This document provides instructions for adding and subtracting decimals. It explains that decimals should be aligned by place value, with zeros added to make the columns even. It also notes that when whole numbers are used in calculations, an "understood" decimal point and zeros are present but not written. Examples are provided demonstrating how to correctly add, subtract, and align decimals by placing them in columns and only combining like place values.

1. Addition & Subtraction of Decimals by Doug McFarland Horizon Academy Roeland Park, Kansas www.horizon-academy.com

2. Add and Subtract like Columns 71 + 58 + 25 = _______ 4 1 15 RULE: Only add and subtract LIKE columns. 71 58 25 + tens ones

3. 7.1 + 5.8 + 2.5 = _______ Add & Subtract like Columns . 4 1 15 RULE: Only add and subtract LIKE columns. 7 . 1 5 . 8 2 . 5 + ones ten ths

4. The “Understood” Decimal Consider the whole number 15 15 = 1 ten + 5 ones (10 + 5). We could put a decimal to separate the whole number from the decimal. 15.0 There is NO value in the tenths column, so we put 0 (zero).

5. Addition with the “Understood” Decimal If you were adding 15 + 12 you could write the problem 15.0 + 12.0 15.0 + 12.0 = 27.0 or 27 When there is no decimal value, the zero and the decimal are NOT written, but they are understood to still be there.

6. Make The Columns Even 34.5 + 21 + 8.5 .0 34.5 21. 0 8.5 + RULE: Add zeros to even the columns 34.5 21 8.5 +

7. Make The Columns Even 44.589 + 7.23 + 5 56.819 1 1 7 23 0 5 000 3 decimal columns 2 decimal columns 0 decimal columns 44.589 . . +

8. Subtracting Decimals Remember how to even your columns. Remember the “understood” . 0 when looking at a whole number like 7 It could be 7. 0 or 7. 00 if needed . In subtraction, it will be needed .

9. Let’s Look at Subtraction 34 – 12 = _____ 34 - 12 22 tens ones

10. Subtract Similar Columns 34 – 1 . 2 = _____ RULE: Only add and subtract LIKE columns. 3 4 - 1.2 2.2 ones ones ten ths tens Warning ! !

11. Subtract Similar Columns 34 – 1.2 = _____ 1 8 2 3 34. 0 - 1. 2 . ones ten ths 3 33

12. Here’s a Tricky One 8 - 3.56 = _______ .00 5.56 1 1 4. 4 4 8 - 3.56 8. 0 0 - 3. 5 6 7 9

13. We’re Done! Nice job following along in the lesson! Try to use what you learned in your work! Doug McFarland ©2006