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
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.
CONFIDENTIAL 3
Place Value
Example: Fifty-hundredths
Ones Tenths Hundredths
0 . 5 0
CONFIDENTIAL 4
Your Turn!
Eight Hundredths
Ones Tenths Hundredths
0 . 0 8
CONFIDENTIAL 5
Place Value
Example: Three hundred forty-four thousandths
Ones Tenths Hundredths
0 . 3 4
Thousandths
4
0.344
CONFIDENTIAL 6
Your Turn
Twenty-seven thousandths
Ones Tenths Hundredths Thousandths
0 . 0 2 7
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
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
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
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
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
CONFIDENTIAL 12
Your Turn
Write a fraction and decimal for the shaded part.
77/100; 0.77
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
CONFIDENTIAL 14
Your Turn
Write a mixed number and a decimal to tell how much is shaded.
100
302 2.3
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.
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
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
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.
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
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
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
CONFIDENTIAL 22
Your Turn
Find 3.38 + 0.34 = 3.72
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
CONFIDENTIAL 24
Your Turn
Add 0.36 + 0.46 = 0.82
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
CONFIDENTIAL 26
Your Turn
Estimate the sum by rounding to the nearest whole number. 5.7 + 4.1 6 + 4 = 10
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.
CONFIDENTIAL 28
Subtracting Decimals Step 2:Cross out 1 whole grid and 90 small squares to show
subtracting 1.9
CONFIDENTIAL 29
Subtracting Decimals Step 3:Write a decimal to show the total number of shaded
squares that are not crossed out.0.6
CONFIDENTIAL 30
Your Turn
Find the difference; 0.9 – 0.2 0.7
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
CONFIDENTIAL 32
Your Turn
Subtract. Check the answer. 0.96 – 0.29 = 0.67 Check: 0.29 + 0.67 = 0.96
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.
CONFIDENTIAL 34
Your Turn
Estimate. Round to the nearest whole number. 9.7 – 4.3 = 10 – 4 = 6
CONFIDENTIAL 35
Let us take a break!
CONFIDENTIAL 36
Jig-Saw puzzle
Click me
Let us see how fast you are on this one!
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
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
CONFIDENTIAL 39
Assessment
1. Write a mixed number and a decimal to tell how much is shaded.
100
671 1.67
CONFIDENTIAL 40
Assessment
2. Write a mixed number and a decimal to tell how much is shaded.
100
552 2.55
CONFIDENTIAL 41
Assessment
Round to the nearest tenth.1. 7.24 = 7.2
Round to the nearest hundredth.2. 8.236 = 8.24
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
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
CONFIDENTIAL 44
Good Job!
You have learned a lot today!!!