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Fractions

Fractions. Ms. Crusenberry 9-2013. Vocabulary. Fraction – part of a whole number Numerator – the number of parts that are used; the number above the fraction line Denominator – the number of parts to the whole; the number below the fraction line. Write the fraction. Comparing Fractions.

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Fractions

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  1. Fractions Ms. Crusenberry 9-2013

  2. Vocabulary • Fraction – part of a whole number • Numerator – the number of parts that are used; the number above the fraction line • Denominator – the number of parts to the whole; the number below the fraction line

  3. Write the fraction

  4. Comparing Fractions • Cross Product – the answer obtained by multiplying the denominator of one fraction by the numerator of another aka cross multiplication Greater than > or Less than <23 multiply 2 x 5 first = 10 3 > 4 multiply 3 x 3 last = 9

  5. Practice • 658 6 • 758 6 • 161517 16 • 5219 7

  6. Answers • 6 x 6 = 12 < 8 x 5 = 40 • 7 x 6 = 42 > 8 x 6 = 40 • 16 x 16 = 256 > 17 x 15 = 255 • 5 x 7 = 35 < 19 x 2 = 38

  7. Simplifying Fractions • Simplest form – a fraction in which the numerator and denominator have no common factor greater than one • Simplify – to express in simplest form

  8. Example 14 ÷ 2 = 716 ÷ 2 = 8 What is the greatest common factor?14 161 x 14 1 x 16 2 x 7 2 x 8 4 x 4 2 is the greatest common factor

  9. Practice • 4/18 • 12/42 • 27/81 • 13/39 • 80/120 • 55/121 • 12/15 • 45/50

  10. Answers • 2/9 • 2/7 • 1/3 • 1/3 • 2/3 • 5/11 • 4/5 • 9/10

  11. Mixed Number/Improper Fractions • Mixed number – number composed of a whole number and a fraction ex. 1 ½ • Improper fraction – fractions who numerators are equal to or greater than their denominators ex. 50/10

  12. Renaming Mixed Numbers as Improper Fractions • Step 1 – multiple the whole number by the denominator • Step 2 – add the numerator • Step 3 – Write the answer over the denominatorEx. 3 ½ 3 x 2 + 1 = 7 2

  13. Practice • 2 ¾ • 8 3/7 • 5 ½ • 6 2/9 • 23 2/5 • 10 ¾

  14. Answers • 11/4 • 59/7 • 11/2 • 56/9 • 115/5 • 43/4

  15. Renaming Improper Fractions as Mixed Numbers Ex. 18/5 Step 1 – divide 18 by 5 3 5 18-15 so, its 3 3/5 3**The number left is the new numerator and you always keep the denominator

  16. Practice • 32/6 • 61/4 • 235/4 • 79/5 • 19/2 • 80/8

  17. Answers • 5 1/3 • 15 ¼ • 5/ ¾ • 15 4/5 • 9 ½ • 10

  18. Writing Mixed Numbers in Simplest Form • 3 2/4 - 2/4 simplifies to ½, so your answer is 3 ½ • 5 16/8 – 16/8 simplifies to 2, so you add that whole number to the one in the mixed number to get the answer 7 • 4 7/6 – 7/6 simplifies to 1 1/6 – so you add that whole number to the one in the mixed number to get the answer 5 1/6

  19. Practice • 6 5/15 • 17 13/10 • 7 6/3 • 6 4/3 • 10 25/6

  20. Answers • 6 1/3 • 18 3/10 • 9 • 7 1/3 • 14 1/6

  21. Multiplying Fractions Ex. 2/7 x 4/5 Step 1 – multiply the numerators 2 x 4 = 8 Step 2 – multiply the denominators 7 x 5 = 35 Answer is 8/35

  22. Continued… Ex. 6 x 4/7 Step 1 – make the whole number a 6 a fraction by putting it over 1 Step 2 – multiply the numerators 6 x 4 = 24 Step 3 – multiply the denominators 1 x 7 = 7Answer is 24/7 (must make an improper fraction) = 3 3/7

  23. Practice • 2/3 x 4/5 • 4/7 x 3/6 • 11/13 x 26/33 • 5/11 x 4/6 • 6/7 x 5/12

  24. Answers • 8/15 • 2/7 • 286/429 • 10/33 • 5/12

  25. Using Cross Simplification Ex. 9 x 14 10 15 Step 1 - Check the first numerator with the second denominator; simply if possible 3 goes into both so 9 becomes a 3 and the 15 becomes a 5 Step 2 – Check the first denominator with the second numerator; simply if possible 2 goes in to both so 10 becomes 5 and 14 becomes 7 New problem is now: 3 x 7 = 21 **This does not simplify any 5 5 25 further

  26. Practice • 4/9 x 7/12 • 6/12 x 2/12 • 3/16 of 8/9 • 4/9 of 7/12 • 7/10 x 5/28

  27. Answers • 7/27 • 1/12 • 1/6 • 7/27 • 1/8

  28. Multiplying Mixed Numbers Ex. 2 ¾ x 1 ½ Step 1: You must change mixed numbers to improper fractions before you can multiply them. 2 ¾ = 11/4 and 1 ½ = 3/2, so 11 x 3 = 33 4 2 8 **you must rename to a mixed number, so the answer is 4 1/8

  29. Practice Cross simplify the improper fractions if you can before multiplying them. • 1 ½ x 2 3/5 • 2 1/6 x 2/3 • 5 1/3 x 2 ½ • 5/6 x 2 3/10 • 3 5/6 x 3/8

  30. Answers • 3 9/10 • 1 4/9 • 13 1/3 • 1 11/12 • 1 7/16

  31. Dividing Fractions Ex. 5/7 ÷ 4/5 Step 1 – keep the first fraction Step 2 – change the ÷ to x Step 3 – do the reciprocal of 4/5, which is 5/4 5/7 x 5/4 = 25/28

  32. Practice Cross simplify if you can after you do the steps but before you divide • 2/7 ÷ 5/6 • 3/8 ÷ ¾ • 4/7 ÷ 5/7 • 2/3 ÷ 5/6 • 3/13 ÷ 5/6 • 9 ÷ 9/10

  33. Answers • 5/21 • ½ • 4/5 • 4/5 • 18/65 • 10

  34. Dividing Mixed Numbers • Just like multiplying mixed numbers, you must change the mixed numbers to improper fractions before you do anything else • Once that is done, change the ÷ to x and then do the reciprocal of the last improper fraction

  35. Example 3 ½ ÷ 2 ½ - change to improper 7/2 ÷ 5/2 – change the sign and use reciprocal 7/2 x 2/5 – cross simplify if possible then multiply 7/1 x 1/5 = 7/5 (this is improper so fix it by changing it to a mixed number) Answer is 1 2/5

  36. Practice • 2 ¾ ÷ 5/6 • 1 1/3 ÷ ¼ • 2 2/7 ÷ 2 2/7 • 7 ½ ÷ 6 2/3 • 5 2/5 ÷ 1 1/5

  37. Answers • 3 3/10 • 5 1/3 • 1 • 1 1/8 • 4 ½

  38. Adding Fractions with Like Denominators Ex. 2/7 + 4/7 = 6/7 Step 1 – add the numerators Step 2 – carry over the denominator Step 3 – simplify if needed Ex. 2 4/5 + 6 3/5 = 8 7/5 = 9 2/5 Step 1 – add the whole numbers Step 2 – add the numerators Step 3 – carry over the denominator Step 4 – simply if needed

  39. Practice • 5/8 + 3/8 • 5/11 + 4/11 • 2 5/16 + 5 1/16 • 3 2/19 + 4 3/19 • 4 17/20 + 3/20

  40. Answers • 1 • 9/11 • 7 3/8 • 7 5/19 • 5

  41. Subtracting with Like Denominators • You do these problems the exact same way as you did the addition, except you are subtracting the numbersEx. 4/7 – 2/7 = 2/7 13 11/12 – 5 5/12 = 8 6/12 = 8 ½

  42. Practice • 7/8 – 3/8 • 11/12 – 1/12 • 25 4/5 – 6 3/5 • 13 3/13 – 2/13 • 19 19/21 – 5 5/21

  43. Answers • ½ • 5/6 • 19 1/5 • 13 1/13 • 14 2/3

  44. Adding with Unlike Denominators • Common denominators – common multiples of two or more denominators • Least common denominator (LCD) – smallest denominator that is a multiple of two denominators

  45. How to Solve these Problems • Step 1 – find the least common multiple of the denominators • Step 2 – use 12 as a new denominator • Step 3 – raise the fractions to higher terms • Step 4 – add the fractions, simplify if needed

  46. Example • 1 + 3 6 4 find the LCD (the smallest number that both 6 and 4 will go into) 6 x 1 = 6 4 x 1 = 4 6 x 2 = 12 4 x 2 = 8 4 x 3 = 12 29 12 + 12 6 goes into 12 twice so 2 x 1 = 2; 4 goes into 12 three times so 3 x 3 = 9 Answer is 11/12

  47. Practice • 2/7 + ¾ • 3/8 + 2/3 • 2/9 + 2/3 • 1/8 + 2/5 • 5/12 + 2/3

  48. Answers • 5/7 • 1 1/24 • 8/9 • 21/40 • 1 1/12

  49. Subtraction with Unlike Denominators • Use solve the problems the exact same way as you did the addition problems except you are subtracting

  50. Practice • 8/9 – 1/3 • 2/3 – 2/5 • 2/3 – 2/7 • 4/5 – 1/3 • 7/10 – 1/2

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