We use the standard algorithm to divide a two-digit number by a one-digit number. To illustrate, let's divide
92
4.
We start by writing down the question using long division notation, as follows:
4
\!\!\require{enclose}\enclose{longdiv}{9 {\:\phantom{|}} 2}
First, we consider the tens. How many times does
4
{\color{red}9}?
{\color{blue}2}
4\times {\color{blue}2} =8,
{\color{red}9} - 8 = 1.
We write the
{\color{blue}2}
8
1.
2
\color{blue}2
4
\!\!\require{enclose}\enclose{longdiv}{{\color{red}9} {\:\phantom{|}} 2}
-\!\!\!\!\!\!\!
8
\color{lightgray}\downarrow
1
\color{lightgray}2
Divide:
{\color{red}9} \div 4 = {\color{blue}2}\,\text{R}\,1
Write over tens:
\color{blue}2
Multiply:
4 \times {\color{blue}2} = 8
Subtract:
{\color{red}9} - 8 = 1
Bring down:
2
Next, we consider the ones. How many times does
4
{\color{red}12}?
{\color{blue}3}
4\times {\color{blue}3} =12,
{\color{red}12} - 12 = 0
We write the
{\color{blue}3}
12
0.
2
\color{blue}3
4
\!\!\require{enclose}\enclose{longdiv}{9 {\:\phantom{|}} 2}
-\!\!\!\!\!\!\!
8
\color{red}1
\color{red}2
-\!\!\!\!\!\!\!
1
2
\fbox{0}
Divide:
{\color{red}12} \div 4 = {\color{blue}3}
Write over ones:
\color{blue}3
Multiply:
4 \times {\color{blue}3} = 12
Subtract:
{\color{red}12} - 12 = \fbox{0}
We've gone through all the digits in the number
92,
Therefore,
92 \div 4 = 23.
We start by writing down the question using long division notation:
2
\!\!\require{enclose}\enclose{longdiv}{8 {\:\phantom{|}} 6}
First, we consider the tens:
\color{blue}4
2
\!\!\require{enclose}\enclose{longdiv}{{\color{red}8} {\:\phantom{|}} 6}
-\!\!\!\!\!\!\!
8
\color{lightgray}\downarrow
0
\color{lightgray}6
Divide:
{\color{red}8} \div 2 = {\color{blue}4}
Write over tens:
\color{blue}4
Multiply:
2 \times {\color{blue}4} = 8
Subtract:
{\color{red}8} - 8 = 0
Bring down:
6
Next, we consider the ones:
4
\color{blue}3
2
\!\!\require{enclose}\enclose{longdiv}{8 {\:\phantom{|}} 6}
-\!\!\!\!\!\!\!
8
0
\color{red}6
-\!\!\!\!
6
\fbox{0}
Divide:
{\color{red}6} \div 2 = {\color{blue}3}
Write over ones:
\color{blue}3
Multiply:
2 \times {\color{blue}3} = 6
Subtract:
{\color{red}6} - 6 = \fbox{0}
We've gone through all the digits in the number
86,
Therefore,
86 \div 2 = 43.
What is $84$ divided by $4?$
a
$24$
b
$21 \,\text{R}\, 1$
c
$20 \,\text{R}\, 3$
d
$22$
e
$21$
We start by writing down the question using long division notation:
$4$
$\!\!\require{enclose}\enclose{longdiv}{8 {\:\phantom{|}} 4}$
First, we consider the tens:
$\color{blue}2$
$4$
$\!\!\require{enclose}\enclose{longdiv}{{\color{red}8} {\:\phantom{|}} 4}$
$-\!\!\!\!\!\!\!$
$8$
$\color{lightgray}\downarrow$
$0$
$\color{lightgray}4$
Divide: ${\color{red}8} \div 4 = {\color{blue}2}$
Write over tens: $\color{blue}2$
Multiply: $4 \times {\color{blue}2} = 8 $
Subtract: ${\color{red}8} - 8 = 0$
Bring down: $4$
Next, we consider the ones:
$2$
$\color{blue}1$
$4$
$\!\!\require{enclose}\enclose{longdiv}{8 {\:\phantom{|}} 4}$
$-\!\!\!\!\!\!\!$
$8$
$0$
$\color{red}4$
$-\!\!\!\!\!$
$4$
$\fbox{0}$
Divide: ${\color{red}4} \div 4 = {\color{blue}1}$
Write over ones: $\color{blue}1$
Multiply: $4 \times {\color{blue}1} = 4$
Subtract: ${\color{red}4} - 4 = \fbox{0}$
We've gone through all the digits in the number $84,$ so the division is done.
Therefore,
\[
84 \div 4 = 21.
\]
What is $82$ divided by $2?$
a
$41$
b
$42$
c
$47$
d
$45$
e
$43$
We start by writing down the question using long division notation:
$2$
$\!\!\require{enclose}\enclose{longdiv}{8 {\:\phantom{|}} 2}$
First, we consider the tens:
$\color{blue}4$
$2$
$\!\!\require{enclose}\enclose{longdiv}{{\color{red}8} {\:\phantom{|}} 2}$
$-\!\!\!\!\!\!\!$
$8$
$\color{lightgray}\downarrow$
$0$
$\color{lightgray}2$
Divide: ${\color{red}8} \div 2 = {\color{blue}4}$
Write over tens: $\color{blue}4$
Multiply: $2 \times {\color{blue}4} = 8 $
Subtract: ${\color{red}8} - 8 = 0$
Bring down: $2$
Next, we consider the ones:
$4$
$\color{blue}1$
$2$
$\!\!\require{enclose}\enclose{longdiv}{8 {\:\phantom{|}} 2}$
$-\!\!\!\!\!\!\!$
$8$
$0$
$\color{red}2$
$-\!\!\!\!\!$
$2$
$\fbox{0}$
Divide: ${\color{red}2} \div 2 = {\color{blue}1}$
Write over ones: $\color{blue}1$
Multiply: $2 \times {\color{blue}1} = 2$
Subtract: ${\color{red}2} - 2 = \fbox{0}$
We've gone through all the digits in the number $82,$ so the division is done.
Therefore,
\[
82 \div 2 = 41.
\]
Harold cuts an
85
5
To find out how long each of the pieces is, we need to divide
85
5.
We start by writing down the question using long division notation:
5
\!\!\require{enclose}\enclose{longdiv}{8 {\:\phantom{|}} 5}
First, we consider the tens:
\color{blue}1
5
\!\!\require{enclose}\enclose{longdiv}{{\color{red}8} {\:\phantom{|}} 5}
-\!\!\!\!\!\!\!
5
\color{lightgray}\downarrow
3
\color{lightgray}5
Divide:
{\color{red}8} \div 5 = {\color{blue}1}\,\text{R}\,3
Write over tens:
\color{blue}1
Multiply:
5 \times {\color{blue}1} = 5
Subtract:
{\color{red}8} - 5 = 3
Bring down:
5
Next, we consider the ones:
1
\color{blue}7
5
\!\!\require{enclose}\enclose{longdiv}{8 {\:\phantom{|}} 5}
-\!\!\!\!\!\!\!
5
\color{red}3
\color{red}5
-\!\!\!\!\!\!\!
3
5
\fbox{0}
Divide:
{\color{red}35} \div 5 = {\color{blue}7}
Write over ones:
\color{blue}7
Multiply:
5 \times {\color{blue}7} = 35
Subtract:
{\color{red}35} - 35 = \fbox{0}
We've gone through all the digits in the number
85,
Therefore,
85 \div 5 = 17.
This means that each piece of rope is
17
Amy cut an $84$-inch long pipe into $7$ pieces of the same length. How long is each piece?
a
$12$ inches
b
$14$ inches
c
$11$ inches
d
$15$ inches
e
$10$ inches
To find out how long each of the pieces is, we need to divide $84$ by $7.$
We start by writing down the question using long division notation:
$7$
$\!\!\require{enclose}\enclose{longdiv}{8 {\:\phantom{|}} 4}$
First, we consider the tens:
$\color{blue}1$
$7$
$\!\!\require{enclose}\enclose{longdiv}{{\color{red}8} {\:\phantom{|}} 4}$
$-\!\!\!\!\!\!\!$
$7$
$\color{lightgray}\downarrow$
$1$
$\color{lightgray}4$
Divide: ${\color{red}8} \div 7 = {\color{blue}1} \,\text{R}\, 1$
Write over tens: $\color{blue}1$
Multiply: $7 \times {\color{blue}1} = 7 $
Subtract: ${\color{red}8} - 7 = 1$
Bring down: $4$
Next, we consider the ones:
$1$
$\color{blue}2$
$7$
$\!\!\require{enclose}\enclose{longdiv}{8 {\:\phantom{|}} 4}$
$-\!\!\!\!\!\!\!$
$7$
$\color{red}1$
$\color{red}4$
$-\!\!\!\!\!\!\!$
$1$
$4$
$\fbox{0}$
Divide: ${\color{red}14} \div 7 = {\color{blue}2}$
Write over ones: $\color{blue}2$
Multiply: $7 \times {\color{blue}2} = 14$
Subtract: ${\color{red}14} - 14 = \fbox{0}$
We've gone through all the digits in the number $84,$ so the division is done.
Therefore,
\[
84 \div 7 = 12.
\]
This means that each piece of pipe is $12$ inches long.
Keith cuts a $54$-inch string into $2$ pieces of the same size. How long is each piece?
a
$27$ inches
b
$23$ inches
c
$29$ inches
d
$28$ inches
e
$25$ inches
To find out how long each of the pieces is, we need to divide $54$ by $2.$
We start by writing down the question using long division notation:
$2$
$\!\!\require{enclose}\enclose{longdiv}{5 {\:\phantom{|}} 4}$
First, we consider the tens:
$\color{blue}2$
$2$
$\!\!\require{enclose}\enclose{longdiv}{{\color{red}5} {\:\phantom{|}} 4}$
$-\!\!\!\!\!\!\!$
$4$
$\color{lightgray}\downarrow$
$1$
$\color{lightgray}4$
Divide: ${\color{red}5} \div 2 = {\color{blue}2} \,\text{R}\, 1$
Write over tens: $\color{blue}2$
Multiply: $2 \times {\color{blue}2} = 4 $
Subtract: ${\color{red}5} - 4 = 1$
Bring down: $4$
Next, we consider the ones:
$2$
$\color{blue}7$
$2$
$\!\!\require{enclose}\enclose{longdiv}{5 {\:\phantom{|}} 4}$
$-\!\!\!\!\!\!\!$
$4$
$\color{red}1$
$\color{red}4$
$-\!\!\!\!\!\!\!$
$1$
$4$
$\fbox{0}$
Divide: ${\color{red}14} \div 2 = {\color{blue}7}$
Write over ones: $\color{blue}7$
Multiply: $2 \times {\color{blue}7} = 14$
Subtract: ${\color{red}14} - 14 = \fbox{0}$
We've gone through all the digits in the number $54,$ so the division is done.
Therefore,
\[
54 \div 2 = 27.
\]
This means that each piece of string is $27$ inches long.
If there is a remainder after using the standard algorithm, we write the remainder in the answer. To illustrate, let's find the remainder of
95\div 8\,.
We start by writing down the question using long division notation:
8
\!\!\require{enclose}\enclose{longdiv}{9 {\:\phantom{|}} 5}
First, we consider the tens:
\color{blue}1
8
\!\!\require{enclose}\enclose{longdiv}{{\color{red}9} {\:\phantom{|}} 5}
-\!\!\!\!\!\!\!
8
\color{lightgray}\downarrow
1
\color{lightgray}5
Divide:
{\color{red}9} \div 8 = {\color{blue}1}\,\text{R}\,1
Write over tens:
\color{blue}1
Multiply:
8 \times {\color{blue}1} = 8
Subtract:
{\color{red}9} - 8 = 1
Bring down:
5
Next, we consider the ones:
1
\color{blue}1
8
\!\!\require{enclose}\enclose{longdiv}{9 {\:\phantom{|}} 5}
-\!\!\!\!\!\!\!
8
\color{red}1
\color{red}5
-\!\!\!\!\!\!\!
8
\fbox{7}
Divide:
{\color{red}15} \div 8 = {\color{blue}1}\,\text{R}\,7
Write over ones:
\color{blue}1
Multiply:
8 \times {\color{blue}1} = 8
Subtract:
{\color{red}15} - 8 = \fbox{7}
We've gone through all the digits in the number
95,
remainder of
\color{blue}7
Therefore,
95 \div 8 = {\color{red}11}\,\text{R}\,{\color{blue}7}.
Here,
\color{red}11
quotient .
From top to bottom, what are the missing digits in the following division problem?
\fbox{[math]\phantom{1}[/math]}
2
7
\!\!\require{enclose}\enclose{longdiv}{8 {\:\phantom{|}} 5}
-\!\!\!
\fbox{[math]\phantom{7}[/math]}
\fbox{[math]\phantom{1}[/math]}
5
-\!\!\!\!\!\!\!
1
4
1
We start by writing down the question using long division notation:
7
\!\!\require{enclose}\enclose{longdiv}{8 {\:\phantom{|}} 5}
First, we consider the tens:
\color{blue}1
7
\!\!\require{enclose}\enclose{longdiv}{{\color{red}8} {\:\phantom{|}} 5}
-\!\!\!\!\!\!\!
7
\color{lightgray}\downarrow
1
\color{lightgray}5
Divide:
{\color{red}8} \div 7 = {\color{blue}1}\,\text{R}\,1
Write over tens:
\color{blue}1
Multiply:
7 \times {\color{blue}1} = 7
Subtract:
{\color{red}8} - 7 = 1
Bring down:
5
Next, we consider the ones:
1
\color{blue}2
7
\!\!\require{enclose}\enclose{longdiv}{8 {\:\phantom{|}} 5}
-\!\!\!\!\!\!\!
7
\color{red}1
\color{red}5
-\!\!\!\!\!\!\!
1
4
\fbox{1}
Divide:
{\color{red}15} \div 7 = {\color{blue}2}\,\text{R}\,1
Write over ones:
\color{blue}2
Multiply:
7 \times {\color{blue}2} = 14
Subtract:
{\color{red}15} - 14 = \fbox{1}
We've gone through all the digits in the number
85,
1
Therefore,
85 \div 7 = 12\,\text{R}\,1.
The missing digits are
1
7
1
\fbox{1}
2
7
\!\!\require{enclose}\enclose{longdiv}{8 {\:\phantom{|}} 5}
-\!\!\!
\fbox{7}
\fbox{1}
5
-\!\!\!\!\!\!\!
1
4
1
From left to right, what are the missing digits in the following division problem?
$1$
$3$
$6$
$\!\!\require{enclose}\enclose{longdiv}{7 {\:\phantom{|}} 9}$
$-\!\!\!\!\!\!\!$
$6$
$\fbox{$\phantom{1}$}$
$\fbox{$\phantom{4}$}$
$-\!\!\!\!\!\!\!$
$1$
$8$
$1$
a
$2$ and $4$
b
$1$ and $9$
c
$3$ and $6$
d
$5$ and $3$
e
$1$ and $8$
We start by writing down the question using long division notation:
$6$
$\!\!\require{enclose}\enclose{longdiv}{7 {\:\phantom{|}} 9}$
First, we consider the tens:
$\color{blue}1$
$6$
$\!\!\require{enclose}\enclose{longdiv}{{\color{red}7} {\:\phantom{|}} 9}$
$-\!\!\!\!\!\!\!$
$6$
$\color{lightgray}\downarrow$
$1$
$\color{lightgray}9$
Divide: ${\color{red}7} \div 6 = {\color{blue}1}\,\text{R}\,1$
Write over tens: $\color{blue}1$
Multiply: $6 \times {\color{blue}1} = 6 $
Subtract: ${\color{red}7} - 6 = 1$
Bring down: $9$
Next, we consider the ones:
$1$
$\color{blue}3$
$6$
$\!\!\require{enclose}\enclose{longdiv}{7 {\:\phantom{|}} 9}$
$-\!\!\!\!\!\!\!$
$6$
$\color{red}1$
$\color{red}9$
$-\!\!\!\!\!\!\!$
$1$
$8$
$\fbox{1}$
Divide: ${\color{red}19} \div 6 = {\color{blue}3}\,\text{R}\,1$
Write over ones: $\color{blue}3$
Multiply: $6 \times {\color{blue}3} = 18$
Subtract: ${\color{red}19} - 18 = \fbox{1}$
We've gone through all the digits in the number $79,$ so the division is done. However, we still have a remainder of $1$, so we include this in our final answer.
Therefore,
\[
79 \div 6 = 13\,\text{R}\,1.
\]
The missing digits are $1$ and $9$:
$1$
$3$
$6$
$\!\!\require{enclose}\enclose{longdiv}{7 {\:\phantom{|}} 9}$
$-\!\!\!\!\!\!\!$
$6$
$\fbox{1}$
$\fbox{9}$
$-\!\!\!\!\!\!\!$
$1$
$8$
$1$
From top to bottom, what are the missing digits in the following division problem?
$\fbox{$\phantom{0}$}$
$4$
$3$
$\!\!\require{enclose}\enclose{longdiv}{4 {\:\phantom{|}} 3}$
$-\!\!\!\!$
$\fbox{$\phantom{0}$}$
$\fbox{$\phantom{0}$}$
$3$
$-\!\!\!\!$
$1$
$2$
$1$
a
$1$, $4$, and $0$
b
$1$, $4$, and $1$
c
$1$, $3$, and $1$
d
$2$, $6$, and $2$
e
$1$, $3$, and $2$
We start by writing down the problem using long division notation:
$3$
$\!\!\require{enclose}\enclose{longdiv}{4 {\:\phantom{|}} 3}$
First, we consider the tens:
$\color{blue}1$
$3$
$\!\!\require{enclose}\enclose{longdiv}{{\color{red}4} {\:\phantom{|}} 3}$
$-\!\!\!\!\!\!\!$
$3$
$\color{lightgray}\downarrow$
$1$
$\color{lightgray}3$
Divide: ${\color{red}4} \div 3 = {\color{blue}1} \,\text{R}\, 1$
Write over tens: $\color{blue}1$
Multiply: $3 \times {\color{blue}1} = 3$
Subtract: ${\color{red}4} - 3 = 1$
Bring down: $3$
Next, we consider the ones:
$1$
$\color{blue}4$
$3$
$\!\!\require{enclose}\enclose{longdiv}{4 {\:\phantom{|}} 3}$
$-\!\!\!\!\!\!\!$
$3$
$\color{red}1$
$\color{red}3$
$-\!\!\!\!\!\!\!$
$1$
$2$
$\fbox{1}$
Divide: ${\color{red}13} \div 3 = {\color{blue}4} \,\text{R}\, 1$
Write over ones: $\color{blue}4$
Multiply: $3 \times {\color{blue}4} = 12$
Subtract: ${\color{red}13} - 12 = \fbox{1}$
We've gone through all the digits in the number $43,$ so the division is done. However, we still have a remainder of $1$, so we include this in our final answer.
Therefore,
\[
43 \div 3 = 14 \,\text{R}\, 1.
\]
The missing digits are $1$, $3$ and $1$:
$\fbox{1}$
$4$
$3$
$\!\!\require{enclose}\enclose{longdiv}{4 {\:\phantom{|}} 3}$
$-\!\!\!\!$
$\fbox{3}$
$\fbox{1}$
$3$
$-\!\!\!\!$
$1$
$2$
$1$
Find the quotient and the remainder of
89\div 6.
We start by writing down the question using long division notation:
6
\!\!\require{enclose}\enclose{longdiv}{8 {\:\phantom{|}} 9}
First, we consider the tens:
\color{blue}1
6
\!\!\require{enclose}\enclose{longdiv}{{\color{red}8} {\:\phantom{|}} 9}
-\!\!\!\!\!\!\!
6
\color{lightgray}\downarrow
2
\color{lightgray}9
Divide:
{\color{red}8} \div 6 = {\color{blue}1}\,\text{R}\,2
Write over tens:
\color{blue}1
Multiply:
6 \times {\color{blue}1} = 6
Subtract:
{\color{red}8} - 6 = 2
Bring down:
9
Next, we consider the ones:
1
\color{blue}4
6
\!\!\require{enclose}\enclose{longdiv}{8 {\:\phantom{|}} 9}
-\!\!\!\!\!\!\!
6
\color{red}2
\color{red}9
-\!\!\!\!\!\!\!
2
4
\fbox{5}
Divide:
{\color{red}29} \div 6 = {\color{blue}4}\,\text{R}\,5
Write over ones:
\color{blue}4
Multiply:
6 \times {\color{blue}4} = 24
Subtract:
{\color{red}29} - 24 = \fbox{5}
We've gone through all the digits in the number
89,
5
Therefore,
89 \div 6 = 14\,\text{R}\,5.
Find the quotient and the remainder of $95\div 8.$
a
$10\,\text{R}\,7$
b
$17\,\text{R}\,7$
c
$11\,\text{R}\,7$
d
$13\,\text{R}\,7$
e
$12\,\text{R}\,7$
We start by writing down the question using long division notation:
$8$
$\!\!\require{enclose}\enclose{longdiv}{9 {\:\phantom{|}} 5}$
First, we consider the tens:
$\color{blue}1$
$8$
$\!\!\require{enclose}\enclose{longdiv}{{\color{red}9} {\:\phantom{|}} 5}$
$-\!\!\!\!\!\!\!$
$8$
$\color{lightgray}\downarrow$
$1$
$\color{lightgray}5$
Divide: ${\color{red}9} \div 8 = {\color{blue}1}\,\text{R}\,1$
Write over tens: $\color{blue}1$
Multiply: $8 \times {\color{blue}1} = 8 $
Subtract: ${\color{red}9} - 8 = 1$
Bring down: $5$
Next, we consider the ones:
$1$
$\color{blue}1$
$8$
$\!\!\require{enclose}\enclose{longdiv}{9 {\:\phantom{|}} 5}$
$-\!\!\!\!\!\!\!$
$8$
$\color{red}1$
$\color{red}5$
$-\!\!\!\!\!\!\!$
$8$
$\fbox{7}$
Divide: ${\color{red}15} \div 8 = {\color{blue}1}\,\text{R}\,7$
Write over ones: $\color{blue}1$
Multiply: $8 \times {\color{blue}1} = 8$
Subtract: ${\color{red}15} - 8 = \fbox{7}$
We've gone through all the digits in the number $95,$ so the division is done. However, we still have a remainder of $7$, so we include this in our final answer.
Therefore,
\[
95 \div 8 = 11\,\text{R}\,7.
\]
Find the quotient and the remainder of $76\div 5.$
a
$18\,\textrm{R}\,1$
b
$16\,\textrm{R}\,1$
c
$17\,\textrm{R}\,1$
d
$15\,\textrm{R}\,1$
e
$14\,\textrm{R}\,1$
We start by writing down the question using long division notation:
$5$
$\!\!\require{enclose}\enclose{longdiv}{7 {\:\phantom{|}} 6}$
First, we consider the tens:
$\color{blue}1$
$5$
$\!\!\require{enclose}\enclose{longdiv}{{\color{red}7} {\:\phantom{|}} 6}$
$-\!\!\!\!\!\!\!$
$5$
$\color{lightgray}\downarrow$
$2$
$\color{lightgray}6$
Divide: ${\color{red}7} \div 5 = {\color{blue}1}\,\text{R}\,2$
Write over tens: $\color{blue}1$
Multiply: $5 \times {\color{blue}1} = 5 $
Subtract: ${\color{red}7} - 5 = 2$
Bring down: $6$
Next, we consider the ones:
$1$
$\color{blue}5$
$5$
$\!\!\require{enclose}\enclose{longdiv}{7 {\:\phantom{|}} 6}$
$-\!\!\!\!\!\!\!$
$5$
$\color{red}2$
$\color{red}6$
$-\!\!\!\!\!\!\!$
$2$
$5$
$\fbox{1}$
Divide: ${\color{red}26} \div 5 = {\color{blue}5}\,\text{R}\,1$
Write over ones: $\color{blue}5$
Multiply: $5 \times {\color{blue}5} = 25$
Subtract: ${\color{red}26} - 25 = \fbox{1}$
We've gone through all the digits in the number $76,$ so the division is done. However, we still have a remainder of $1$, so we include this in our final answer.
Therefore,
\[
76 \div 5 = 15\,\text{R}\,1.
\]
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