RationalNumbers
Integers: …, -3, -2, -1, 0, 1, 2, 3, …A Rational Number can be written in theform a , where a and b are integers andb ≠ 0....
Representing fractions               2                                     3Area modelNumber Line Model                   ...
Equivalent (equal) fractions represent the samenumber.                                        2 2       4                 ...
2       6Show that and are equal by finding           3       9a common denominator.  The least common denominator of twof...
2       6Show that and are equal by              3       9simplifying both fractions.    A fraction is in simplest form if...
2        6Show that and        3        9   are equal by crossmultiplying.        a    c               if ad bc        b  ...
Ordering rational numbersPlace <, > or = between the two numbers:  2 3    <                  0    1   2   3   4   5   6   ...
1     1Find one rational number between   and                                 5     4    1 4            1 5         LCD = ...
1     1Find two rational numbers between   and                                  6     5   1 5             1 6         LCD ...
A mixed number represents the sum of an integerand a fraction.          1                  1      1   2         1        2...
2Change   1   3               to an improper fraction.An improper fraction has a numerator that is greater         than or...
Change 5 to a mixed number.       2                                    1                                2   2       1     ...
Adding Rational Numbers    1   1     2        1    4   4     4        2 3 1    1 4 3 4    3 4     3 4           7    12 12...
2       31   3   2   4                    2 4        8                1   3 4   1   12                               9    ...
2       31   3   2   4                    2   5 4    20                1   3   3 4    12                    3   11 3   33 ...
Subtracting Rational Numbers 4 2       1 3       8     3    5 4 9      12 3      36    36   36 2 2      1 5        4     5...
1       24   5   1   3                    1 3                          3 3 18                4   5 3   4 15               ...
1       2 4   5   1   33 21     5 53 5      3 5  63     25  15     15  38        8         2  15       15
Multiplication of Rational Numbers 3·2 =6                       3 groups of 2 3·½                                 =       ...
2 1   2           a c   a c        =    3 4 12            b d   b d    Rectangle model                1                423
1       1              1         12   4   1   2                      (2   4   )(1   2   )9 3             274 2            ...
Dividing rational numbers 6 3 =2                   3            3               How many threes are in six? 6 2 =3        ...
6 ½= 12       How many one-halfs are in six?6 ¼= 24       How many one-fourths are in six?
1   13   6      =2       How many one-sixths are in one-third?           a    c      a d           b    d      b c       1...
Jane has 20 yards of fabric. How many blousescan she make if each blouse requires:a) 2 yards of fabric         20 2 = 10 b...
Jane has 20 yards of fabric. How many blousescan she make if each blouse requires:b) 2 ½ yards of fabric                  ...
Jane has 20 yards of fabric. How many blousescan she make if each blouse requires:c)   2 1             yards of fabric    ...
1150 day 8
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1150 day 8

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1150 day 8

  1. 1. RationalNumbers
  2. 2. Integers: …, -3, -2, -1, 0, 1, 2, 3, …A Rational Number can be written in theform a , where a and b are integers andb ≠ 0. b 2 3 www.visualfractions.com
  3. 3. Representing fractions 2 3Area modelNumber Line Model 0 1 2 1 3 3Set model
  4. 4. Equivalent (equal) fractions represent the samenumber. 2 2 4 3 2 6 2 3 6 3 3 9 Fundamental Law of Fractions a a c b b c
  5. 5. 2 6Show that and are equal by finding 3 9a common denominator. The least common denominator of twofractions is the LCM of their denominators.LCM(3,9) = 9 2 3 6 3 3 9
  6. 6. 2 6Show that and are equal by 3 9simplifying both fractions. A fraction is in simplest form if its numerator and denominator have no common factor other than 1. 2 is simplified 6 3 2 3 9 3 3
  7. 7. 2 6Show that and 3 9 are equal by crossmultiplying. a c if ad bc b d 18 18 18 = 18 2 6 so 2 6 3 9 3 9
  8. 8. Ordering rational numbersPlace <, > or = between the two numbers: 2 3 < 0 1 2 3 4 5 6 1 7 7 7 7 7 7 7 7 7 1 3 > 7 5 5 1 1 1 < 5 5 4 1 4
  9. 9. 1 1Find one rational number between and 5 4 1 4 1 5 LCD = 20 5 4 4 5 4 2 5 2 20 2 20 2 9 8 10 40 40 40
  10. 10. 1 1Find two rational numbers between and 6 5 1 5 1 6 LCD = 30 6 5 5 6 5 2 6 2 30 2 30 2 10 2 12 2 60 2 60 2 21 22 23 20 24 , , 120 120 120 120 120
  11. 11. A mixed number represents the sum of an integerand a fraction. 1 1 1 2 1 2 1 1 1 2 1 2 -2 11 2 -1 0 1 1 1 2 2
  12. 12. 2Change 1 3 to an improper fraction.An improper fraction has a numerator that is greater than or equal to its denominator. 2 3 2 1 3 3 3 2 1 3 5 3
  13. 13. Change 5 to a mixed number. 2 1 2 2 1 1 1 2 2 2 5 2R1 4 2 1 2 1
  14. 14. Adding Rational Numbers 1 1 2 1 4 4 4 2 3 1 1 4 3 4 3 4 3 4 7 12 12 12
  15. 15. 2 31 3 2 4 2 4 8 1 3 4 1 12 9 2 3 3 4 3 2 12 17 3 12 5 4 12
  16. 16. 2 31 3 2 4 2 5 4 20 1 3 3 4 12 3 11 3 33 2 4 4 3 12 53 12 5 4 12
  17. 17. Subtracting Rational Numbers 4 2 1 3 8 3 5 4 9 12 3 36 36 36 2 2 1 5 4 5 1 2 5 2 5 10 10 10
  18. 18. 1 24 5 1 3 1 3 3 3 18 4 5 3 4 15 2 5 10 1 3 5 1 15 8 2 15
  19. 19. 1 2 4 5 1 33 21 5 53 5 3 5 63 25 15 15 38 8 2 15 15
  20. 20. Multiplication of Rational Numbers 3·2 =6 3 groups of 2 3·½ = 3 = 1 ½ or 2 3 groups of ½
  21. 21. 2 1 2 a c a c = 3 4 12 b d b d Rectangle model 1 423
  22. 22. 1 1 1 12 4 1 2 (2 4 )(1 2 )9 3 274 2 8 3 3 8
  23. 23. Dividing rational numbers 6 3 =2 3 3 How many threes are in six? 6 2 =3 2 2 2 How many twos are in six?
  24. 24. 6 ½= 12 How many one-halfs are in six?6 ¼= 24 How many one-fourths are in six?
  25. 25. 1 13 6 =2 How many one-sixths are in one-third? a c a d b d b c 1 1 1 6 6 2 3 6 3 1 3
  26. 26. Jane has 20 yards of fabric. How many blousescan she make if each blouse requires:a) 2 yards of fabric 20 2 = 10 blouses
  27. 27. Jane has 20 yards of fabric. How many blousescan she make if each blouse requires:b) 2 ½ yards of fabric 8 blouses 1 5 20 2 40 20 2 2 20 2 1 5 5 =8 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
  28. 28. Jane has 20 yards of fabric. How many blousescan she make if each blouse requires:c) 2 1 yards of fabric 8 blouses 3 1 7 20 3 60 4 20 2 3 20 3 1 7 7 8 7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20d) How many yards of fabric is left over? 1 7 56 2 Fabric used: 8 2 3 8 3 3 18 3 yards Fabric left: 20 18 2 1 1 yards 3 3

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