Transcript Document

Good Afternoon!
Today we will review the Chapter:
Adding & Subtracting Decimals
Let’s Warm up:.
1) 3 + 4 x 7 =
2) (35 ÷ 5) - 7 =
3) 9 + 54 ÷ 6 =
4) 65 - 7 x 9 =
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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.
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 0.3 and 0.30 are equivalent
decimals.
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Place Value
 Example:
 Fifty-hundredths
Ones
0
Tenths
.
5
Hundredths
0
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Your Turn!
 Eight Hundredths
Ones
Tenths
Hundredths
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Place Value
 Example:
 Three hundred forty-four thousandths
Ones
0
Tenths
.
3
Hundredths
4
Thousandths
4
0.344
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Your Turn
 Twenty-seven thousandths
Ones
Tenths
Hundredths
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Thousandths
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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.
5.7
Think: 5 = 5
5.9
 Step 2
 Compare the tenths
5.7
Think: 7 < 9
5.9
5.7 < 5.9
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Your Turn
 Order 5.49, 5.4, 5.57, and 6.03 from greatest
to least
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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
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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.
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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
3
18
100
as a decimal.
Three and eighteen hundredths
3.18
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Your Turn
 Write a mixed number and a decimal to tell how much is
shaded.
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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
5.0
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
6.0
 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
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Your Turn
5.0
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
6.0
 Round 5.6 to the nearest whole number
 Round 5.2 to the nearest whole number
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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
1.50
1.51 1.52
1.53
1.54
1.55
1.56 1.57
1.58 1.59
1.60
 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
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Your Turn
1.50
1.51 1.52
1.53
1.54
1.55
1.56 1.57
1.58 1.59
1.60
 Round 1.58 to the nearest tenth
 Round 1.52 to the nearest tenth
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Adding Decimals
 Use models to add decimals

Step 1: Draw two 10 by 10
grids on graph paper



Find: 1.5 + 0.35
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.
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1.85
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Your Turn
 Find 3.38 + 0.34
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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
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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
Think: 4 < 5
Round down
Think: 9 > 5
Round up
+
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586
24
610
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Your Turn
 Estimate the sum by rounding to the nearest
whole number. 5.7 + 4.1
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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
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Subtracting Decimals
 Step 1:Line up the
decimal points. Insert a
zero if needed.
 Example: 25.8 – 14.25
 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.
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25.80
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
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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
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Let us take a break!
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Jig-Saw puzzle
Let us see how fast you are on this one!
 Click me
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Assessment
Use place value chart to read and write decimals:
1. 7/1,000
2. 513/1,000
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Assessment
Order from greatest to least:
1. 3.2, 4.5, 3.9, 4.1
2. 5.33, 4.91, 5.19, 5.52
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Assessment
1. Write a mixed number and a decimal to tell how much is
shaded.
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Assessment
2. Write a mixed number and a decimal to tell how much is
shaded.
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Assessment
Round to the nearest tenth.
1. 7.24
Round to the nearest hundredth.
2. 8.236
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Assessment
1. Add
4.718
5.2
+ 3.989
2. Add. Estimate to check for reasonableness.
19.76 + 9.55
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Assessment
1. Subtract. Check answer.
1.54
- 0.39
2. Subtract. Estimate to check for reasonableness.
7.1 – 2.70
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Good Job!
 You have learned a lot today!!!
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