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.

FLAG

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?

EXPLANATION

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.

FLAG

What is the value of $5,486 \div 26?$

a
$201$
b
$221$
c
$219$
d
$211$
e
$215$

$2,964 \div 26 =$

a
$117$
b
$118$
c
$114$
d
$115$
e
$116$

What is the quotient of 7,368 \div 73?

EXPLANATION

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.

FLAG

What is the quotient of $2,165 \div 24?$

a
$91$
b
$90$
c
$88$
d
$92$
e
$89$

What is the quotient of $4,214 \div 42?$

a
$110$
b
$101$
c
$111$
d
$100$
e
$114$

Find the remainder of 3,528 \div 34.

EXPLANATION

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}.

FLAG

What is the remainder of $7,231 \div 36?$

a
$200$
b
$31$
c
$39$
d
$37$
e
$29$

Find the remainder of $2,550 \div 24.$

a
$6$
b
$26$
c
$18$
d
$1$
e
$8$

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 \, .

FLAG

Find the quotient of 3,755 \div 65.

EXPLANATION

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.

FLAG

What is the quotient of $1,058 \div 35?$

a
$38$
b
$40$
c
$30$
d
$28$
e
$32$

What is the value of of $2,052 \div 57?$

a
$38$
b
$35$
c
$34$
d
$36$
e
$37$
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