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WRITTEN DIVISION
Two ticket for a boat ride €2,684. How much does one ticket cost?
€?
€?
€
€?
We can do the division in writing.
We start division with the number with the largest
Mark the two thousands: 2’684. 2 T
divided by 2 is 1 T, since 1 T \latex{ \times } 2 = 2 E. 0
thousands are needed to 2 T to make 2 T.
∙
Mark the number in the next place value
and write it by the remainder from the
thousands. 6 h divided by 2 is 3 h, since
∙
3 h \latex{ \times } 2 = 6 h. 0 hundredts are needed to
Mark the number in the next place
value and writ it by the remainder from
the hundreds. 8 t divided by 2 is 4 t,
since 4 t \latex{ \times } 2 = 8 t. 0 tens are needed to
8 t to make 8 t.
∙
Mark the number in the next place
value and write it by the remainder
from the tens. 4 u divided by 2 is 2 u,
since 2 u \latex{ \times } 2 = 4 u. 0 units are needed
to 4 u to make 4 u.
∙
T
h
t
u
T
h
t
u
The quotient is
.
Check the result by written multiplicaiton.
Check:
One ticket costs €
.
\latex{ \div } 2 =
2'
6'
8'
4'
1
3
4
2
\latex{ - }2
0
6
\latex{ - }6
0
8
\latex{ - }8
0
4
\latex{ - }4
0
1 T \latex{ \times } 2
3 h \latex{ \times } 2
4 t \latex{ \times } 2
2 u \latex{ \times } 2
1342·2
tickets
ticket
€
6 h to make 6 h.
place value.
{{exercise_number}}.
Complete the written divisions. Check your answer with written multiplication.
Estimate the number of digits in the quotient. 6 hundreds divided by 3 is 2 hundreds, so the
quotient will have three digits. Use dots to show the place value of the quotient.
693÷3=
264÷2=
628÷2=
C:
C:
C:
·3
The quotient will have three digits. Mark the digits first.
∙
7 h divided by 3 is 2 h, since 2 h \latex{ \times} 3 = 6 h. 1 h is needed to
make 7 h from 6 h.
∙
Write down the tens digit (5) next, to the remainder in the
hundreds place. 1 h = 10 t, 15 t divided by 3 is 5 t, since
5 t \latex{ \times } 3 = 15 t. 0 t is needed to 15 t to make 15 t.
∙
Write down the units digit 3 next to the 0. 3 u divided by 3
is 1 u, since 1 u \latex{ \times } 3 = 3 u. 0 u is needed to 3 u to make 3 u.
What is the quotient if the dividend is 753 and the divisor is 3?
Check:
251·3
753
7
5
3
-6
15
-15
03
-3
0
÷3=
2
5
1
{{exercise_number}}. Estimate how many digits the quotient will have. Complete the written divisions. Check with multiplication.
a)
b)
526÷2=
729÷3=
452÷2=
6,274 \latex{ \div } 2
5,684 \latex{ \div } 4
9,513 \latex{ \div } 3
4,924 \latex{ \div } 4
3,864 \latex{ \div } 2
{{exercise_number}}. Write the quotients in the right parts of the set diagram.
1 is in the hundreds place value
It is 2,000 rounded to thousands
4,382 \latex{ \div } 2
5,139 \latex{ \div } 3
4,684 \latex{ \div } 4
585 \latex{ \div } 5
3,354 \latex{ \div } 3
=
=
=
=
=
{{exercise_number}}.
- Which one is more? Use the right relational sign.
6,586 \latex{ \div } 2
9,513 \latex{ \div } 3
3,642 \latex{ \div } 2
8,476 \latex{ \div } 4
726 \latex{ \div } 6
655 \latex{ \div } 5
∙
b) Which number did I think of?
twice the number is 6,724.
∙
Half of six times the number is 423.
\latex{ \times } 2
\latex{ \div } 2
6,724
423
\latex{ \times }
\latex{ \times }
\latex{ \div }
\latex{ \div }
When dividing in writing we can have remainders at several place values.
T
h
t
u
T
h
t
u
4'
8'
1'
2'
\latex{ \div } 3 =
1
6
0
4
.
.
.
.
\latex{ - }3
1
\latex{ - }1
8
8
0
1
\latex{ - }0
1
\latex{ - }1
2
2
0
4812÷3=1604
-3
18
-18
01
-0
12
-12
0
.
.
.
.
Check:
1604·3
4812
{{exercise_number}}. Estimate how many digits the quotient will have. Complete the written divisions. Check your answers with written multiplication.
5718÷2=
4326÷3=
952÷4=
C:
C:
C:
Written division can be written in a short form, if the remainders are done in your head.
T
h
t
u
T
h
t
u
4'
8'
1'
2'
\latex{ \div } 3 =
1
6
0
4
1
8
0
1
1
2
0
.
.
.
.
4812÷3=1604
18
01
12
0
Check:
1604·3
4812
.
.
.
.
{{exercise_number}}. Do the written divisions. Estimate how many digits the quotient will have first, then check your answer.
792÷3=
8736÷4=
8757÷7=
C:
C:
C:
{{exercise_number}}. Which numbers make the statements true?
4,564 \latex{ \div } 4 <
2,358 \latex{ \div } 2 >
6,275 \latex{ \div } 5 <
< 4,842 \latex{ \div } 3
:
:
:
,
,
,
...
,
,
,
,
,
,
...
...
{{exercise_number}}. Complete the written multiplications, check them with written division.
E:
C:
1189·4
137·5
2821·3
{{exercise_number}}.Complete the written divisions. Pay attention to the \latex{ 0 } digits!
5,019 \latex{ \div } 3
4,828 \latex{ \div } 4
4,156 \latex{ \div } 4
7,470 \latex{ \div } 6
6,516 \latex{ \div } 3
{{exercise_number}}. Count according to the arrows.
5,736
\latex{ \div }3
\latex{ \div }2
\latex{ \div }2
\latex{ \times }4
\latex{ \times }5
{{exercise_number}}. Use the digits 2, 4, 5 and 7 to make numbers greater than 3,000, but less than 6,000 without repeating the digits.
a) Divide the even numbers by 2. b) Divide the odd numbers by 3.
{{exercise_number}}. Solve the written exercises.
a) 3 tubes of toothpaste cost €8, 2 shampoos cost €10. What costs more, 1 sampoo
or 1 toothpaste?
b) Teams of 4 participate in the academic competition. How many teams were there, if
524 students participated?
c) Half of the people in a town are members of the
library. How many people are members if there
are 7,278 people in town? On third of library members
are retired. How many retired members are there?
d) Victor read fourth of a 552 page book. How many
pages are left?
e) Third of a school’s students studies german the others
study Spanish. If there are 534 students, how many
study each language?
They pack rolls at a bakery in packs of 5.
How many packs can they make from 576 rolls?
576 \latex{ \div } 5 =
If the remainder is not 0 during division,
then during checking we get the divisor
by adding the remainder to the product.
576 divided by 5
is 115 and the
remainder is 1.
115 packs were made 1 roll was left out.
Check:
rolls
1 pack
number of packs
576
5
?
h
t
u
h
t
u
5'
7'
6'
\latex{ \div } 5 =
1
1
5
.
.
.
0
7
2
6
1
115·5
575
575+1=576
{{exercise_number}}. Esimate how many digits the quotient will have. Complete the divisions with remainders. Check with multiplications.
a)
b)
8957÷3=
978÷5=
678÷4=
C:
9,473 \latex{ \div } 9
8,795 \latex{ \div } 7
893 \latex{ \div } 8
7,275 \latex{ \div } 6
5,729 \latex{ \div } 2
{{exercise_number}}. Fill out the tables.
dividend
divisor
quotient
remainder
remainder
dividend
divisor
quotient
7,003
8,914
7
4
2
6
1,523
3,457
1
4
{{exercise_number}}. Solve the written exercises.
a) At a hardware store they pack screws in packs of 5.
How many packs do 648 screws go in?
b) At a shop, they put 4 balls of yarn in a bag. How many
bags can they make from 653 balls of yarn?
c) Packing eggs by 6, 128 boxes were filled and 4 eggs
were left over. How many eggs were there?
What is the quotient if the dividend is 4,515 and the divisor is 6?
Since 4 T divided by 6 is less than 1 T the quotient will have
three digits.
Divide the thousands along with the hundreds. 4 T = 40 h, 45 h
divided by 6 is 7 h, since 7 h \latex{ \times } 6 = 42 h, 3 h has to be added
to 42 h to make 45 h.
The quotient is 752.
Check:
4512÷6=752
31
12
0
752·6
4512
{{exercise_number}}.
- Estimate the number of digits in the quotient. Complete the written divisions. Check your answers with multiplication.
b) Complete the calculations, check them with the opposite operation.
3414÷6=
2757÷3=
472÷8=
504 \latex{ \times } 9
1,834 \latex{ \div } 8
1,012 \latex{ \div } 2
4,617 \latex{ \div } 2
749 \latex{ \times } 6
{{exercise_number}}. Complete the divisions. Colour the quotients the right colours.
5
7
4
6
1
5
2
9
4
1
6
2
4
4
8
7
0
8
1
5
0
0
3
7
5
1
6
5
0
5
1
3
7
3
9
4
7
9
2
9
0
5
1
6
6
2
8
5
5,649\latex{ \div }3
4,735\latex{ \div }5
3,032\latex{ \div }8
4,260\latex{ \div }4
8,715\latex{ \div }7
{{exercise_number}}. Determine the rule. Fill in the table.
A
B
C
3,741
5,584
6,942
4,030
9,128
3
8
6
5
4
7
8
9
1,247
698
1,157
853
1,207
1,034
C =
A =
{{exercise_number}}.
The remainder is always less than the divisor.
If one of the factors of the multiplication is 0, than the product is 0.
It is possible to divide by 0.
The product of the quotient and the divisor is always equal
to the dividend.
True or false? Circle the right letter.
The solution:
.
True
False
{{exercise_number}}.
a) On Monday they took 645 roses to market
in bouquets of three. How many bouquets
did they take to market?
b) On Friday they took twice as many roses,
tied in bouquets of five. How many more
bouquets did the take on Friday, than on
Monday?
Mike’s parents grow roses.
{{exercise_number}}. Angela got 5,716 at the end of a series of calculation. When checking the answer she noticed that she multiplied by 2, instead of dividing by 2. What was the correct answer?
{{exercise_number}}.
a) Linda’s dad is a truck driver. He drove 8,436 km during the first 3 months of the year.
On average, how much did he drive in one month?
The term average means, how many kilometres did he drive in one month, if he
drove the same amount every month.
b) In the next quarter of the year, he made
precise records of how much he drove:
How many kilometres did he drive in one
month on average during this period?
To find the average of several terms, divide their sum, by the number of terms.
Altogether he drove this much during the second quarter:
km +
km +
km =
km
On average, during one month he drove:
km \latex{ \div } 3 =
km
April:
May:
June:
km \latex{ \div } 3 =
km
2,395 km
2,618 km
2,523 km
{{exercise_number}}. Calculate the averages of the numbers in the table.
numbers
average
average
numbers
3,491;2,913
456;719;547;354
1,756;1,757;1,758
1,349;2,047,1;965
{{exercise_number}}.
- There are 992 students at a lower school. On average, how many students are in one grade? What is the average class size, if there are 4 classes in every grade?
- 2,535 people visited an exhibit over a week. One third of the visitors arrived during the weekend. On average, how many people saw the exhibit on a weekday?
