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M4.A.3 Compute accurately and fluently and make reasonable estimates.

Learn how to compute accurately and fluently using fractions or decimals, specifically for addition and subtraction problems involving decimals through hundredths.

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M4.A.3 Compute accurately and fluently and make reasonable estimates.

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  1. M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally - straight computation only).

  2. M4.A.3.2 Eligible Content • M4.A.3.2.1 Solve addition or subtraction problems involving decimals through hundredths (decimal numbers must have the same number of places). • M4.A.3.2.2 Solve addition or subtraction problems with fractions with like denominators (denominators to 10, no simplifying necessary).

  3. M4.A.3.2.1 Solve addition or subtraction problems involving decimals through hundredths (decimal numbers must have the same number of places).

  4. PSSA Sample Item

  5. Adding and Subtracting Decimals When adding & subtracting numbers with decimals, stack the numbers on top of each other lining the decimals up. Remember, if a number doesn’t have a decimal, it comes at the end of the number. EX: 5.2 + 97.44  97.44 + 5.2 I can fill in empty spots with zeros. When I subtract, I have to fill in empty spots with 0’s. It’s not necessary with addition.

  6. Adding and Subtracting Decimals EX: 5.2 + 97.44  97.44 + 5.20 102.64 I can fill in empty spots with zeros. When I subtract, I have to fill in empty spots with 0’s. It’s not necessary with addition.

  7. Addition of Decimals 2.35 + 4.92

  8. Addition Algorithm for Decimals 2.35 + 4.92 7 Place Value: Start with smallest pieces (hundredths) Basic Fact: 5 hundredths + 2 hundredths = 7 hundredths Basic Fact: 5 + 2 = 7 Rename: not needed

  9. Addition Algorithm for Decimals 1 2.35 + 4.92 .27 Place Value: tenths Basic Fact: 3 tenths + 9 tenths = 12 tenths Basic Fact: 3 + 9 = 12 Rename: 12 tenths as 1 one + 2 tenths

  10. Addition Algorithm for Decimals 1 2.35 + 4.92 7.27 Place Value: ones Basic Fact: 1 one + 2 ones + 4 ones = 7 ones Basic Fact: 1 + 2 + 4 = 7 Rename: not needed

  11. 722.86 + 0.02 722.86 + 0.02 722.88 ON ADDITION, you don’t have to fill in 0’s but you can. With SUBTRACTION, you need to fill in 0’s if the number is on top. EX: 8 – 2.54 8.00 • 2.54 5.46

  12. 75 – 0.24  75 (add a decimal - 0.24 & a couple 0’s) 75.00 • 0.24 74.76 Now try these: • 10 - 0.25 b) 100 – 0.48 c) 342.7 – 3.86 d) 43 – 7.23

  13. 72.3 – 4 • 89 – 42.36 • 44.2 – 39.67 • 66.23 – 44.97 • Line up the decimals as shown below • These will all need 0’s added. • 72.3 89.00 44.20 66.23 - 4.0 -42.36-39.67 -44.97

  14. Lesson 35: Add, Subtract, Multiply & Divide Decimal Numbers Rule for adding and subtracting decimals: Line up the decimal point!! Example 1: Add 3.6 + .36 + 36 3.6 + .36 Add “0” if needed to keep decimal place. 3.60 + 0.36 Answer: 3.96

  15. Example 2: Subtract 12.3 - 4.567 Step 1: write the numbers vertical, aligning the decimal point 12.3 - 4.567 12.300 - 4.567 Add “0” to even out the places Step 2: Subtract (be sure to borrow correctly when needed) Answer: 12.300 - 4.567 7.733

  16. Adding and Subtracting Decimals • LINE UP DECIMAL POINTS BEFORE YOU ADD OR SUBTRACT. 123.76 0.0009 +34.098 123.76 0.0009 +34.098 Now you can’t confuse the VALUE of each digit. Now, just add or subtract as you normally would. You may add zeros to the end of a decimal to line up place values – just like comparing decimals. Trying to add like this can be confusing, the place values are all mixed up

  17. Subtracting Decimal Numbers Ex) Max went to Wal-Mart with $812.50. He then bought a television for $599.87. How much money did he have left over?

  18. Subtracting Decimal Numbers Ex) Max went to Wal-Mart with $812.50. He then bought a television for $599.87. How much money did he have left over? Solution: Line up the numbers vertically according to place value.

  19. Subtracting Decimal Numbers 8 1 2 . 5 0 - 5 9 9 . 8 7

  20. Subtracting Decimal Numbers 8 1 2 . 5 0 - 5 9 9 . 8 7

  21. Subtracting Decimal Numbers 4 8 1 2 . 5 0 - 5 9 9 . 8 7

  22. Subtracting Decimal Numbers 4 8 1 2 . 5 10 - 5 9 9 . 8 7

  23. Subtracting Decimal Numbers 4 8 1 2 . 5 10 - 5 9 9 . 8 7 3

  24. Subtracting Decimal Numbers 1 4 8 1 2 . 5 10 - 5 9 9 . 8 7 3

  25. Subtracting Decimal Numbers 1 14 8 1 2 . 5 10 - 5 9 9 . 8 7 3

  26. Subtracting Decimal Numbers 1 14 8 1 2 . 5 10 - 5 9 9 . 8 7 6 3

  27. Subtracting Decimal Numbers 1 14 8 1 2 . 5 10 - 5 9 9 . 8 7 . 6 3

  28. Subtracting Decimal Numbers 0 11 14 8 1 2 . 5 10 - 5 9 9 . 8 7 . 6 3

  29. Subtracting Decimal Numbers 0 11 14 8 1 2 . 5 10 - 5 9 9 . 8 7 2 . 6 3

  30. Subtracting Decimal Numbers 71011 14 8 1 2 . 5 10 - 5 9 9 . 8 7 2 . 6 3

  31. Subtracting Decimal Numbers 71011 14 8 1 2 . 5 10 - 5 9 9 . 8 7 1 2 . 6 3

  32. Subtracting Decimal Numbers 71011 14 8 1 2 . 5 10 - 5 9 9 . 8 7 2 1 2 . 6 3

  33. Subtracting Decimal Numbers 71011 14 8 1 2 . 5 10 - 5 9 9 . 8 7 2 1 2 . 6 3 Max had $212.63 left.

  34. Practice Adding Decimals a) 4.2 + 5.6 b) 3.2+ 1.5 c) .7+ .4 d) .2+ .3 e) .49+ .35 f) .32+ .69 g) 4.54+ 5.94 h) 3.03+ 4.15

  35. Practice Adding Decimals a) 4.2 + 5.6 9.8 b) 3.2+ 1.5 4.7 c) .7+ .4 1.1 d) .2+ .3 .5 e) .49+ .35 .84 f) .32+ .69 1.01 g) 4.54+ 5.94 10.48 h) 3.03+ 4.15 7.18

  36. Practice Subtracting Decimals b) .5- .2 c) .8- .7 a) .9- .3 d) 6.7- 5.2 e) 4.9- 3.3 f) 7.89- 3.96 g) 14.34- 6.36 h)3.71- .4 

  37. Practice Subtracting Decimals b) .5- .2 .3 c) .8- .7 .1 a) .9- .3 .6 d) 6.7- 5.2 1.5 e) 4.9- 3.3 1.6 f) 7.89- 3.96 3.93 g) 14.34- 6.36 7.98 h)3.71- .4  3.31

  38. M4.A.3.2.2 Solve addition or subtraction problems with fractions with like denominators (denominators to 10, no simplifying necessary).

  39. PSSA Sample Item

  40. PSSA Sample Item

  41. PSSA Sample Item

  42. Parts of a Fraction 3 = the number of parts 4 = the total number of parts that equal a whole

  43. Parts of a Fraction 3 = numerator 4 = denominator

  44. Adding and Subtracting Fractions with like Denominators You know that the bottom number of a fraction tells how may parts each whole is divided into. In this picture each circle is divided into 4 parts so the bottom number for this fractions is 4. 4 We use or shade 5 parts so the top number of this fraction is 5. The picture shows the fraction 5 . 4 In a fraction the bottom number has a special name. The bottom number in a fraction is called the denominator. The denominator or the bottom number in a fraction tells how many parts each whole is divided into.

  45. 1 2 4 6 7 8 7 5 2 3 What are the denominators in these fractions? Two Six Eight Five Three Remember the bottom number in a fraction is called the denominator.

  46. You have learned to add fractions using pictures. + = 1 4 5 3 3 3 Fractions can be added and subtracted without using pictures. Here’s a problem. 5 3 4 4 When you add and subtract fractions you do not work on the top and the bottom the same way. + = = +

  47. + = When you add and subtract fractions you COPY the denominator, then you work on the top. Remember, you copy the denominator and then you work on the top. 5 3 4 4 Look at this problem. What is the denominator? Yes, it’s 4. What do you do with the denominator? Right, you copy it in the answer so the denominator in the answer is 4. Now we can add the numbers on the top. What do we get when we add 5 + 3? Correct, 5 + 3 = 8. We put the 8 on top in the answer so 5 + 3 = 8 . 4 4 4 4

  48. - = 7 2 • 5 Here’s a different problem. First look at the sign. We are subtracting in this problem. Next look at the denominators. What do we do with the denominator? Yes, we copy it in the answer. On the top the sign tells us to subtract. 7 – 2, what’s the answer? Right, 7 – 2 = 5. We put the 5 on top. 5 5 7 2 5 5 5 5 5 - =

  49. Let’s try another problem. - = 4 3 • 2 First you copy the denominator then you work the top. What is the denominator? Yes, it’s 2. Now work on the top. What is 4 – 3? Right, it’s 1. So 4 3 1 2 2 2 2 - =

  50. Here’s a new problem. + = 2 3 • 4 What do we do with the denominator? Yes, we copy the 4. 4 What do we get on top? Good Job! 2 + 3 = 5. 2 3 5 4 4 4 + =

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