New PDF release: Arithmetic and Algebra Again: Leaving Math Anxiety Behind

By Britta Immergut, Jean Burr Smith

ISBN-10: 0071435336

ISBN-13: 9780071435338

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Additional info for Arithmetic and Algebra Again: Leaving Math Anxiety Behind Forever, Second Edition

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7. 8. 9. 10. 11. 12. 13. 14. 4 ORDER OF OPERATIONS We have learned that neither order nor grouping matter in addition or multiplication. 3+2=2+3 3•2=2•3 (3 + 2) + 1 = 3 + (2 + 1) (3 • 2) • 1 = 3 • (2 • 1) Addition and multiplication are commutative and associative. Now we will see what happens when two or more operations occur in the same example. In 3 + 2 • 4 we can apparently get two different answers. 1. 2. If we add and then multiply, we get 3 + 2 • 4 = 5 • 4 = 20. If we multiply and then add, we get 3 + 2 • 4 = 3 + 8 = 11.

For most people this is the nightmare of mathematics. It is true that many 30 PART I ARITHMETIC math problems are not well written, interesting, or practical. However, it is hard to find or create good problems that illustrate each step in the learning process of mathematics. Some problems will have to be artificial in order to show a particular point. If you are going to master mathematics in a practical way, you need to understand many smaller steps. You will find many more application problems in Part III of this book.

How many miles does he drive during the fall semester (76 days)? Solution 1. 2. 3. 4. 5. Draw a picture. Harvey drives 23 miles 76 times. We could add 23 miles 76 times, but it will be quicker to multiply. 23 × 76 ≈ 20 × 80 = 1600 23 × 76 = 1748 1748 ≈ 1600. Harvey drives 1748 miles during the fall semester. EXAMPLE Pat bought a boat for $329, patched it, and painted it. She then sold the boat for $450. How much profit did she make on the sale? Solution 1. 2. 3. 4. 5. Pat bought something and sold it for more.

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Arithmetic and Algebra Again: Leaving Math Anxiety Behind Forever, Second Edition by Britta Immergut, Jean Burr Smith


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