1. Adding & Subtracting Decimals
Good Afternoon!
Today we will review the Chapter:
Adding & Subtracting Decimals
Let’s Warm up:.
1) x 7 =
2) (35 ÷ 5) - 7 =
3) ÷ 6 =
4) x 9 =
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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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3. Place Value Example: Fifty-hundredths . 5 Ones Tenths Hundredths. 5
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4. Your Turn!
Eight Hundredths
Ones
Tenths
Hundredths
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5. Place Value Example: Three hundred forty-four thousandths . 3 4 4
Ones
Tenths
Hundredths
Thousandths . 3 4 4
0.344
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6. Your Turn Twenty-seven thousandths Ones Tenths Hundredths Thousandths
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7. Compare & Order Decimals
Use a number line
Compare 5.7 and 5.9
5.7 is to the left of 5.9, 5.7 < 5.9
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8. Compare & Order Decimals
Use place value
Step 1
Line up the decimal points. Compare the ones.
5.7
5.9
Step 2
Compare the tenths
Think: 5 = 5
Think: 7 < 9
5.7 < 5.9
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9. Your Turn Order 5.49, 5.4, 5.57, and 6.03 from greatest to least
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10. Decimals and fractions
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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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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12. Your Turn Write a fraction and decimal for the shaded part.
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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.
Three and eighteen hundredths
3.18
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14. Your Turn
Write a mixed number and a decimal to tell how much is shaded.
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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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16. Rounding Round 5.3 to the nearest whole number
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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17. Your Turn Round 5.6 to the nearest whole number
Round 5.6 to the nearest whole number
Round 5.2 to the nearest whole number
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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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19. Rounding Round 1.56 to the nearest tenth
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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20. Your Turn Round 1.58 to the nearest tenth
Round 1.58 to the nearest tenth
Round 1.52 to the nearest tenth
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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:
1.85
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22. Your Turn
Find
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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
1.17
+ 1.38
2.55
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24. Your Turn
Add
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25. Estimate Sums Use Rounding For Example: Estimate: 586.47 + 23.97
Step 1: Round each addend to the nearest whole number
Step 2: Add
For Example: Estimate:
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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26. Your Turn
Estimate the sum by rounding to the nearest whole number
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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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28. Subtracting Decimals
Step 2:Cross out 1 whole grid and 90 small squares to show subtracting 1.9
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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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30. Your Turn
Find the difference; 0.9 – 0.2
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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 – 14.25
25.80
7 10
11.55
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32. Your Turn
Subtract. Check the answer.
0.96 – 0.29
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33. Estimate Differences Use Rounding Example: Estimate 12.25 – 5.79
To estimate differences of decimals, round each decimal to the nearest whole number.
Then subtract the rounded numbers.
Example: Estimate – 5.79
12.25: Round down to 12
5.79: Round up to 6
Subtract: 12 – 6 = 6
So – 5.79 is about 6.
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34. Your Turn Estimate. Round to the nearest whole number. 9.7 – 4.3
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35. Let us take a break!
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36. Let us see how fast you are on this one!
Jig-Saw puzzle
Let us see how fast you are on this one!
Click me
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37. Assessment Use place value chart to read and write decimals: 7/1,000
513/1,000
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38. Assessment Order from greatest to least: 3.2, 4.5, 3.9, 4.1
5.33, 4.91, 5.19, 5.52
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39. Assessment
Write a mixed number and a decimal to tell how much is shaded.
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40. Assessment
Write a mixed number and a decimal to tell how much is shaded.
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41. Assessment Round to the nearest tenth. 7.24
Round to the nearest hundredth.
8.236
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42. Assessment
Add
4.718
5.2
Add. Estimate to check for reasonableness.
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43. Assessment Subtract. Check answer. 1.54 - 0.39
- 0.39
Subtract. Estimate to check for reasonableness.
7.1 – 2.70
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44. Good Job!
You have learned a lot today!!!
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