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Today we will review the Chapter: Adding & Subtracting Decimals

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Good Afternoon!

Today we will review the Chapter:

Adding & Subtracting Decimals

Let’s Warm up:.

1) 3 + 4 x 7 = 31

2) (35 ÷ 5) - 7 = 0

3) 9 + 54 ÷ 6 = 18

4) 65 - 7 x 9 = 2

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- Decimal: A number that uses place value and a decimal point to show tenths, hundredths, and thousandths.
- 0.1 is a decimal number for one tenth.
- 0.12 is a decimal for twelve hundredths.
- 0.125 is a decimal for one hundred twenty-five thousandths.

- Decimal point: A period separating the ones and the tenths in a decimal.
- 2.7

- Equivalent Decimals: Decimals that name the same number.
- 0.3 and 0.30 are equivalent decimals.

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- Example:
- Fifty-hundredths

Hundredths

Ones

Tenths

0

.

5

0

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- Eight Hundredths

Hundredths

Ones

Tenths

0

.

8

0

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- Example:
- Three hundred forty-four thousandths

Hundredths

Ones

Tenths

Thousandths

0

.

3

4

4

0.344

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- Twenty-seven thousandths

Hundredths

Ones

Tenths

Thousandths

.

0

2

0

7

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- Use a number line
- Compare 5.7 and 5.9

5.0 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6.0

5.7 is to the left of 5.9, 5.7 < 5.9

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- Use place value
- Step 1
- Line up the decimal points. Compare the ones.
5.7

5.9

- Line up the decimal points. Compare the ones.
- Step 2
- Compare the tenths
5.7

5.9

- Compare the tenths

- Step 1

Think: 5 = 5

Think: 7 < 9

5.7 < 5.9

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- Order 5.49, 5.4, 5.57, and 6.03 from greatest to least
- 6.03, 5.57, 5.49, 5.4

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- Use models

This model shows 1

This model shows 1 divided into 100 equal parts. The shaded portion shows 1/100. It can be written as 0.01

This model shows 1 divided into 10 equal parts. The shaded portion shows 1/10. It can be written as 0.1

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- Use models
- Show twenty-five hundredths as a decimal
- Use graph paper to model fractions and decimals
- Count 10 rows of 10 squares each for a total of 100 squares
- Color 25 squares in the 100 square grid
- Write the fraction of the grid that is shaded: 25/100
- Place a zero and a decimal point in front of the numerator of the fraction to make the decimal 25/100 = 0.25

- Show twenty-five hundredths as a decimal

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- Write a fraction and decimal for the shaded part.
- 77/100; 0.77

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- Decimals greater than 1
- A mixed number is made up of a whole and a part of a whole
- Example: Writeas a decimal.

Three and eighteen hundredths

3.18

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- Write a mixed number and a decimal to tell how much is shaded.

2.3

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- Use a number line to round decimals
- To round a decimal to the nearest whole number, look at the digit in the tenths place.
- If the tenths digit is 5 or greater, round up to the nearest one.
- If the tenths digit is less than 5, round down to the nearest one.

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- Round 5.3 to the nearest whole number
- Think: 5.3 is closer to 5 than 6
- So, 5.3 rounds down to 5

- Round 5.8 to the nearest whole number
- Think: 5.8 is closer to 6 than 5
- So, 5.8 rounds up to 6

5.0 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6.0

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- Round 5.6 to the nearest whole number
- 6

- Round 5.2 to the nearest whole number
- 5

5.0 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6.0

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- To round to the nearest tenth, look at the digit in the hundredths place.
- If the hundredths digit is 5 or greater, round up to the nearest tenth.
- If the hundredths digit is less than 5, round down to the nearest tenth.

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- Round 1.56 to the nearest tenth
- Think: 1.56 is closer to 1.60 than 1.50
- So, 1.56 rounds up to 1.60

- Round 1.51 to the nearest tenth
- Think: 1.51 is closer to 1.50 than 1.60
- So, 1.51 rounds down to 1.50

1.50 1.51 1.52 1.53 1.54 1.55 1.56 1.57 1.58 1.59 1.60

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- Round 1.58 to the nearest tenth
- 1.6

- Round 1.52 to the nearest tenth
- 1.5

1.50 1.51 1.52 1.53 1.54 1.55 1.56 1.57 1.58 1.59 1.60

CONFIDENTIAL

- Use models to add decimals
- Step 1: Draw two 10 by 10 grids on graph paper
- Show 1.5 by coloring one whole grid red and coloring 50/100 of the second grid red.

- Step 2: Show 0.35 by coloring 35/100 of the second grid blue.
- Step 3:Count the shaded squares in each grid. Write this in decimal form.

- Step 1: Draw two 10 by 10 grids on graph paper

Find: 1.5 + 0.35

1.85

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- Find 3.38 + 0.34 = 3.72

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- Step 1: Line up the decimal points
- Step 2: Add each place. Regroup if needed. Write the decimal point in the sum.
- Example: Find 1.17 + 1.38
1

1.17

+1.38

2.55

- Example: Find 1.17 + 1.38

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- Add 0.36 + 0.46 = 0.82

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Use Rounding

Step 1: Round each addend to the nearest whole number

Step 2: Add

For Example: Estimate: 586.47 + 23.97

586.47 rounds to 586

23.97 rounds to 24

586

+ 24

610

Think: 4 < 5 Round down

Think: 9 > 5 Round up

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- Estimate the sum by rounding to the nearest whole number. 5.7 + 4.1
- 6 + 4 = 10

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- Use models
- Example: Find 2.5 – 1.9
- Step 1:Draw three 10 by 10 grids; show 2.5 by coloring 2 whole grids and 50 small squares red.

- Example: Find 2.5 – 1.9

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- Step 2:Cross out 1 whole grid and 90 small squares to show subtracting 1.9

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- Step 3:Write a decimal to show the total number of shaded squares that are not crossed out.
0.6

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- Find the difference; 0.9 – 0.2
- 0.7

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Step 1:Line up the decimal points. Insert a zero if needed.

Step 2:Subtract each place. Regroup if needed. Write the decimal point.

Step 3: You can use the inverse relationship between addition and subtraction to check.

Example: 25.8 – 14.25

25.80

- 14.25

7 10

25.80

-14.25

11.55

11.55

+14.25

25.80

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- Subtract. Check the answer.
- 0.96 – 0.29 = 0.67
- Check: 0.29 + 0.67 = 0.96

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- Use Rounding
- To estimate differences of decimals, round each decimal to the nearest whole number.
- Then subtract the rounded numbers.

- Example: Estimate 12.25 – 5.79
- 12.25: Round down to 12
- 5.79: Round up to 6
- Subtract: 12 – 6 = 6

- So 12.25 – 5.79 is about 6.

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- Estimate. Round to the nearest whole number.
- 9.7 – 4.3 = 10 – 4 = 6

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Let us see how fast you are on this one!

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Use place value chart to read and write decimals:

- 7/1,000 = seven thousandths = 0.007
- 513/1,000=five hundred thirteen thousandths = 0.513

Hundredths

Ones

Tenths

Thousandths

.

0

0

0

7

Hundredths

Ones

Tenths

Thousandths

.

5

1

0

3

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Order from greatest to least:

- 3.2, 4.5, 3.9, 4.1
- 4.5, 4.1, 3.9, 3.2

- 5.33, 4.91, 5.19, 5.52
- 5.52, 5.33, 5.19, 4.91

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- Write a mixed number and a decimal to tell how much is shaded.

1.67

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- Write a mixed number and a decimal to tell how much is shaded.

2.55

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Round to the nearest tenth.

- 7.24 = 7.2
Round to the nearest hundredth.

- 8.236 = 8.24

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- Add
4.718

5.200

+3.989

13.907

- Add. Estimate to check for reasonableness.
19.76 + 9.55 = 29.31

Estimate: 20 + 10 = 30

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- Subtract. Check answer.
1.54

-0.39

1.15

Chcek: 1.15 + 0.39 = 1.54

- Subtract. Estimate to check for reasonableness.
7.1 – 2.70 = 7.10 – 2.70 = 4.40

Estimate: 7 – 3 = 4

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- You have learned a lot today!!!

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