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Numbers and Their Application to Math and Science

Homework for Numbers Lesson 7

  1. Use Pascal's Triangle to expand (2x + 3)6 by examining (2x + 3)2, (2x + 3)3, ...

     

      Simplify completely problems 2–6 using a common denominator.  SHOW WORK!

  2. 1/7 + 1/11.

     

  3. 1/7 + 1/13.

     

  4. 1/11 + 1/13.

     

  5. 1/7 + 1/11 + 1/13.

     

  6. 9/143 + 18/77 + 8/91.

     

  7. Find 25% of 16.

     

  8. Find 250% of 16.

     

  9. The owner of a $50,000 (state equalize value, which should be about half the market value) house must calculate how much a proposed 2 mill road improvement tax will cost him. Help him!

     

  10. Express the number 2.7 as;  a) an improper fraction;  b) a mixed number.

  11. Divide 50 by 1/2 then add 3.

     

  12. Convert 22/7 exactly into a decimal fraction.

     

  13. Simplify completely:
    2/3 + 1/2
    5/12 - 1/4

     

  14. Simplify completely: (factor and cancel common terms)
     6  ×  15 × 77
    35229

     

  15. Simplify completely:
     35   ÷  15 ×   6 
    17347

     
    For problems 16-18:
    Egyptian fraction is another name for unit fraction. In ancient Egypt, these were the only fractions allowed. Other fractions between zero and one were always expressed as a sum of distinct Egyptian fractions. The greedy algorithm was commonly used to render fractions, such as 3/5, into unit fractions. The algorithm begins by finding two consecutive unit fractions that the given fraction is between ( 1/2 < 3/5 < 1/1). Using the smallest fraction, subtract it from the given fraction. This new number plus the smaller fraction is the result. The greedy Egyption number for 3/5 is 1/2 + 1/10 (3/5 - 1/2 = 6/10 - 5/10 = 1/10). Of course, there is no guarantee the result is a unit fraction, so more than 2 fractions may well be required. (See MMPC 1996, part II, problem 1.)

  16. Explicitly show how 1/2 + 1/10 = 1/3 + 1/4 + 1/60.

  17. Find the greedy representation for 2/13.

  18. Find the greedy representation for 9/10.

  19. Using your corrected list of the first 15 Fibonacci Numbers from homework 2 problem 3, find the approximate decimal ratio of consecutive pairs. Bonus: what is the exact limiting value this approaches?

     

  20. Write the word name for the number which corresponds to 232 - 1. Express this number in binary, hexadecimal, and base 10.

     

  21. Read section 11.2 of your geometry textbooks for further examples for lesson 6. See especially problems 15-20.

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