!\! \\
\hline
& & \!\!\!\! \!\!\!& \!\!\! {\color{blue}9} \!\!\!\! &
\end{array}
\]
Step 2. Subtracting the tens, ${\color{blue}8} - {\color{blue}3} = {\color{blue}5}{:}$
\[
\begin{array}{cccccccc}
& & \!\!\!\! \small{\color{blue}8} \!\!\!& \!\!\! \small{14} \!\!\!\! \\
& & \!\!\!\! \cancel{9} \!\!\!& \!\!\! \cancel{4} \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! {\color{blue}3} \!\!\!& \!\!\! 5 \!\!\!\! \\
\hline
& & \!\!\!\! {\color{blue}5} \!\!\!& \!\!\! 9 \!\!\!\! &
\end{array}
\]
Therefore, $94 - 35 = \bbox[3pt,Gainsboro]{\color{blue}59}.$
A college basketball team scored
25
82
To find the number of points the team scored this month, we need to find
82-25.
First, we line up our numbers (ones over ones and tens over tens ):
\begin{array}{cccccccc}
& & \!\!\!\! 8 \!\!\!\!& \!\!\!\! 2 \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 2 \!\!\!\!& \!\!\!\! 5 \!\!\!\! \\
\hline
& & & &
\end{array}
Next, we proceed by subtracting the numbers in each place value (from right to left):
Step 1. We cannot compute
2 - 5.
1
tens place. Then we have
8 - 1 = {\color{red}7}
\color{red}12
\require{cancel}
\begin{array}{cccccccc}
& & \!\!\!\! \small{\color{red}7} \!\!\!& \!\!\! \small{\color{red}12} \!\!\!\! \\
& & \!\!\!\! \cancel{8} \!\!\!& \!\!\! \cancel{2} \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 2 \!\!\!& \!\!\! 5 \!\!\!\! \\
\hline
& & \!\!\!\! \!\!\!& \!\!\! \!\!\!\!
\end{array}
Now, subtracting the ones,
{\color{blue}12} - {\color{blue}5} = {\color{blue}7}{:}
\begin{array}{cccccccc}
& & \!\!\!\! \small{7} \!\!\!& \!\!\! \small{\color{blue}12} \!\!\!\! \\
& & \!\!\!\! \cancel{8} \!\!\!& \!\!\! \cancel{2} \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 2 \!\!\!& \!\!\! {\color{blue}5} \!\!\!\! \\
\hline
& & \!\!\!\! \!\!\!& \!\!\! {\color{blue}7} \!\!\!\!
\end{array}
Step 2. Subtracting the tens,
{\color{blue}7} - {\color{blue}2} = {\color{blue}5}{:}
\begin{array}{cccccccc}
& & \!\!\!\! \small{\color{blue}7} \!\!\!& \!\!\! \small{12} \!\!\!\! \\
& & \!\!\!\! \cancel{8} \!\!\!& \!\!\! \cancel{2} \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! {\color{blue}2} \!\!\!& \!\!\! 5 \!\!\!\! \\
\hline
& & \!\!\!\! {\color{blue}5} \!\!\!& \!\!\! 7 \!\!\!\!
\end{array}
Therefore, the team scored
57
Angie is reading a book with $74$ pages. So far, she has read $31$ pages. How many pages does Angie have left to read?
a
$47$ pages
b
$27$ pages
c
$43$ pages
d
$37$ pages
e
$33$ pages
To find how many pages Angie has left to read, we need to find $74-31.$
First, we line up our numbers (ones over ones and tens over tens ):
\[
\begin{array}{cccccccc}
& & \!\!\!\! 7 \!\!\!\!& \!\!\!\! 4 \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 3 \!\!\!\!& \!\!\!\! 1 \!\!\!\! \\
\hline
& & & &
\end{array}
\]
Next, we proceed by subtracting the numbers in each place value (from right to left):
Step 1. Subtracting the ones, ${\color{blue}4} - {\color{blue}1} = {\color{blue}3}{:}$
\[
\begin{array}{cccccccc}
& & \!\!\!\! 7 \!\!\!\!& \!\!\!\! {\color{blue}4} \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 3 \!\!\!\!& \!\!\!\! {\color{blue}1} \!\!\!\! \\
\hline
& & \!\!\!\! \!\!\!\!& \!\!\!\! {\color{blue}3} \!\!\!\!
\end{array}
\]
Step 2. Subtracting the tens, ${\color{blue}7 } - {\color{blue}3} = {\color{blue}4}{:}$
\[
\begin{array}{cccccccc}
& & \!\!\!\! {\color{blue}7} \!\!\!\!& \!\!\!\! 4 \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! {\color{blue}3} \!\!\!\!& \!\!\!\! 1 \!\!\!\! \\
\hline
& & \!\!\!\! {\color{blue}4} \!\!\!\!& \!\!\!\! 3 \!\!\!\!
\end{array}
\]
Therefore Ange has $43$ pages left to read.
Pam bought $36$ candies for Halloween. During the day, $18$ trick-or-treaters knocked on her door. Given that each trick-or-treater receives one candy each, how many candies does Pam have remaining?
a
$12$ candies
b
$18$ candies
c
$14$ candies
d
$22$ candies
e
$16$ candies
To find how many candies Pam has remaining, we need to find $36-18.$
First, we line up our numbers (ones over ones and tens over tens ):
\[
\begin{array}{cccccccc}
& & \!\!\!\! 3 \!\!\!\!& \!\!\!\! 6 \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 1 \!\!\!\!& \!\!\!\! 8 \!\!\!\! \\
\hline
& & & &
\end{array}
\]
Next, we proceed by subtracting the numbers in each place value (from right to left):
Step 1. We cannot compute $6 - 8.$ So, we borrow $1$ from the tens place. Then, we have $3 - 1 = {\color{red}2}$ tens and $\color{red}16$ ones:
\[
\require{cancel}
\begin{array}{cccccccc}
& & \!\!\!\! \small{\color{red}2} \!\!\!& \!\!\! \small{\color{red}16} \!\!\!\! \\
& & \!\!\!\! \cancel{3} \!\!\!& \!\!\! \cancel{6} \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 1 \!\!\!& \!\!\! 8 \!\!\!\! \\
\hline
& & \!\!\!\! \!\!\!& \!\!\! 8 \!\!\!\!
\end{array}
\]
Now, subtracting the ones, ${\color{blue}16} - {\color{blue}8} = {\color{blue}8}{:}$
\[
\begin{array}{cccccccc}
& & \!\!\!\! \small{2} \!\!\!& \!\!\! \small{\color{blue}16} \!\!\!\! \\
& & \!\!\!\! \cancel{3} \!\!\!& \!\!\! \cancel{6} \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! 1 \!\!\!& \!\!\! {\color{blue}8} \!\!\!\! \\
\hline
& & \!\!\!\! \!\!\!& \!\!\! {\color{blue}8} \!\!\!\!
\end{array}
\]
Step 2. Subtracting the tens, ${\color{blue}2} - {\color{blue}1} = {\color{blue}1}{:}$
\[
\begin{array}{cccccccc}
& & \!\!\!\! \small{\color{blue}2} \!\!\!& \!\!\! \small{16} \!\!\!\! \\
& & \!\!\!\! \cancel{3} \!\!\!& \!\!\! \cancel{6} \!\!\!\! \\
\!\!\!\!-\!\!\!\! & & \!\!\!\! {\color{blue}1} \!\!\!& \!\!\! 8 \!\!\!\! \\
\hline
& & \!\!\!\! {\color{blue}1} \!\!\!& \!\!\! 8 \!\!\!\!
\end{array}
\]
Therefore Pam has $18$ candies remaining.
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