We can use the standard algorithm for division to divide four-digit numbers by two-digit numbers.
To illustrate, let's use the algorithm to find the value of
4,564 \div 14.
We start by writing down the question using long division notation:
14
\!\require{enclose}\enclose{longdiv}{4 {\:\phantom{|}} 5 {\:\phantom{|}} 6 {\:\phantom{|}} 4}
First, we consider the thousands and hundreds. Notice that
14
goes
{\color{blue}3}
times into
{\color{red}45}.
So, we get:
\color{blue}3
14
\!\require{enclose}\enclose{longdiv}{{\color{red}4} {\:\phantom{|}} {\color{red}5} {\:\phantom{|}} 6 {\:\phantom{|}} 4}
-\!\!\!\!
4
2
\color{lightgray}\downarrow
3
\color{lightgray}6
Write over hundreds:
\color{blue}3
Multiply:
14 \times {\color{blue}3} = 42
Subtract:
{\color{red}45} - 42 = 3
Bring down:
6
Next, notice that
14
goes
{\color{blue}2}
times into
{\color{red}36}.
So, we get:
3
\color{blue}2
14
\!\require{enclose}\enclose{longdiv}{4 {\:\phantom{|}} 5 {\:\phantom{|}} 6 {\:\phantom{|}} 4}
-\!\!\!\!
4
2
\color{lightgray}\downarrow
\color{red}3
\color{red}6
\color{lightgray}\downarrow
-\!\!\!\!
2
8
\color{lightgray}\downarrow
8
\color{lightgray}4
Write over tens:
\color{blue}2
Multiply:
14 \times {\color{blue}2} = 28
Subtract:
{\color{red}36} - 28 = 8
Bring down:
4
Finally, notice that
14
goes
{\color{blue}6}
times into
{\color{red}84}.
So, we get:
3
2
\color{blue}6
14
\!\require{enclose}\enclose{longdiv}{4 {\:\phantom{|}} 5 {\:\phantom{|}} 6 {\:\phantom{|}} 4}
-\!\!\!\!
4
2
3
6
-\!\!\!\!
2
8
\color{red}8
\color{red}4
-\!\!\!\!
8
4
0
Write over ones:
\color{blue}6
Multiply:
14 \times {\color{blue}6} = 84
Subtract:
{\color{red}84} - 84 = 0
We've gone through all the digits, and the remainder is
0,
so the division is done.
Therefore,
4,564 \div 14 = 326.
A hardware store owner cuts a
1,560
-inch electrical cable into
15
pieces of equal length for retail sale. How long is each piece?
To find out the length of each piece of cable, we need to divide
1,560
by
15.
We start by writing down the question using long division notation:
15
\!\require{enclose}\enclose{longdiv}{1 {\:\phantom{|}} 5 {\:\phantom{|}} 6 {\:\phantom{|}} 0}
Next, we consider the thousands and hundreds. Notice that
15
goes
{\color{blue}1}
time into
{\color{red}15}.
So, we get:
\color{blue}1
15
\!\require{enclose}\enclose{longdiv}{{\color{red}1} {\:\phantom{|}} {\color{red}5} {\:\phantom{|}} 6 {\:\phantom{|}} 0}
-\!\!\!\!
1
5
\color{lightgray}\downarrow
0
\color{lightgray}6
Write over hundreds:
\color{blue}1
Multiply:
15 \times {\color{blue}1} = 15
Subtract:
{\color{red}15} - 15 = 0
Bring down:
6
Since
15
goes
{\color{blue}0}
times into
{\color{red}6}
, we need to bring one more digit down. So, we get:
1
\color{blue}0
15
\!\require{enclose}\enclose{longdiv}{1 {\:\phantom{|}} 5 {\:\phantom{|}} 6 {\:\phantom{|}} 0}
-\!\!\!\!
1
5
\color{lightgray}\downarrow
0
\color{red}6
\color{lightgray}0
Write over tens:
\color{blue}0
Bring down:
0
Finally, notice that
15
goes
{\color{blue}4}
times into
{\color{red}60}.
So, we get:
1
0
\color{blue}4
15
\!\require{enclose}\enclose{longdiv}{1 {\:\phantom{|}} 5 {\:\phantom{|}} 6 {\:\phantom{|}} 0}
-\!\!\!\!
1
5
0
\color{red}6
\color{red}0
-\!\!\!\!
6
0
0
Write over ones:
\color{blue}4
Multiply:
15 \times {\color{blue}4} = 60
Subtract:
{\color{red}60} - 60 = 0
We've gone through all the digits in the number
1,560
, so the division is done.
Therefore,
1,560 \div 15 = 104.
This means that each piece of cable is
104
inches long.
What is the value of $5,486 \div 26?$
a
$201$
b
$221$
c
$219$
d
$211$
e
$215$
We start by writing down the question using long division notation:
$26$
$\!\!\require{enclose}\enclose{longdiv}{5 {\:\phantom{|}} 4 {\:\phantom{|}} 8 {\:\phantom{|}} 6}$
Next, we consider the thousands and hundreds. Notice that $26$ goes ${\color{blue}2}$ times into ${\color{red}54}.$ Hence, we get:
$\color{blue}2$
$26$
$\!\!\require{enclose}\enclose{longdiv}{{\color{red}5} {\:\phantom{|}} {\color{red}4} {\:\phantom{|}} 8 {\:\phantom{|}} 6}$
$-\!\!\!\!$
$5$
$2$
$\color{lightgray}\downarrow$
$2$
$\color{lightgray}8$
Write over hundreds: $\color{blue}2$
Multiply: $26 \times {\color{blue}2} = 52$
Subtract: ${\color{red}54} - 52 = 2$
Bring down: $8$
Next, notice that $26$ goes ${\color{blue}1}$ times into ${\color{red}28}.$ Hence, we get:
$2$
$\color{blue}1$
$26$
$\!\!\require{enclose}\enclose{longdiv}{5 {\:\phantom{|}} 4 {\:\phantom{|}} 8 {\:\phantom{|}} 6}$
$-\!\!\!\!$
$5$
$2$
$\color{lightgray}\downarrow$
$\color{red}2$
$\color{red}8$
$\color{lightgray}\downarrow$
$-\!\!\!\!$
$2$
$6$
$\color{lightgray}\downarrow$
$2$
$\color{lightgray}6$
Write over tens: $\color{blue}1$
Multiply: $26 \times {\color{blue}1} = 26$
Subtract: ${\color{red}28} - 26 = 2$
Bring down: $6$
Finally, notice that $26$ goes ${\color{blue}1}$ times into ${\color{red}26}.$ Hence, we get:
$2$
$1$
$\color{blue}1$
$26$
$\!\!\require{enclose}\enclose{longdiv}{5 {\:\phantom{|}} 4 {\:\phantom{|}} 8 {\:\phantom{|}} 6}$
$-\!\!\!\!$
$5$
$2$
$2$
$8$
$-\!\!\!\!$
$2$
$6$
$\color{red}2$
$\color{red}6$
$-\!\!\!\!$
$2$
$6$
$0$
Write over ones: $\color{blue}1$
Multiply: $26 \times {\color{blue}1} = 26$
Subtract: ${\color{red}26} - 26 = 0$
We've gone through all the digits in the number $5,486$, so the division is done.
Therefore,
\[
5,486 \div 26 = 211.
\]
a
$117$
b
$118$
c
$114$
d
$115$
e
$116$
We start by writing down the question using long division notation:
$26$
$\!\!\require{enclose}\enclose{longdiv}{2 {\:\phantom{|}} 9 {\:\phantom{|}} 6 {\:\phantom{|}} 4}$
Next, we consider the thousands and hundreds. Notice that $26$ goes ${\color{blue}1}$ times into ${\color{red}{29}}.$ Hence, we get:
$\color{blue}1$
$26$
$\!\!\require{enclose}\enclose{longdiv}{{\color{red}2} {\:\phantom{|}} {\color{red}9} {\:\phantom{|}} 6 {\:\phantom{|}} 4}$
$-\!\!\!\!$
$2$
$6$
$\color{lightgray}\downarrow$
$3$
$\color{lightgray}6$
Write over hundreds: $\color{blue}1$
Multiply: $26 \times {\color{blue}1} = 26$
Subtract: ${\color{red}29} - 26 = 3$
Bring down: $6$
Next, notice that $26$ goes ${\color{blue}1}$ times into ${\color{red}{36}}.$ Hence, we get:
$1$
$\color{blue}1$
$26$
$\!\!\require{enclose}\enclose{longdiv}{2 {\:\phantom{|}} 9 {\:\phantom{|}} 6 {\:\phantom{|}} 4}$
$-\!\!\!\!$
$2$
$6$
$\color{lightgray}\downarrow$
$\color{red}3$
$\color{red}6$
$\color{lightgray}\downarrow$
$-\!\!\!\!$
$2$
$6$
$\color{lightgray}\downarrow$
$1$
$0$
$\color{lightgray}4$
Write over tens: $\color{blue}1$
Multiply: $26 \times {\color{blue}1} = 26$
Subtract: ${\color{red}36} - 26 = 10$
Bring down: $4$
Finally, notice that $26$ goes ${\color{blue}4}$ times into ${\color{red}{104}}.$ Hence, we get:
$1$
$1$
$\color{blue}4$
$26$
$\!\!\require{enclose}\enclose{longdiv}{2 {\:\phantom{|}} 9 {\:\phantom{|}} 6 {\:\phantom{|}} 4}$
$-\!\!\!\!$
$2$
$6$
$3$
$6$
$-\!\!\!\!$
$2$
$6$
$\color{red}1$
$\color{red}0$
$\color{red}4$
$-\!\!\!\!$
$1$
$0$
$4$
$0$
Write over ones: $\color{blue}4$
Multiply: $26 \times {\color{blue}4} = 104$
Subtract: ${\color{red}104} - 104 = 0$
We've gone through all the digits in the number $2,964$, so the division is done.
Therefore,
\[
2,964 \div 26 = 114.
\]
What is the quotient of
7,368 \div 73?
We start by writing down the question using long division notation:
73
\!\require{enclose}\enclose{longdiv}{7 {\:\phantom{|}} 3 {\:\phantom{|}} 6 {\:\phantom{|}} 8}
Next, we consider the thousands and hundreds. Notice that
73
goes
{\color{blue}1}
time into
{\color{red}73}.
So, we get:
\color{blue}1
73
\!\require{enclose}\enclose{longdiv}{{\color{red}7} {\:\phantom{|}} {\color{red}3} {\:\phantom{|}} 6 {\:\phantom{|}} 8}
-\!\!\!\!
7
3
\color{lightgray}\downarrow
0
\color{lightgray}6
Write over hundreds:
\color{blue}1
Multiply:
73 \times {\color{blue}1} = 73
Subtract:
{\color{red}73} - 73 = 0
Bring down:
6
Since
73
goes
{\color{blue}0}
times into
{\color{red}6}
, we need to bring one more digit down. So, we get:
1
\color{blue}0
73
\!\require{enclose}\enclose{longdiv}{7 {\:\phantom{|}} 3 {\:\phantom{|}} 6 {\:\phantom{|}} 8}
-\!\!\!\!
7
3
\color{lightgray}\downarrow
0
\color{red}6
\color{lightgray}8
Write over tens:
\color{blue}0
Bring down:
8
Finally, notice that
73
goes
{\color{blue}0}
times into
{\color{red}68}.
So,
{\color{red}68}
is the remainder and we get:
1
0
\color{blue}0
73
\!\require{enclose}\enclose{longdiv}{7 {\:\phantom{|}} 3 {\:\phantom{|}} 6 {\:\phantom{|}} 8}
-\!\!\!\!
7
3
0
\color{red}6
\color{red}8
Write over ones:
\color{blue}0
We've gone through all the digits in the number
7,368
, so the division is done.
Therefore,
7,368 \div 73 = 100\,\text{R}\,68.
So, the quotient is
100.
What is the quotient of $2,165 \div 24?$
a
$91$
b
$90$
c
$88$
d
$92$
e
$89$
We start by writing down the question using long division notation:
$24$
$\!\!\require{enclose}\enclose{longdiv}{2 {\:\phantom{|}} 1 {\:\phantom{|}} 6 {\:\phantom{|}} 5}$
Since $24$ does not go into $21$, we consider the thousands, hundreds and tens. Notice that $24$ goes ${\color{blue}9}$ times into ${\color{red}216}.$ Hence, we get:
$\color{blue}9$
$24$
$\!\!\require{enclose}\enclose{longdiv}{{\color{red}2} {\:\phantom{|}} {\color{red}1} {\:\phantom{|}} {\color{red}6} {\:\phantom{|}} 5}$
$-\!\!\!\!$
$2$
$1$
$6$
$\color{lightgray}\downarrow$
$0$
$\color{lightgray}5$
Write over tens: $\color{blue}9$
Multiply: $24 \times {\color{blue}9} = 216$
Subtract: ${\color{red}216} - 216 = 0$
Bring down: $5$
Finally, notice that $24$ goes ${\color{blue}0}$ times into ${\color{red}5}.$ Hence, $\color{red}5$ is the remainder and we get:
$9$
$\color{blue}0$
$24$
$\!\!\require{enclose}\enclose{longdiv}{{2} {\:\phantom{|}} {1} {\:\phantom{|}} {6} {\:\phantom{|}} 5}$
$-\!\!\!\!$
$2$
$1$
$6$
$\color{red}0$
$\color{red}5$
Write over ones: $\color{blue}0$
We've gone through all the digits in the number $ 2,165,$ so the division is done. Since we have a remainder of $5$, we conclude that
\[
2,165 \div 24 = 90\,\text{R}\,5.
\]
Therefore, the quotient is $90.$
What is the quotient of $4,214 \div 42?$
a
$110$
b
$101$
c
$111$
d
$100$
e
$114$
We start by writing down the question using long division notation:
$42$
$\!\!\require{enclose}\enclose{longdiv}{4 {\:\phantom{|}} 2 {\:\phantom{|}} 1 {\:\phantom{|}} 4}$
Next, we consider the thousands and hundreds. Notice that $42$ goes ${\color{blue}1}$ times into ${\color{red}42}.$ Hence, we get:
$\color{blue}1$
$42$
$\!\!\require{enclose}\enclose{longdiv}{{\color{red}4} {\:\phantom{|}} {\color{red}2} {\:\phantom{|}} 1 {\:\phantom{|}} 4}$
$-\!\!\!\!$
$4$
$2$
$\color{lightgray}\downarrow$
$0$
$\color{lightgray}1$
Write over hundreds: $\color{blue}1$
Multiply: $42 \times {\color{blue}1} = 42$
Subtract: ${\color{red}42} - 42 = 0$
Bring down: $1$
Since $42$ goes $\color{blue}0$ times into ${\color{red}1}$, we need to bring one more digit down. Hence, we get:
$1$
$\color{blue}0$
$42$
$\!\!\require{enclose}\enclose{longdiv}{4 {\:\phantom{|}} 2 {\:\phantom{|}} 1 {\:\phantom{|}} 4}$
$-\!\!\!\!$
$4$
$2$
$\color{lightgray}\downarrow$
$0$
$\color{red}1$
$\color{lightgray}4$
Write over tens: $\color{blue}0$
Bring down: $4$
Finally, notice that $42$ goes $\color{blue}0$ times into ${\color{red}14}.$ Hence, ${\color{red}14}$ is the remainder and we get:
$1$
$0$
$\color{blue}0$
$42$
$\!\!\require{enclose}\enclose{longdiv}{4 {\:\phantom{|}} 2 {\:\phantom{|}} 1 {\:\phantom{|}} 4}$
$-\!\!\!\!$
$4$
$2$
$0$
$\color{red}1$
$\color{red}4$
Write over ones: $\color{blue}0$
We've gone through all the digits in the number $ 4,214,$ so the division is done. Since we have a remainder of $14$, we conclude that
\[
4,214 \div 42 = 100\,\text{R}\,14.
\]
Therefore, the quotient is $100.$
Find the remainder of
3,528 \div 34.
We start by writing down the question using long division notation:
34
\!\require{enclose}\enclose{longdiv}{3 {\:\phantom{|}} 5 {\:\phantom{|}} 2 {\:\phantom{|}} 8}
Next, we consider the thousands and hundreds. Notice that
34
goes
{\color{blue}1}
time into
{\color{red}35}.
So, we get:
\color{blue}1
34
\!\require{enclose}\enclose{longdiv}{{\color{red}3} {\:\phantom{|}} {\color{red}5} {\:\phantom{|}} 2 {\:\phantom{|}} 8}
-\!\!\!\!
3
4
\color{lightgray}\downarrow
1
\color{lightgray}2
Write over hundreds:
\color{blue}1
Multiply:
34 \times {\color{blue}1} = 34
Subtract:
{\color{red}35} - 34 = 1
Bring down:
2
Since
34
goes
{\color{blue}0}
times into
{\color{red}12}
, we need to bring one more digit down. So, we get:
1
\color{blue}0
34
\!\require{enclose}\enclose{longdiv}{3 {\:\phantom{|}} 5 {\:\phantom{|}} 2 {\:\phantom{|}} 8}
-\!\!\!\!
3
4
\color{lightgray}\downarrow
\color{red}1
\color{red}2
\color{lightgray}8
Write over tens:
\color{blue}0
Bring down:
8
Finally, notice that
34
goes
{\color{blue}3}
times into
{\color{red}128}.
So, we get:
1
0
\color{blue}3
34
\!\require{enclose}\enclose{longdiv}{3 {\:\phantom{|}} 5 {\:\phantom{|}} 2 {\:\phantom{|}} 8}
-\!\!\!\!
3
4
\color{red}1
\color{red}2
\color{red}8
-\!\!\!\!
1
0
2
2
6
Write over ones:
\color{blue}3
Multiply:
34 \times {\color{blue}3} = 102
Subtract:
{\color{red}128} - 102 = 26
We've gone through all the digits in the number
3,528
, so the division is done.
Therefore,
3,528 \div 34 = 103\,\text{R}\,26 \, .
So, the remainder is
{\color{black}26}.
What is the remainder of $7,231 \div 36?$
a
$200$
b
$31$
c
$39$
d
$37$
e
$29$
We start by writing down the question using long division notation:
$36$
$\!\!\require{enclose}\enclose{longdiv}{7 {\:\phantom{|}} 2 {\:\phantom{|}} 3 {\:\phantom{|}} 1}$
Next, we consider the thousands and hundreds. Notice that $36$ goes ${\color{blue}2}$ times into ${\color{red}72}.$ Hence, we get:
$\color{blue}2$
$36$
$\!\!\require{enclose}\enclose{longdiv}{{\color{red}7} {\:\phantom{|}} {\color{red}2} {\:\phantom{|}} 3 {\:\phantom{|}} 1}$
$-\!\!\!\!$
$7$
$2$
$\color{lightgray}\downarrow$
$0$
$\color{lightgray}3$
Write over hundreds: $\color{blue}2$
Multiply: $36 \times {\color{blue}2} = 72$
Subtract: ${\color{red}72} - 72 = 0$
Bring down: $3$
Since $36$ goes ${\color{blue}0}$ times into ${\color{red}3}$, we need to bring one more digit down. Hence, we get:
$2$
$\color{blue}0$
$36$
$\!\!\require{enclose}\enclose{longdiv}{7 {\:\phantom{|}} 2 {\:\phantom{|}} 3 {\:\phantom{|}} 1}$
$-\!\!\!\!$
$7$
$2$
$\color{lightgray}\downarrow$
$0$
$\color{red}3$
$\color{lightgray}1$
Write over tens: $\color{blue}0$
Bring down: $1$
Finally, notice that $36$ goes ${\color{blue}0}$ times into ${\color{red}31}.$ Hence, ${\color{red}31}$ is the remainder and we get:
$2$
$0$
$\color{blue}0$
$36$
$\!\!\require{enclose}\enclose{longdiv}{7 {\:\phantom{|}} 2 {\:\phantom{|}} 3 {\:\phantom{|}} 1}$
$-\!\!\!\!$
$7$
$2$
$0$
$\color{red}3$
$\color{red}1$
Write over ones: $\color{blue}0$
We've gone through all the digits in the number $7,231$, so the division is done.
Therefore,
\[
7,231 \div 36 = 200\,\text{R}\,31.
\]
So, the remainder is $31.$
Find the remainder of $2,550 \div 24.$
a
$6$
b
$26$
c
$18$
d
$1$
e
$8$
We start by writing down the question using long division notation:
$24$
$\!\!\require{enclose}\enclose{longdiv}{2 {\:\phantom{|}} 5 {\:\phantom{|}} 5 {\:\phantom{|}} 0}$
Next, we consider the thousands and hundreds. Notice that $24$ goes ${\color{blue}1}$ times into ${\color{red}25}.$ Hence, we get:
$\color{blue}1$
$24$
$\!\!\require{enclose}\enclose{longdiv}{{\color{red}2} {\:\phantom{|}} {\color{red}5} {\:\phantom{|}} 5 {\:\phantom{|}} 0}$
$-\!\!\!\!$
$2$
$4$
$\color{lightgray}\downarrow$
$1$
$\color{lightgray}5$
Write over hundreds: $\color{blue}1$
Multiply: $24 \times {\color{blue}1} = 24$
Subtract: ${\color{red}25} - 24 = 1$
Bring down: $5$
Since $24$ goes ${\color{blue}0}$ times into ${\color{red}15}$, we need to bring one more digit down. Hence, we get:
$1$
$\color{blue}0$
$24$
$\!\!\require{enclose}\enclose{longdiv}{2 {\:\phantom{|}} 5 {\:\phantom{|}} 5 {\:\phantom{|}} 0}$
$-\!\!\!\!$
$2$
$4$
$\color{lightgray}\downarrow$
$\color{red}1$
$\color{red}5$
$\color{lightgray}0$
Write over tens: $\color{blue}0$
Bring down: $0$
Finally, notice that $24$ goes ${\color{blue}6}$ times into ${\color{red}150}.$ Hence, we get:
$1$
$0$
$\color{blue}6$
$24$
$\!\!\require{enclose}\enclose{longdiv}{2 {\:\phantom{|}} 5 {\:\phantom{|}} 5 {\:\phantom{|}} 0}$
$-\!\!\!\!$
$2$
$4$
$\color{red}1$
$\color{red}5$
$\color{red}0$
$-\!\!\!\!$
$1$
$4$
$4$
$6$
Write over ones: $\color{blue}6$
Multiply: $24 \times {\color{blue}6} = 144$
Subtract: ${\color{red}150} - 144 = 6$
We've gone through all the digits in the number $2,550$, so the division is done.
Therefore,
\[
2,550 \div 24 = 106\,\text{R}\,6.
\]
So, the remainder is $6.$
Sometimes, we need to consider the thousands, hundreds, and tens digits in the first step when applying the standard algorithm.
To illustrate, let's calculate
1,967 \div 28.
We start by writing down the question using long division notation:
28
\!\require{enclose}\enclose{longdiv}{1 {\:\phantom{|}} 9 {\:\phantom{|}} 6 {\:\phantom{|}} 7}
Notice that
28
does not go into
19.
So, we need to consider the thousands, hundreds, and tens.
Now, we see that
28
goes
{\color{blue}7}
times into
{\color{red}196}.
So, we get:
\color{blue}7
28
\!\require{enclose}\enclose{longdiv}{{\color{red}1} {\:\phantom{|}} {\color{red}9} {\:\phantom{|}} {\color{red}6} {\:\phantom{|}} 7}
-\!\!\!\!
1
9
6
\color{lightgray}\downarrow
0
\color{lightgray}7
Write over tens:
\color{blue}7
Multiply:
28 \times {\color{blue}7} = 196
Subtract:
{\color{red}196} - 196 = 0
Bring down:
7
Finally, notice that
28
goes
{\color{blue}0}
times into
{\color{red}7}.
So
\color{red}7
is the remainder and we get:
7
\color{blue}0
28
\!\require{enclose}\enclose{longdiv}{1 {\:\phantom{|}} 9 {\:\phantom{|}} 6 {\:\phantom{|}} 7}
-\!\!\!\!
1
9
6
0
\color{red}7
Write over ones:
\color{blue}0
We've gone through all the digits, so the division is done.
Therefore,
1,967 \div 28 = 70\,\text{R}\,7 \, .
Find the quotient of
3,755 \div 65.
We start by writing down the question using long division notation:
65
\!\require{enclose}\enclose{longdiv}{3 {\:\phantom{|}} 7 {\:\phantom{|}} 5 {\:\phantom{|}} 5}
Since
65
does not go into
37
, we consider the thousands, hundreds and tens. Notice that
65
goes
{\color{blue}5}
times into
{\color{red}375}.
So, we get:
\color{blue}5
65
\!\require{enclose}\enclose{longdiv}{{\color{red}3} {\:\phantom{|}} {\color{red}7} {\:\phantom{|}} {\color{red}5} {\:\phantom{|}} 5}
-\!\!\!\!
3
2
5
\color{lightgray}\downarrow
5
0
\color{lightgray}5
Write over tens:
\color{blue}5
Multiply:
65 \times {\color{blue}5} = 325
Subtract:
{\color{red}375} - 325 = 50
Bring down:
5
Finally, notice that
65
goes
{\color{blue}7}
times into
{\color{red}505}.
So, we get:
5
\color{blue}7
65
\!\require{enclose}\enclose{longdiv}{3 {\:\phantom{|}} 7 {\:\phantom{|}} 5 {\:\phantom{|}} 5}
-\!\!\!\!
3
2
5
\color{red}5
\color{red}0
\color{red}5
-\!\!\!\!
4
5
5
5
0
Write over ones:
\color{blue}7
Multiply:
65 \times {\color{blue}7} = 455
Subtract:
{\color{red}505} - 455 = 50
We've gone through all the digits in the number
3,755
, so the division is done.
So,
3,755 \div 65 = 57\,\text{R}\,50 \, .
Therefore, the quotient is
57.
What is the quotient of $1,058 \div 35?$
a
$38$
b
$40$
c
$30$
d
$28$
e
$32$
We start by writing down the question using long division notation:
$35$
$\!\!\require{enclose}\enclose{longdiv}{1 {\:\phantom{|}} 0 {\:\phantom{|}} 5 {\:\phantom{|}} 8}$
Since $35$ does not go into $10$, we consider the thousands, hundreds and tens. Notice that $35$ goes ${\color{blue}3}$ times into ${\color{red}{105}}.$ Hence, we get:
$\color{blue}3$
$35$
$\!\!\require{enclose}\enclose{longdiv}{{\color{red}1} {\:\phantom{|}} {\color{red}0} {\:\phantom{|}} {\color{red}5} {\:\phantom{|}} 8}$
$-\!\!\!\!$
$1$
$0$
$5$
$\color{lightgray}\downarrow$
$0$
$\color{lightgray}8$
Write over tens: $\color{blue}3$
Multiply: $35 \times {\color{blue}3} = 105$
Subtract: ${\color{red}105} - 105 = 0$
Bring down: $8$
Finally, notice that $35$ goes ${\color{blue}0}$ times into ${\color{red}{8}}.$ Hence, $\color{red}8$ is the remainder and we get:
$3$
$\color{blue}0$
$35$
$\!\!\require{enclose}\enclose{longdiv}{1 {\:\phantom{|}} 0 {\:\phantom{|}} 5 {\:\phantom{|}} 8}$
$-\!\!\!\!$
$1$
$0$
$5$
$0$
$\color{red}8$
Write over ones: $\color{blue}0$
We've gone through all the digits in the number $1,058$, so the division is done.
Therefore,
\[
1,058 \div 35 = 30\,\text{R}\,8.
\]
So, the quotient is $30.$
What is the value of of $2,052 \div 57?$
a
$38$
b
$35$
c
$34$
d
$36$
e
$37$
We start by writing down the question using long division notation:
$57$
$\!\!\require{enclose}\enclose{longdiv}{2 {\:\phantom{|}} 0 {\:\phantom{|}} 5 {\:\phantom{|}} 2}$
Since $57$ does not go into $20$, we consider the thousands, hundreds and tens. Notice that $57$ goes ${\color{blue}3}$ times into ${\color{red}205}.$ Hence, we get:
$\color{blue}3$
$57$
$\!\!\require{enclose}\enclose{longdiv}{{\color{red}2} {\:\phantom{|}} {\color{red}0} {\:\phantom{|}} {\color{red}5} {\:\phantom{|}} 2}$
$-\!\!\!\!$
$1$
$7$
$1$
$\color{lightgray}\downarrow$
$3$
$4$
$\color{lightgray}2$
Write over tens: $\color{blue}3$
Multiply: $57 \times {\color{blue}3} = 171$
Subtract: ${\color{red}205} - 171 = 34$
Bring down: $2$
Finally, notice that $57$ goes ${\color{blue}6}$ times into ${\color{red}342}.$ Hence, we get:
$3$
$\color{blue}6$
$57$
$\!\!\require{enclose}\enclose{longdiv}{2 {\:\phantom{|}} 0 {\:\phantom{|}} 5 {\:\phantom{|}} 2}$
$-\!\!\!\!$
$1$
$7$
$1$
$\color{red}3$
$\color{red}4$
$\color{red}2$
$-\!\!\!\!$
$3$
$4$
$2$
$0$
Write over ones: $\color{blue}6$
Multiply: $57 \times {\color{blue}6} = 342$
Subtract: ${\color{red}342} - 342 = 0$
We've gone through all the digits in the number $2,052$, so the division is done.
Therefore,
\[
2,052 \div 57 = 36.
\]
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