Confidential 1

Adding and Subtracting Decimals

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Warm Up

1. Round 32,586 to the nearest ten 32,590

2. Round 42.007 to the nearest hundredth 42.08

3. 0.686 will become 1 if we round to the nearest

Tenth place value

4. Which one is greater

0.01 < 0.10

9.01 > 9.00

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Let's review what we learned in the last lesson.

We can round decimals to any place

value.

Find the place value you want (the "rounding digit") and look at the digit just to the right of it.

If that digit is less than 5, do not change the rounding digit but drop all digits to the right of it.

If that digit is greater than or equal to five, add one to the rounding digit and drop all digits to the right of it.

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Review

Let us round 34,563 to the nearest hundred

The rounding digit here is 5

The digit to its right is 6

6 > 5 so add 1 to rounding digit

We get 34,600

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We can also round the decimals to their nearest

Fractions in the same way

Review

Lets round 8. 27 to the nearest tenth place

The rounding digit here is 2 and the digit to its right is 7

7 is greater than 5 so we add one to the rounding digit

We get 8.3

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Modeling Decimal Sums

• Example: To find the sum of 1.15 and 0.95– Step1 : Model the numbers using base-ten pieces.

+

1.150.95

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Modeling Decimal Sums• Step 2: Combine the pieces.

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Modeling Decimal Sums

• Step 3: Trade 10 tenths for 1 one and 10 hundredths for 1 tenth.

2.1

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Modeling Decimal Sums

• Use base-ten pieces to find the sum.• 2.1 + 0.9 = 3.0

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Lets get started with our lesson

Today we will learn about

Adding and Subtracting Decimals

Let us recall adding and subtracting Integers

If we want to add

34,562

+ 23,478

58,040

111

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Lets add 34.567, 12,345.32 and 7.3

34 . 567

12,345 . 32

7 . 3

To add Decimals all we need to do is to align all decimal points in one line

12,387 . 187

11Remember

we start from the right end and the carry goes across the decimal point

Start

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Let us take another example

Lets us add 132.32 and 68.771

132 . 32

68 . 771

201 . 091

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Properties of Addition

• Commutative Property– Changing the order of the addends does not change

the sum.• 3.6 + 7 = 7 + 3.6

• Associative Property– Changing the grouping of the addends does not

change the sum.• (3.6 + 7) + 3 = 3.6 + (7 + 3)

• Identity Property– The sum of 0 and any number is that number.

• 3.6 + 0 = 0 + 3.6 = 3.6

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Using the properties of addition

• You can simplify an expression by replacing it with the simplest name for its value.– Use mental math to find the sum of 42 + 13.9 + 58.

• What you think– 42 and 58 are easy to add. Adding 42 and 58 gives you 100. Adding

100 and 13.9 gives you 113.9. So, 42 + 13.9 + 58 = 113.9

• Why it works42 + 13.9 + 58 = 42 + 58 + 13.9 Commutative property

= (42 + 58) + 13.9 Associative property

= 100 + 13.9 Add inside the parenthesis

= 113.9 Simplify

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Using the properties of addition

• Use mental math to find the sum8.9 + 0 + 5.0 = 13.9

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Modeling Decimal Differences

• Draw a model to find the difference 1.4 – 0.6.

Remove six tenths from fourteen tenths.Eight tenths remain.

1.4 – 0.6 = 0.8

Draw two tenths grid and shade all tenths in the first grid and shade four tenths in the second grid.

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Modeling Decimal Differences

• Draw a model to find 1.5 – 1.2 = 0.3

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We can subtract decimals the same way.

Align all decimals so that the decimal points

are in a vertical line

Subtracting Decimals

Lets subtract 15.68 from 54.7

54 . 70

15 . 68

39 . 02

Add zeros to the right side of the decimal with fewer decimal places so that each decimal has the same number of decimal places.

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Lets us take another example

Subtract 331.44 from 4000

4000 . 00

331 . 44

3668 . 56

We need to add two zeros to the right of decimal to make the decimal places equal

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Estimating

• Example: Subtract 78.0 – 74.9– Estimate ≈ 78 – 75, or 3

78.0 Rename 8 as 7 and 10 tenths

-74.9 Subtract 74.9

3.1 Simplify

The difference is 3.1

• Check for Reasonableness: The difference 3.1 is reasonable since it is close to 3

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Estimating

• First estimate and then find the difference 2.7 – 0.9 = 1.6

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Try these yourself

1.) 43.768 + 23.656

2.) 12.528 + 44.21

3.) 87.85 - 20.85

4.) 65.85 - 65.50

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Try these yourself

1.) 43.768 + 23.656 = 67.424

2.) 12.528 + 44.21 = 56.738

3.) 87.85 - 20.85 = 67

4.) 65.85 - 65.50 = 0.35

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Break

Time

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Game Time

Click here to play a Game

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Jack borrowed $32.50 from Ben and $61.50 from Sue.

After a month of savings Jack now has only $30 to be

returned. Find out how much money Jack still owes to

both his friends

He still owes $64

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A pillar is to be made to support a bridge.

The depth of the river is 34.52 meter

While the height of the bridge is 20 .35 meters

Find out the total length of the pillar.

Total length of the pillar is 54.87

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The marks of two students of grade six are as under. Find out their total marks. The teacher has awarded student 1 and 3 a penalty of 5 marks for bad behavior

Subjects Student 1 Student 2 student 3

Math 83.5 82.8 80.8

Science 92.6 97.5 91.8

English 75.8 70.3 88.9

Total 251.9 250.6 261.5

Penalty -5.0 -5.0

246.9 250.6 256.5

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Assessment

1. First estimate and then find each sum.1. 0.6 + 3.4 = 4.02. 6.2 + 0.444= 6.6443. 8.001 + 0.77= 8.771

2. First estimate and then find each difference.

1. 22.2 – 4.3= 17.92. 8.91 – 6.08= 2.833. 9.45 – 3.76=5.79

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Assessment

3. Find each missing number. Name the property of addition that you used.

1. 6.37 + 0 + 2.43 = 6.37 + 2.43 Identity2. 0.43 + 0 = 0.43 Identity Property3. (2.1 + 0.3) + 4 = 2.1 + (0.3 + 4) Associative

4. You have a balance of $141.82 in an account. You withdraw $30 and then deposit a check for $41.93. What is the new balance? $153.75

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Let us review what we have learnt today

To add Decimals all we need to do is to align all decimal points in one line

We start from the right end and the carry goes across the decimal point

62 . 72

+18 . 51

81 . 23

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Review

To subtract Decimals align all decimals so that the

decimal points are in a vertical line.Add zeros to the right side of the decimal with fewer decimal places so that each decimal has the same number of decimal places.

89 . 30

45 . 11

44 . 19

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You had a GREAT lesson today!

Be sure to practice what you learned!