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Division and rational number

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Slide Ini dibuat untuk memenuhu salah satu Tugas Mata Kuliah Bahasa Inggris Program studi. Pend. Matematika di FKIP Universitas Singaperbangsa Karawang...

By. Panggita Inoprasetyo

Published in: Education, Technology, Business
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Division and rational number

  1. 1. Division and rational number. Any two integers have such that xq = y. The process for finding q when three such an integer is called division, and q is called the quotient. Since division is not always possible in the set of integers, it is advantageous to create a larger set of number which division is possible in more casess. The number which are introduced for this prpose are the fractions, and the union of the set of fractions and the set of integers is the set of rational number
  2. 2. Division is splitting into equal parts or groups. It is the result of "fair sharing".
  3. 3. 12 Chocolates 12 Chocolates Divided by 3 Answer: 12 divided by 3 is 4: they get 4 each.
  4. 4. We use the ÷ symbol, or sometimes the / symbol to mean divide: 12 ÷ 3 = 4 12 / 3 = 4 ÷/
  5. 5. Division is the opposite of multiplying. When we know a multiplication fact we can find a division fact: Example: 3 × 5 = 15, so 15 / 5 = 3. Also 15 / 3 = 5.
  6. 6. Multiplication... ...Division 3 groups of 5 make 15... so 15 divided by 3 is 5 and also: 5 groups of 3 make 15... so 15 divided by 5 is 3. So there are four related facts: 3 × 5 = 15 5 × 3 = 15 1a5 / 3 = 5 15 / 5 = 3
  7. 7. Searching around the multiplication table we find that 28 is 4 × 7, so 28 divided by 7 must be 4.? Answer: 28 ÷ 7 = 4
  8. 8. There are special names for each number in a division: dividend ÷ divisor = quotient Example: in 12 ÷ 3 = 4: 12 is the dividend 3 is the divisor 4 is the quotient
  9. 9. Example: There are 7 bones But 7 cannot be divided exactly into 2 groups, to share with 2 pups. so each pup gets 3 bones, but there will be 1 left over: Hahahaha... :D
  10. 10. A Rational Number is a real number that can be written as a simple fraction (i.e. as a ratio). Example: 1.5 is a rational number because 1.5 = 3/2 (it can be written as a fraction)
  11. 11. Number As a Fraction Rational? 5 5/1 Yes 1.75 7/4 Yes .001 1/1000 Yes 0.111... 1/9 Yes √2 (square root of 2) ? NO !
  12. 12. More formally we would say: A rational number is a number that can be in the form p/q where p and q are integers a nd q is not equal to zero. So, a rational number can be: p q
  13. 13. Using Rational Numbers P q p/q = 1 1 1/1 1 1 2 ½ 0.5 55 100 55/100 0.55 1 1000 1/1000 0.001 253 10 253/10 25.3 7/0 No! "q" can't be zero! 7 0 If a rational number is still in the form "p/q" it can be a little difficult to use, so I have a special page on how to: Add, Subtract, Multiply and Divide Rational Numbers
  14. 14. The ancient greek mathematician Pythagoras believed that all numbers were rational (could be written as a fraction), but one of his students Hippasus proved (using geometry, it is thought) that you could not represent the square root of 2 as a fraction, and so it was irrational. However Pythagoras could not accept the existence of irrational numbers, because he believed that all numbers had perfect values. But he could not disprove Hippasus' "irrational numbers" and so Hippasus was thrown overboard and drowned!

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