1. Today we will be learning about Dividing with decimal remainders
Good Afternoon!
Today we will be learning about
Dividing with decimal remainders
Let’s warm up :
Divide:
1) 42 ÷ 4
1) 10.5
2) ÷ 8
2) 3.24
3) 23 ÷ 40
3) 0.575
4) ÷ 15
4) 5.184
5) ÷ 13
5) 6.48
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2. Dividend = Divisor X Quotient + Remainder
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.
quotient
5)43
dividend
divisor remainder
Dividend  = Divisor X Quotient + Remainder
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3. Multiplication is repeated subtraction. So, 4.5 ÷ 3 = 1.5
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 1 2 3 4 5
1.5
1.5
1.5
There are 3 jumps of value 1.5 from 4.5 to 0.
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4. Expressing the quotient as a decimal
Review
Expressing the quotient as a decimal
Divide 17 by 5. 3 5 17
There are no more digits in the dividend.
-15 2
3.4
Place a decimal point and bring it up to the quotient. 5
17.0
-15
Add a 0 onto the remainder. 20
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.
-20 00
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5. The dividend less than the divisor
Review
The dividend less than the divisor
Divide 7 by 8.
The dividend 7 is less than the divisor 8.
0.875
Place a decimal point and bring it up to the quotient. 8
7.0
Add a 0 onto the dividend.
-64 60
- 56
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. 40
- 40 00
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6. When the dividend is a decimal, and the divisor a whole number
Review
When the dividend is a decimal, and the divisor a whole number
Divide: ÷ 2
Division with decimals is easier to understand if the divisor (the dividend is divided by the divisor) is a whole number.
STEP 1:
Place the divisor (2) before the division bracket and place the dividend (7.64) under it. 2
7.64
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7. Review
To divide a decimal by a whole number, divide as you would for whole numbers.
STEP 2:
3.82
Place a decimal point in the answer so that it lines up with the decimal point in the Dividend. 2
7.64 -6 16
-16
004
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. -4
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8. We added a trailing zero to 8.66 when 4 would not divide into 2.
Review
Divide: ÷ 4
We can find the solution as follows:
Note:
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.
2.165 4
8.66 -8 06 -4 26
-24 20
-20 00
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9. 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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10. Round to the nearest hundredths place.
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. 12
5.00
- 48 20
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11. The remainder is still not zero. The remainder continues to be 8.
0.416 12
5.000
Add a 0 onto the dividend. Start dividing. The remainder is not zero, so add another zero to the dividend.
- 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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12. Place the numbers in the division equation format.
We will see another problem:
Divide: ÷ 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. 4
233.4
- 20 3
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13. 58
Now bring down the next 3, so we must divide 33 by 4. This gives us 8 with a remainder of 1. 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. 4
233.4
- 20 33
- 32 14
- 12 2
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14. 58.35 4
233.40
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.
- 20 33
- 33 14
- 12 20
- 20 00
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15. BREAK
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16. Click on the link below for some exciting puzzle
GAME
Click on the link below for some exciting puzzle
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17. Divide. Round to the nearest hundredths place:
Assignments
Divide. Round to the nearest hundredths place:
1) 23 ÷ 16
1) 1.44
3) 67 ÷ 9
3) 7.44
2) 13 ÷ 15
4) 7 ÷ 8
4) 0.88
2) 0.87
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18. Divide. Round to the nearest thousandths place:
5) ÷ 13
7) ÷ 11 5) 7)
6) ÷ 9
8) ÷ 45 8) 6)
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19. 9) Tina bought 6 ice creams for $15.9. Find the cost of one ice-cream.
9) $2.65
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20. 10) Four tanks can store 550 liters of water
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) liters
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21. 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.
CONFIDENTIAL

22. Place the numbers in the division equation format.
Review
We saw the following problem:
Divide: ÷ 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. 4
233.4
- 20 3
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23. Review 58
Now bring down the next 3, so we must divide 33 by 4. This gives us 8 with a remainder of 1. 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. 4
233.4
- 20 33
- 32 14
- 12 2
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24. Review
58.35 4
233.40
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.
- 20 33
- 33 14
- 12 20
- 20 00
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25. See you in the next session.
You have done a nice job.
See you in the next session.
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