Today we will review the Chapter: Adding & Subtracting Decimals
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CONFIDENTIAL 1
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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CONFIDENTIAL 2
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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CONFIDENTIAL 3
Place Value
Example: Fifty-hundredths
Ones Tenths Hundredths
0 . 5 0
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CONFIDENTIAL 4
Your Turn!
Eight Hundredths
Ones Tenths Hundredths
0 . 0 8
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CONFIDENTIAL 5
Place Value
Example: Three hundred forty-four thousandths
Ones Tenths Hundredths
0 . 3 4
Thousandths
4
0.344
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CONFIDENTIAL 6
Your Turn
Twenty-seven thousandths
Ones Tenths Hundredths Thousandths
0 . 0 2 7
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CONFIDENTIAL 7
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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CONFIDENTIAL 8
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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CONFIDENTIAL 9
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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CONFIDENTIAL 10
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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CONFIDENTIAL 11
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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CONFIDENTIAL 12
Your Turn
Write a fraction and decimal for the shaded part.
77/100; 0.77
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CONFIDENTIAL 13
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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CONFIDENTIAL 14
Your Turn
Write a mixed number and a decimal to tell how much is shaded.
100
302 2.3
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CONFIDENTIAL 15
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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CONFIDENTIAL 16
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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CONFIDENTIAL 17
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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CONFIDENTIAL 18
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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CONFIDENTIAL 19
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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CONFIDENTIAL 20
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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CONFIDENTIAL 21
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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CONFIDENTIAL 22
Your Turn
Find 3.38 + 0.34 = 3.72
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CONFIDENTIAL 23
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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CONFIDENTIAL 24
Your Turn
Add 0.36 + 0.46 = 0.82
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CONFIDENTIAL 25
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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CONFIDENTIAL 26
Your Turn
Estimate the sum by rounding to the nearest whole number. 5.7 + 4.1 6 + 4 = 10
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CONFIDENTIAL 27
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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CONFIDENTIAL 28
Subtracting Decimals Step 2:Cross out 1 whole grid and 90 small squares to show
subtracting 1.9
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CONFIDENTIAL 29
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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CONFIDENTIAL 30
Your Turn
Find the difference; 0.9 – 0.2 0.7
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CONFIDENTIAL 31
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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CONFIDENTIAL 32
Your Turn
Subtract. Check the answer. 0.96 – 0.29 = 0.67 Check: 0.29 + 0.67 = 0.96
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CONFIDENTIAL 33
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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CONFIDENTIAL 34
Your Turn
Estimate. Round to the nearest whole number. 9.7 – 4.3 = 10 – 4 = 6
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CONFIDENTIAL 35
Let us take a break!
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CONFIDENTIAL 36
Jig-Saw puzzle
Click me
Let us see how fast you are on this one!
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CONFIDENTIAL 37
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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CONFIDENTIAL 38
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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CONFIDENTIAL 39
Assessment
1. Write a mixed number and a decimal to tell how much is shaded.
100
671 1.67
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CONFIDENTIAL 40
Assessment
2. Write a mixed number and a decimal to tell how much is shaded.
100
552 2.55
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CONFIDENTIAL 41
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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CONFIDENTIAL 42
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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CONFIDENTIAL 43
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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CONFIDENTIAL 44
Good Job!
You have learned a lot today!!!