Download Long Division

Common
Core
Aligned
Name________________
Practice Sheet
Understand division terms
and meanings
Fundamental skill to
4.NBT.6
Vocabulary:
1. divisor ~ the number of groups to divide into
2. dividend ~ the number to be divided
3. quotient ~ the answer to a division problem
There are 3 ways division problems can be written:
Ex. 1
divisor
Ex. 2
quotient
28 ÷ 4 = 7
dividend
4
quotient
divisor
7
28
dividend
Application:
Ex. 3
dividend
divisor
28
4 =7
quotient
dividend
divisor
42
7 =6
divisor: ____
dividend: ____
quotient:____
=
÷
_________
__________
quotient
_________
A. 100 pushups
1,000 pushupsA
Elle’ plantsB. 20 flowers
in 5 rows. She
C. 4 flowers
10,000 pushups
will have
in each row.
D. 20,000 pushups
divisor:_____ dividend:_____ quotient:______
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4.NBT.6
Page 1
Name________________
Practice Sheet
Understand meaning
of division
Fundamental skill to
4.NBT.6
Meaning of division:
Divide a number to find equal groups.
Peter has 12 calculators. He is sharing them equally with the 4 groups in
his class. How many calculators should each group get?
Think:
Put 12 calculators into 4 equal groups. How many calculators are
in each group?
Show:
4 equal groups
Write:
The equation is 12 ÷ 4 = 3.
Draw pictures to solve
Vicky has 24 candles to
put in 6 boxes. How many
candles will be in each
box?
You need to arrange 32
chairs into 8 rows. How
many chairs will be in each
row?
______ ÷ _______ = _________
______ ÷ _______ = _________
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Chris makes 4 bracelets using 28
rubber bands. He uses an equal
number of rubber bands on each
bracelet. How many rubber bands
will he have on each bracelet?
_____ ÷ _____ = ________
4.NBT6
Page 2
Name________________
Practice Sheet
Relating multiplication
& division
Fundamental skill
Multiplication and division are related:
Multiplication and division share the same fact families,
just like addition and subtraction share the same fact families.
Ex. 5 x 8 = 40
8 x 5 = 40
40 ÷ 8 = 5
40 ÷ 5 = 8
Multiplication and division are inverse
operations. They undo each other.
Complete each fact family:
1.
6x
48 ÷
= 48
=
2.
X 6 = 54
54 ÷ =
Use inverse of multiplication to divide:
Solve 42 ÷ 6
Think
6 x what = 42
Say
Answer
6 x 7 = 42
42 ÷ 6 = 7
Find the quotients:
1.
21 ÷ 3 = ___
2.
30 ÷ 6 = ___
3.
18 ÷ 2 = ___
4.
72 ÷ 8 = ___
5.
16 ÷ 4 = ___
6.
40 ÷ 5 = ___
7.
56 ÷ 8 = ___
8.
49 ÷ 7 = ___
9.
64 ÷ 8 = ___
10. 54 ÷ 9 = ___
11.
48 ÷ 6 = ___
12. 84 ÷ 7 = ___
13. 20 ÷ 5 = ___
14.
24 ÷ 6 = ___
15. 35 ÷ 7 = ___
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4.NBT.6
Page 3
Name________________
Practice Sheet
Dividing using
place-value, mental
math, and
multiples
Divide using patterns:
35 ÷ 5 = 7
350 ÷ 5 = 70
3,500 ÷ 5 = 700
35,000 ÷ 5 = 7,000
20 ÷ 5 = ____
200 ÷ 5 =_____
2,000 ÷ 5 =_____
20,000 ÷ 5 =______
18 ÷ 3 =_____
180 ÷ 3 =_____
1,800 ÷ 3 =_____
18,000 ÷ 3 =____
42 ÷ 6 = 7
420 ÷ 6 = 70
4,200 ÷ 6 = 700
42,000 ÷ 6 = 7,000
25 ÷ 5 =____
250 ÷ 5 =_____
2,500 ÷ 5 =_____
25,000 ÷ 5 =_____
27 ÷ 3 =_____
270 ÷ 3 =_____
2,700 ÷ 3 =____
27,000 ÷ 3 =____
Divide using mental math/multiples:
1.
4.
7.
10.
240 ÷ 4 = ___
400 ÷ 4 = ___
360 ÷ 6 = ___
150 ÷ 5 = ___
2.
5.
8.
11.
1,000 ÷ 2 = ___
7,200 ÷ 8 = ___
45,000 ÷ 5 = ___
18,000 ÷ 6 = ___
3.
6.
9.
12.
300 ÷ 6 =___
540 ÷ 9 =___
4,200 ÷7 =___
3,000 ÷5 =___
13. Trisha bought a pack of goldfish
14. Sydney sold 300 cups of lemonade
at the store. There are 240 goldfish
in the pack. She wants to split the
goldfish equally between her four
friends. How many goldfish should
each friend get?
in five hours. She sold an equal
amount of cups per hour. How many
cups of lemonade did she sell each
hour?
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4.NBT.6
Page 4
Name________________
Practice Sheet
Dividing with
remainders
Divide with Remainders
The remainder is the part that is left over in a division problem.
Tony is arranging 22 trophies onto 4 shelves so
that each shelf has the same number of
trophies. How many trophies are on each shelf?
How many trophies are left over?
Solve: 22 ÷ 4
Show
Think
25 ÷ 7 = __r_
2. 73 ÷ 8 = __r_
3. 13 ÷ 2 = __r_
4. 58 ÷ 8 = __r_
5. 26 ÷ 5 = __r_
6. 33 ÷ 4 = __r_
7. 28 ÷ 6 = __r_
8. 48 ÷ 5 = __r_
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22 ÷ 4 = 5 R 2
5 x 4 = 20
Divide:
1.
Write
22 ÷ 4 =
5 x 4 = 20 so
22÷ 4 = 5 with 2 left
over
4
5
The remainder should
always be less than
the divisor.
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9. Gabrielle has 23 lollipops to
share with her 5 friends. She
will eat the left over lollipops.
How many lollipops will each
friend get? How many lollipops
will Gabrielle get?
4.NBT.6
Page 5
Name________________
Practice Sheet
Identify division terms
and divide using place
value, multiplication,
and pictures
Put It All Together
Label the quotient, divisor, and dividend.
8
6 48
56 ÷ 8 = 7
Divide using mental math:
360 ÷ 6 = ___ 720 ÷ 9 = ___
Complete each:
6x
24 ÷
= 24
=6
400 ÷ 8 = ___ 180 ÷ 2 = ___
Find the inverse:
21 ÷ 3 = 7
45 ÷ 9 =
56 ÷ 7 =
84 ÷ 7 =
35 ÷ 5 =
18 ÷ 3 =
250 ÷ 5 = ___ 420 ÷ 7 = ___
8x
= 48
48 ÷ 8 =
Divide using patterns:
Draw a picture to solve:
42 ÷ 7 = ___
420 ÷ 7 = ____
4,200 ÷ 7 = _____
42,000 ÷ 7 = ______
Cheryl has 16 beads. She
uses 4 beads to make one
pair of earrings. How many
pairs of earrings can she
make?
(because 3 x 7 = 21)
_____
_____
_____
_____
_____
Gavin has 55 Skittles. He has
an equal number of red,
orange, yellow, green, and
purple. How many of each
color does Gavin have?
Divide with remainders:
20 ÷ 8 = ____R__
36 ÷ 5 = ____R__
19 ÷ 4 = ____R__
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4.NBT.6
Page 6
Name________________
Practice Sheet
Use multiples to
estimate quotients.
Estimate Quotients Using Multiples
Step 1:
Think of multiples of
the divisor. Ex: 6, 12, 18, 24
Step 2: Underline the two multiples the
dividend falls between.
Ex: 136: 13 is between 12 and 18
Step 3: Estimate the quotient.
Ex: 136 is about 20
Find two numbers the quotient is between.
Then, estimate the quotient.
3 x 30 = 90 & 3 x 40 = 120
9 x 20 = 180 & 9 x 30 = 270
107 ÷ 8 =
3
. 8 x 10 = 80 & 8 x 20 = 160
95 is closer to 90
than it is to 120, so
95 ÷ 3 is about 30
255 is closer to 270
than it is to 180, so
255 ÷ 9 is about 30
107 is closer to ___
than it is to___, so
107 ÷ 8 is about ___.
1
4
95 ÷ 3 =
272 ÷ 5 =
255 ÷ 9 =
2
347 ÷ 7 =
5
5x_=_ & 5x_=_
7x_=_ & 7x_=_
272 ÷ 5 is about ___
347 ÷ 7 is about ___
7
73 ÷ 4 =
377 ÷ 6 =
8
58 ÷ 3 =
6
. 3x_=_ & 3x_=_
58 ÷ 3 is about ___
9
179 ÷ 2 =
4x_=_ & 4x_=_
6x_=_ & 6x_=_
2x_=_ & 2x_=_
73 ÷ 4 is about ___
377 ÷ 6 is about ___
179 ÷ 2 is about ___
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4.NBT.6
Page 7
Name________________
Practice Sheet
Divide using baseand
Use ten
theblocks
distributive
place value.
property
with
pictures to find
quotients
Divide Using Distributive Property with Pictures
Step 1:
Step 2:
Draw a picture to show dividend.
Ex:
65 ÷ 5
Think about the best way to
break apart the dividend.
1
Step 3: Draw circles to show
5 tens ÷ 5 & 15 ones ÷ 5
2 &3
(50 ÷ 5) +
(15 ÷ 5)
5 tens ÷ 5 15 ones ÷ 5
Step 4: Add the partial quotients.
111111 .
11111
4 (50 ÷ 5) + (15 ÷ 5)
Use pictures to model the quotient.
1
10
2
84 ÷ 4 =
7 x ( ___ + ___ + ___ + __
3
....
... ... ... ... ...
21 ÷ 3 =
4
+
3
= 13
62 ÷ 2 =
96 ÷ 6 =
(7 x ___) + (7 x ___) +
+ ____ + ____ + ___ + ___ = _____
5. Choose the correct distributive form for 78 ÷ 6
A.
(60 ÷ 6) + (18 ÷ 6)
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B.
(70 ÷ 6) + (8 ÷ 6)
4.NBT.6
Page 8
Name________________
Practice Sheet
Divide Using Distributive Property with Area Models
Use the distributive
property with area
models to find
quotients
81 ÷ 3 = (60 ÷ 3) + (21 ÷ 3)
= 20 + 7
60
21
= 27
10
8
54 ÷ 3 = (30 ÷ 3) + (24 ÷ 3)
= 10 + 8
30
3
24
= 18
Find the quotient using the distributive property.
1
2
42 ÷ 3
52 ÷ 4
3
30
70 ÷ 5
4
_
90 ÷ 6
_+
____
4.NBT.6
Page 9
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Name________________
Practice Sheet
Use the partial
products to find
quotients.
Divide using Partial Quotients
Step
Step
Step
Step
1:
2:
3:
4:
Subtract multiples of hundreds first.
Subtract multiples of tens.
Subtract multiples of ones.
Add partial quotients to get final quotient.
Example 1
Find the quotient using partial products.
1
2
30
__
6 684
4 71655
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Example 2
3
3 435
4.NBT.6
Page 10
Name________________
Practice Sheet
Use pictures,
distributive property,
and partial products
to find quotients.
Put It All Together
Use pictures to model the quotient.
1
96 ÷ 3 =
2
48 ÷ 2 =
Find the quotient using the distributive property.
3
4
56 ÷ 4
85 ÷ 5
Find the quotient using partial products.
5
6
30
__
5 745
2 86455
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7
7 924
4.NBT.6
Page 11
Name________________
Practice Sheet
Divide Using the Traditional Method: “Long Division”
Use the traditional
algorithm (long
division) to find
quotients.
4.NBT.6
Page 12
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Name________________
Practice Sheet
Use the traditional
algorithm (long
division) to find
quotients.
Divide Using the Traditional Method
Dad (divide) ~ Mom (multiply) ~ Sister (subtract)
Brother (bring down) ~ Rover (remainder/repeat)
Find the quotient using the traditional algorithm. Then, multiply to check.
1
Ex 1 3 6 R 0
2
30
__
4 544 Multiply to
5 667
2 47855
-4
check.
-_
-_
__
14
__
-__
-__
-12
1 36
__
__
24
x 4
-__
-__
- 24
54 4
__
__
0
3
30
__
4
30
8 92335
__
5
4 59255
7 898
6. Oak Grove Elementary School has 546 students in 2nd, 3rd,
and 4th grade. If there are an equal number of students in
each grade, how many students are in 4th grade?
4.NBT.6
Page 13
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Name________________
Practice Sheet
Use the traditional
algorithm (long
division) to find
quotients.
Divide Using the Traditional Method
Dad (divide) ~ Mom (multiply) ~ Sister (subtract)
Brother (bring down) ~ Rover (remainder/repeat)
Find the quotient using the traditional algorithm. Then, multiply to check.
1
Ex 1 3 5 6 R 2
2
30
__
4 5426 Multiply to
5 6025
2 374655
-4
check:
14
-12
1356
22
x 4
- 20
5424
26 + 2
- 24
5426
2
3
30
__
4
30
8 381235
__
3 485455
5
9 2893
4.NBT.6
Page 14
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Name________________
Practice Sheet
Put It All Together: Estimate the quotient, solve using
Estimate quotients and
use partial products
and traditional
algorithm to find
quotients.
partial quotients & traditional algorithm, and check with multiplication.
Estimate
Partial Quotients
Traditional
Check
1 36 R 3
Ex
30 __
136
4
547
4
547
547 ÷ 4 = ___
x 4
- 400 4x100=400
-4
40, 44, 48, 52, 56
544
1 47
14
-----------+ 3
- 1 20 4x30=120
4 x 130 = 520 &
-12
547
27
4 x 140 = 560
27
- 24 4x6 = 24
- 24
547 is closer to 560
3
than it is to 520, so
3
100+30+6 = 136 R3
547 ÷ 4 is about 140
1
30 __
348 ÷ 3 = ___
2
3 348
3 348
30 __
728 ÷ 5 = ___
5 728
5 728
4.NBT.6
Page 15
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Name________________
Practice Sheet
Solve word
problems to find
quotients.
Word Problem Practice
Solve the problems below using your method of choice.
Gregory earned $84
dollars mowing lawns.
If he charges $7 per lawn,
how many lawns did he mow?
1
Mrs. Baker made 4 cherry
3 pies with the same number
of cherries in each pie. If
she used 632 cherries in all,
how many cherries were in
each pie?
Mallory is sharing candy
5 with her 7 friends. She
has 38 pieces of candy. If
she gives each friend the
same amount and she eats the
leftovers, how many pieces of
candy will Mallory get?
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family stayed at a
2 Ahotel
for 6 nights, and
their bill was $738. What
was the cost of the hotel
room for each night?
bought 4 pairs
4 Richard
of jeans and he spent
$128. If each pair of jeans
was same price, what was
the price for one pair of
jeans?
6 Write your own division word
problem and solve it. 
4.NBT.6
Page 16
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