Today we will review the Chapter: Adding & Subtracting Decimals

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Today we will review the Chapter:

Adding & Subtracting Decimals

Good Afternoon!

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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Decimals

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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Place Value

Example: Fifty-hundredths

Ones Tenths Hundredths

0 . 5 0

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Your Turn!

Eight Hundredths

Ones Tenths Hundredths

0 . 0 8

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Place Value

Example: Three hundred forty-four thousandths

Ones Tenths Hundredths

0 . 3 4

Thousandths

4

0.344

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Your Turn

Twenty-seven thousandths

Ones Tenths Hundredths Thousandths

0 . 0 2 7

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Compare & Order Decimals

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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Compare & Order Decimals

Use place value Step 1

Line up the decimal points. Compare the ones.5.75.9

Step 2 Compare the tenths5.75.9

Think: 5 = 5

Think: 7 < 9

5.7 < 5.9

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Your Turn

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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Decimals and fractions

Use models

This model shows 1

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

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

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Decimals and fractions

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

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Your Turn

Write a fraction and decimal for the shaded part.

77/100; 0.77

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Decimals and Mixed Numbers

Decimals greater than 1 A mixed number is made up of a whole and a part of a

whole Example: Write as a decimal. 100

183

Three and eighteen hundredths3.18

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Your Turn

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

100

302 2.3

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Rounding

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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Rounding

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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Your Turn

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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Rounding

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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Rounding

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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Your Turn

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

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Adding Decimals

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.

Find: 1.5 + 0.35

1.85

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Your Turn

Find 3.38 + 0.34 = 3.72

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Adding Decimals

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

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Your Turn

Add 0.36 + 0.46 = 0.82

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Estimate Sums

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

+ 24610

Think: 4 < 5 Round

down

Think: 9 > 5 Round

up

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Your Turn

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

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Subtracting Decimals

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.

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Subtracting Decimals Step 2:Cross out 1 whole grid and 90 small squares to show

subtracting 1.9

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Subtracting Decimals Step 3:Write a decimal to show the total number of shaded

squares that are not crossed out.0.6

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Your Turn

Find the difference; 0.9 – 0.2 0.7

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Subtracting Decimals

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 – 14.2525.80

- 14.25

7 10

25.80- 14.25

11.55

11.55+ 14.25

25.80

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Your Turn

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

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Estimate Differences

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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Your Turn

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

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Let us take a break!

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Jig-Saw puzzle

Click me

Let us see how fast you are on this one!

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Assessment

Use place value chart to read and write decimals:1. 7/1,000 = seven thousandths = 0.007

2. 513/1,000=five hundred thirteen thousandths = 0.513

Ones Tenths Hundredths Thousandths

0 . 0 0 7

Ones Tenths Hundredths Thousandths

0 . 5 1 3

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Assessment

Order from greatest to least:1. 3.2, 4.5, 3.9, 4.1

• 4.5, 4.1, 3.9, 3.2

2. 5.33, 4.91, 5.19, 5.52• 5.52, 5.33, 5.19, 4.91

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Assessment

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

100

671 1.67

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Assessment

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

100

552 2.55

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Assessment

Round to the nearest tenth.1. 7.24 = 7.2

Round to the nearest hundredth.2. 8.236 = 8.24

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Assessment

1. Add4.7185.200

+ 3.989 13.9072. Add. Estimate to check for reasonableness.19.76 + 9.55 = 29.31Estimate: 20 + 10 = 30

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Assessment

1. Subtract. Check answer.1.54

- 0.391.15

Chcek: 1.15 + 0.39 = 1.542. Subtract. Estimate to check for reasonableness.

7.1 – 2.70 = 7.10 – 2.70 = 4.40Estimate: 7 – 3 = 4

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Good Job!

You have learned a lot today!!!