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Continued fractions by C. D Olds

By C. D Olds

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65 degrees Fahrenheit Mentally do the following 2-digit division problems. 16. 975 ÷ 13 17. 259 ÷ 31 33 18. 490 ÷ 62 (use overshooting) 19. 183 ÷ 19 (use overshooting) Do the following division problems by ¿rst simplifying the problem to an easier division problem. 20. 4200 ÷ 8 21. 654 ÷ 36 22. 369 ÷ 45 23. 5 24. Give the decimal expansions for 1/7, 2/7, 3/7, 4/7, 5/7, and 6/7. 25. Give the decimal expansion for 5/16. 26. Give the decimal expansion for 12/35. 27. When he was growing up, Professor Benjamin’s favorite number was 2520.

04 (= $920; exact answer: $938). 5%. answers to multiplication or Suppose a bank offers an interest rate of 3% per division problems, year on its savings accounts. You can ¿nd out how long it will take to double your money using the it’s important to “Rule of 70”; this calculation is 70 divided by the ¿rst determine the interest rate. order of magnitude of the answer. Suppose you borrow $200,000 to buy a house, and the bank charges an interest rate of 6% per year, compounded monthly. What that means is that the bank is charging you 6/12%, or 1/2%, interest for every month of your loan.

We replace one of the 13s with 10; then, since we’ve gone down 3, we need to go back up by adding 3 to the other 13 to get 16. The ¿rst part of the calculation is now 10 × 16. To that result, we add the square of the number that went up and down (3): 10 × 16 = 160 and 160 + 32 = 169. Numbers that end in 5 are especially easy to square using this method, as are If you’re quick with 2-by-1 numbers near 100. multiplications, you can practice the “math of Finally, our ¿fth mental multiplication strategy is the close-together method, least resistance”—look which we saw in the last lecture.

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