Transcript Document

Good Afternoon!
Today we will be learning about
Dividing with decimal remainders
Let’s warm up :
Divide:
1) 42 ÷ 4
1) 10.5
2) 3.24
2) 25.93 ÷ 8
3) 23 ÷ 40
3) 0.575
4) 77.76 ÷ 15
4) 5.184
5) 84.21 ÷ 13
5) 6.48
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Let’s first review what we learnt about division in the
previous session before proceeding further.
There are four terms which describe the four numbers in a
division problem.
Dividend.
Divisor.
Quotient.
Remainder.
.
8
5)43
40
divisor 3
quotient
dividend
remainder
Dividend = Divisor X Quotient + Remainder
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Find 4.5 ÷ 3 .
Multiplication is repeated subtraction.
So, 4.5 ÷ 3 = 1.5
This can be represented on the number line as follows:
You can count backward in groups of 1.5.
4.5
0
1
1.5
2
3
1.5
4
5
1.5
There are 3 jumps of value 1.5 from 4.5 to 0.
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Review
Expressing the quotient as a decimal
3
5
17
-15
2
3.4
5
17.0
-15
20
-20
00
Divide 17 by 5.
There are no more digits in the dividend.
Place a decimal point and bring it up to the quotient.
Add a 0 onto the remainder.
Continue dividing. Add a 0 onto each remainder
until the division is exact. If the division is not
exact, round off the quotient to the required
number of decimal places.
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Review
The dividend less than the divisor
Divide 7 by 8.
The dividend 7 is less than the divisor 8.
0.875
8
7.0
-64
60
- 56
40
- 40
00
Place a decimal point and bring it up to the quotient.
Add a 0 onto the dividend.
Start dividing. Add a 0 onto each remainder
until the division is exact. If the division is
not exact, round off the quotient to the
required number of decimal places.
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Review
When the dividend is a decimal, and the
divisor a whole number
Divide: 7.64 ÷ 2
Division with decimals is easier to understand if the divisor
(the dividend is divided by the divisor) is a whole number.
STEP 1:
2
7.64
Place the divisor (2) before the
division bracket and place the
dividend (7.64) under it.
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Review
To divide a decimal by a whole number,
divide as you would for whole numbers.
STEP 2:
3.82
2
7.64
-6
16
-16
004
-4
0
Place a decimal point in the answer
so that it lines up with the decimal
point in the Dividend.
If after dividing you have a
remainder, add a zero to the dividend
and continue to divide until there is
no remainder or the decimals recur.
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Review
Divide: 8.66 ÷ 4
We can find the solution as follows:
Note:
2.165
4
8.66
-8
06
-4
26
-24
20
-20
00
We added a trailing zero to 8.66 when 4
would not divide into 2.
Adding a trailing zero (or zeros) to a
decimal number does not alter its value.
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Let’s start
When we are given a long division to do, sometimes
there will be numbers left over. These are known as
Remainders.
We can use the long division process to work out the
answer to a number of decimal places.
Division with decimals is easier to understand if the divisor
(the dividend is divided by the divisor) is a whole number.
If the divisor has a decimal in it, we can make it a whole
number by moving the decimal point the appropriate
number of places to the right.
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Divide: 5 ÷ 12.
Round to the nearest hundredths place.
Note: Since we must round to the hundredths place, we will
carry the answer out 1 place beyond the hundredths place.)
 Place the numbers in the division equation format.
12
5
0.4
 The dividend 5 is less than the divisor 12. Place
a decimal point and bring it up to the quotient.
CONFIDENTIAL
12
5.00
- 48
20
10
0.416
 Add a 0 onto the dividend. Start
dividing. The remainder is not zero, so
add another zero to the dividend.
12
5.000
- 48
20
- 12
80
- 72
8
The remainder is still not zero.
The remainder continues to be 8.
This is a repeating decimal.
We need our answer rounded to the nearest
hundredths place, so we are ready to round.
0.416 rounded to the nearest hundredths place is 0.42
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We will see another problem:
Divide: 233.4 ÷ 4
 Place the numbers in the division equation format.
4
233.4
5
 Begin the division with 4 into 23 (since 4 cannot
go into 2). This gives us 5 with a remainder of 3.
CONFIDENTIAL
4
233.4
- 20
3
12
 Now bring down the next 3, so we
must divide 33 by 4. This gives us 8
with a remainder of 1.
58
4
233.4
- 20
33
- 32
14
58.3
 Now bring down 4, so we must divide
14 by 4. Here, 4 occurs in the dividend
after the decimal , so we put a decimal in
the quotient after 8. This gives us 3
with a remainder of 2.
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233.4
- 20
33
- 32
14
- 12
2
13
58.35
 If after dividing you have a remainder, add a
zero to the dividend and continue to divide until
there is no remainder or the decimals recur.
Now bring down the next 0, so we must divide
20 by 4. This gives us 5 with a remainder of 0.
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233.40
- 20
33
- 33
14
- 12
20
- 20
00
14
BREAK
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GAME
Click on the link below for some exciting puzzle
http://www.thekidzpage.com/onlinejigsawpuzzles/kids-jigsawpuzzles/12-piece-jigsaw/03-27-07-bunnybee.html
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Assignments
Divide. Round to the nearest hundredths place:
1) 23 ÷ 16
1) 1.44
2) 13 ÷ 15
2) 0.87
3) 67 ÷ 9
3) 7.44
4) 7 ÷ 8
4) 0.88
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Divide. Round to the nearest thousandths place:
5) 355.67 ÷ 13
5) 27.359
6) 246.8 ÷ 9
6) 27.422
7) 685.53 ÷ 11
7) 62.321
8) 513.56 ÷ 45
8) 11.412
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9) Tina bought 6 ice creams for $15.9. Find the cost of one ice-cream.
9) $2.65
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10) Four tanks can store 550 liters of water. If the capacity
of the tanks is equal, then what is the capacity of one tank?
10) 137.5 liters
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Very Good!
Let's Review
When we are given a long division to do, sometimes
there will be numbers left over. These are known as
Remainders.
We can use the long division process to work out the
answer to a number of decimal places.
Division with decimals is easier to understand if the divisor
(the dividend is divided by the divisor) is a whole number.
If the divisor has a decimal in it, we can make it a whole
number by moving the decimal point the appropriate
number of places to the right.
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Review
We saw the following problem:
Divide: 233.4 ÷ 4
 Place the numbers in the division equation format.
 Begin the division with 4 into 23 (since 4 cannot
go into 2). This gives us 5 with a remainder of 3.
CONFIDENTIAL
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233.4
5
4
233.4
- 20
3
22
Review
 Now bring down the next 3, so we
must divide 33 by 4. This gives us 8
with a remainder of 1.
58
4
233.4
- 20
33
- 32
14
58.3
 Now bring down 4, so we must divide
14 by 4. Here, 4 occurs in the dividend
after the decimal , so we put a decimal in
the quotient after 8. This gives us 3
with a remainder of 2.
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233.4
- 20
33
- 32
14
- 12
2
23
Review
58.35
 If after dividing you have a remainder, add a
zero to the dividend and continue to divide until
there is no remainder or the decimals recur.
Now bring down the next 0, so we must divide
20 by 4. This gives us 5 with a remainder of 0.
CONFIDENTIAL
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233.40
- 20
33
- 33
14
- 12
20
- 20
00
24
You have done a nice job.
See you in the next session.
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