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Decimals: The Basic Steps in Adding and Subtracting

Learn the essential steps for adding and subtracting decimals, including alignment, zero filling, and using addition properties. Understand why estimating is crucial and how to subtract across zeroes. Practice with mental math techniques and homework exercises.

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Decimals: The Basic Steps in Adding and Subtracting

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  1. Adding and Subtracting Decimals Lesson 1-5

  2. The Basic Steps: • Line up the numbers by the decimal point. • Fill in missing places with zeroes. • Add or subtract.

  3. Addition Properties Commutative Property of Addition: Numbers can be added in any order. Example: 5+3=3+5 Associative Property of Addition: Numbers can be grouped in any way. Example: (7+3) + 5 = 7 + (3+5) Identity Property of Addition: The sum of any number and zero is that number. Example: 18 + 0 = 18

  4. Mental Math • Addition properties can be used to quickly find sums. • Example: What is 52 + 12.4 + 48? • We can use an addition property to quickly add this. • First, change the order: 52 + 48 + 12.4 ________________ property. • Then, group the first two addends together: (52 + 48) + 12.4________________ property • 100 + 12.4 = 112.4 commutative associative

  5. Why Estimate? • Before adding your numbers, use one of the estimating strategies you learned to see what the answer should be close to. • When you add, you can see if your answer is reasonable.

  6. Example: 28.9 + 13.31 This can estimate to 30 + 13, which is 43. (Compatible numbers) 28.9 0 + 13.31 42.21 The answer is close to the estimate.

  7. Subtracting • The addition properties do not work for subtraction. • Estimate and subtract to find what the answer is close to. • Subtract to find the real answer.

  8. Subtracting Across Zeroes • If you have several zeroes in a row, and you need to borrow, go to the first digit that is not zero, and borrow. • All middle zeroes become 9’s. • The final zero becomes 10.

  9. Example: 15 – 9.372 0 1 4 9 9 10 .000 15 - 9.372 5 . 6 2 8

  10. Homework Time The above image is a royalty free picture provided by http://www.bigfoto.com

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