By A. I. Kostrikin, I. R. Shafarevich

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**Extra info for Algebra II - Noncommunicative Rings, Identities**

**Example text**

A subtracted from b 61. The difference of 3 and 2 is 1. 62. The difference of 10 and y is 5. 63. The difference of 37 and 9x is 10. 64. The difference of 3x and 2y is 15. 65. The difference of 2y and 15x is 24. 66. The difference of 25x and 9y is 16. 67. The difference of (x + 2) and 68. The difference of (x − 2) and (x + 1) is 1. (x − 4) is 2. 4 Problem Set D 39 Applying the Concepts Not all of the following application problems involve only subtraction. Some involve addition as well. Be sure to read each problem carefully.

Subtract. a. 684 − 431 b. 7,406 − 3,405 EXAMPLE 1 SOLUTION Subtract: 376 − 241 We write the problem vertically, aligning digits with the same place value. Then we subtract in columns. 376 − 241 m888 Subtract the bottom number in each column 135 2. a. Subtract 405 from 6,857. b. Subtract 234 from 345. from the number above it EXAMPLE 2 SOLUTION Subtract 503 from 7,835. In symbols this statement is equivalent to 7,835 − 503 To subtract we write 503 below 7,835 and then subtract in columns. m888888888888888 Answers 1.

Use the associative property of addition to rewrite each sum. a. (3 + 2) + 9 b. (4 + 10) + 1 c. 5 + (9 + 1) d. 3 + (8 + n) Chapter 1 Whole Numbers EXAMPLE 6 Use the associative property of addition to rewrite each sum. a. (5 + 6) + 7 SOLUTION b. (3 + 9) + 1 c. 6 + (8 + 2) d. 4 + (9 + n) The associative property of addition indicates that we are free to regroup the numbers in a sum without changing the result. a. (5 + 6) + 7 = 5 + (6 + 7) b. (3 + 9) + 1 = 3 + (9 + 1) c. 6 + (8 + 2) = (6 + 8) + 2 d.

### Algebra II - Noncommunicative Rings, Identities by A. I. Kostrikin, I. R. Shafarevich

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