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1.3 Subtraction of Whole Numbers 1 Subtraction can be expressed by the equation a–b = c, where a is the minuend, b is the subtrahend, and c is the difference. a–b = c is only true if the inverse c + b = a is true. Subtraction is the operation where one amount is "taken away" from another amount leaving the difference. Example: Minuend Subtrahend Difference Phrases that indicate Subtraction: Minus Subtract Takeaway Difference Subtracted from * Less than * Decreased by Note: The order for the phrases in red are reversed. Examples: Translated 12 minus 412 – 4 The difference of 9 and 29 – 2 5 subtracted from 1717 – 5 4 less than 1010 – 4 In this section, we are only working with whole numbers, i.e, 0, 1, 2, 3 … We are not working with negative numbers, but we understand a little about them. If the temperature is –17°, it’s cold. If your checking account is $–24, you’re broke. So, 4 less than 10 translates to 10 – 4. If you did it incorrectly, and wrote 4 – 10, the answer would be –6. Subtraction is not commutative; order does matter.

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1.3 Subtraction of Whole Numbers 2 Since 7 is greater than 3, borrow a “1” from the 7 and write it in front of the 3. 6 1 5 7 3 - 3 8 7 Borrowing is the process that is used when the lower digit is larger than the upper digit. Procedure for Subtraction - Borrowing: 1.Line out the digit to the left of the upper digit, subtract 1 from it and write this new digit above. 2.Line out the original upper digit, add 10 to it, and write this number above. 3.Subtract the lower digit. 4.Proceed to the next column on the left. Example:Solution: 5 7 3 - 3 8 7 Now we can subtract 7 from 13. 6 Since 8 is larger than 6, borrow again. Subtract 1 from 5 and write the 1 in front of the 6. Then we can subtract. 4 1 8 1 Answer: 186 Your Turn Problem #1 Translate and Simplify a)15 subtracted from 49. b)The difference of 8 and 5. Answers: a)49 – 15 = 34 b)8 – 5 = 3

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1.3 Subtraction of Whole Numbers 3 Borrowing from 0. When the digit(s) to the left of the upper digit is 0, the 0(s) are lined out and replaced by 9(s), and then the first non zero digit to the left is borrowed from. Since 5 is greater than 2, borrow a “1” from the 4 and write 9’s in front of the zeros up to the last number. The last number gets a 1 in front of it. 1 3 9 9 1 6 2 7 Answer: 1627 4 0 0 2 - 2 3 7 5 Example:Solution: 4 0 0 2 - 2 3 7 5 (You can also think of it as borrowing a 1 from the 400 which becomes 399.) Answers: a)15,678 b)80,173 Your Turn Problem #2 Subtract a)45,354 – 29,676 b)98,000 – 17,827 Now we can subtract.

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1.3 Subtraction of Whole Numbers 4 Example: In June the Big Bear Boutique sold $24,760 worth of merchandise, but in July, it sold only $19,458 worth of merchandise. How much more did the boutique sell in June than in July? Solution: “How much more” indicates subtraction. 24,760 – 19,458 Answer: $5,302 Your Turn Problem #3 The attendance for a concert was 12,329 on Friday and 23,421 on Saturday. How many more people attended on Saturday than on Friday? Answer: 11,092 The End B.R. 6-2-08

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