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**Extra resources for Arithmetic Groups and Their Generalizations What, Why, and How**

**Example text**

The second type is phrased as an addition problem with a missing addend. Example: Maria received 72 points on her last math test, but needed 90 points to receive an A. How many more points would she have needed to earn an A? ) 72 ϩ ? ϭ 90 is equivalent to 90 Ϫ 72 ϭ ? Because 90 Ϫ 72 ϭ 18, Maria would have needed 18 more points. Example 6 Solving an Application Problem Skill Practice A biology class started with 35 students. By midsemester, 7 students had dropped. How many students are still in the class?

10 Ϫ 6 ϭ 4 because 4 ϩ 6 ϭ 10 c. 5 Ϫ 0 ϭ 5 because 5ϩ0ϭ5 d. 3 Ϫ 3 ϭ 0 because 0ϩ3ϭ3 2. Subtraction of Whole Numbers When subtracting large numbers, it is usually more convenient to write the numbers vertically. We write the minuend on top and the subtrahend below it. Starting from the ones column, we subtract digits having corresponding place values. Skill Practice Example 2 Subtract. Check by using addition. 5. 6. 3947 472 Ϫ 137 Ϫ 261 Subtracting Whole Numbers Subtract and check the answer by using addition.

73. 93 Ϫ 27 74. 80 Ϫ 20 75. 165 Ϫ 85 76. 171 Ϫ 42 77. Use the expression 7 – 4 to explain why subtraction is not commutative. 78. Is subtraction associative? Use the numbers 10, 6, 2 to explain. 79. A $50 bill was used to purchase $17 worth of gasoline. Find the amount of change received. 80. There are 55 DVDs to shelve one evening at a video rental store. If Jason puts away 39 before leaving for the day, how many are left for Patty to put away? 3 Subtraction of Whole Numbers 29 81. The songwriting team of John Lennon and Paul McCartney had 118 chart hits while Mick Jagger and Keith Richards had 63.