CONFIDENTIAL1 Good Afternoon! Today we will be learning about Dividing with decimal remainders...

CONFIDENTIAL 1

Good Afternoon!Today we will be learning about Dividing with decimal remainders

Let’s warm up :

Divide:

1) 42 ÷ 4

2) 25.93 ÷ 8

3) 23 ÷ 40

4) 77.76 ÷ 15

5) 84.21 ÷ 13

1) 10.5

2) 3.24

3) 0.575

4) 5.184

5) 6.48

CONFIDENTIAL 2

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.

Dividend  Dividend  ==  DivisorDivisor XX QuotientQuotient + + RemainderRemainder

. 8 quotient 5)43 40 dividenddivisor 3

remainder

CONFIDENTIAL 3

This can be represented on the number line as follows:

Multiplication is repeated subtraction.So, 4.5 ÷ 3 = 1.5

10 2 3 4

1.5 1.5

5

1.5

You can count backward in groups of 1.5.

There are 3 jumps of value 1.5 from 4.5 to 0.

Find 4.5 ÷ 3 .

4.5

CONFIDENTIAL 4

Expressing the quotient as a decimal

Divide 17 by 5.

5 17

3

-152

There are no more digits in the dividend.

Place a decimal point and bring it up to the quotient. 5 17.0

3.4

-1520

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.

-2000

Review

CONFIDENTIAL 5

Review

The dividend less than the divisor

Divide 7 by 8.

The dividend 7 is less than the divisor 8.

8 7.0

0.875

-6460

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.

- 5640

- 4000

CONFIDENTIAL 6

Review

When the dividend is a decimal, and the divisor a whole number

Divide: 7.64 ÷ 2

Place the divisor (2) before the division bracket and place the

dividend (7.64) under it.

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

CONFIDENTIAL 7

Review

To divide a decimal by a whole number, divide as you would for whole

numbers.

2 7.64

3.82

-6 16

Place a decimal point in the answer so that it lines up with the

decimal point in the Dividend.

-16004

-4

0

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.

STEP 2:

CONFIDENTIAL 8

Review

Divide: 8.66 ÷ 4

We can find the solution as follows:

4 8.66

2.165

-8 06-426

-2420

-2000

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.

CONFIDENTIAL 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.

CONFIDENTIAL 10

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.)

12 5 Place the numbers in the division equation format.

The dividend 5 is less than the divisor 12. Place a decimal point and bring it up to the

quotient.

12 5.00

0.4

- 4820

CONFIDENTIAL 11

12 5.000

0.416

- 4820

- 1280

Add a 0 onto the dividend. Start dividing. The remainder is not zero,

so add another zero to the dividend.

- 728

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

CONFIDENTIAL 12

4 233.4 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.

4 233.4

5

- 203

Divide: 233.4 ÷ 4

We will see another problem:

CONFIDENTIAL 13

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

58

- 2033

- 3214

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

58.3

- 2033

- 3214

- 122

CONFIDENTIAL 14

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.

4 233.40

58.35

- 2033

- 3314

- 1220

- 2000

CONFIDENTIAL 15

BREAK

CONFIDENTIAL 16

GAME

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CONFIDENTIAL 17

Assignments

1) 23 ÷ 16

2) 13 ÷ 15

Divide. Round to the nearest hundredths place:

3) 67 ÷ 9

4) 7 ÷ 8

1) 1.44 3) 7.44

2) 0.87 4) 0.88

CONFIDENTIAL 18

6) 246.8 ÷ 9

7) 685.53 ÷ 11

5) 355.67 ÷ 13

Divide. Round to the nearest thousandths place:

8) 513.56 ÷ 45

5) 27.359 7) 62.321

6) 27.422 8) 11.412

CONFIDENTIAL 19

9) Tina bought 6 ice creams for $15.9. Find the cost of one ice-cream.

9) $2.65

CONFIDENTIAL 20

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

CONFIDENTIAL 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

Review

4 233.4 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. 4 233.4

5

- 203

Divide: 233.4 ÷ 4

We saw the following problem:

CONFIDENTIAL 23

Review

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

58

- 2033

- 3214

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

58.3

- 2033

- 3214

- 122

CONFIDENTIAL 24

Review

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.

4 233.40

58.35

- 2033

- 3314

- 1220

- 2000

CONFIDENTIAL 25

You have done a nice job.See you in the next session.