2. a/b by n Division of Fractions Dividing a fraction by a whole number. To divide a fraction by a whole number simply multiply it by the reciprocal of the number. Example 1: 5 8 3  = 5 8 x 1 3 = 5 24 A visual explanation of this is shown in the diagrams below. 5 8 Taking a 1/3 of 5/8 by dividing it by 3 5 24 “INVERT and MULTIPLY”

3. Questions 1 Answer the following questions: 1 4 3 4  3  3 2 3  5  5 5 6  2  2 1 5  5  5 1 6  6  6 5 8  4  4 3 4  4  4 7 10  8  8 5 12  3  3 a b c d e f g h i 2 15 5 12 1 25 1 36 5 32 3 16 7 80 5 36

4. n by a/b Dividing a whole number by a fraction. To divide a whole number by a fraction simply multiply it by the reciprocal of the fraction. Example 1: 2 3 4  = 4 1 x 3 2 A visual explanation of this is shown in the diagrams below. “INVERT and MULTIPLY” = 6 12 2 = How many 2/3 in 4? Division of Fractions

5. Questions2 Answer the following questions: 3 4 3  a 2 3 5  1 3 2  1 5 7  5 8 6  4 5 7  1 11 11  1 6 9  7 8 4  4 7 1 2 b c d e f g h i 6 35 9 3 5 8 3 4 12154 4 4 7

6. Whole Number Dividing general fractions. To divide any fraction by another simply multiply by the reciprocal of the fraction that you are dividing by. = 3 4 x 3 2 “INVERT and MULTIPLY” = 9 8 Example 1: 2 3  3 4 = 1 1 8 = 11 12 x 9 2 = 99 24 Example 2: 2 9  11 12 = 4 1 8 Division of Fractions

7. Questions 3 Answer the following questions: 2 1 4 1 3  3 4 1 8  6 7 2 3  1 8 1 4  2 9 3 4  7 10 9  5 6 1 2  13 15 2 3  1 12 2 15  19 20 a b c d e f g h i 6 6 7 3 16 8 9 14 15 25 27 1 11 15 1 8 7 1 8

8. Why 1 Why do we multiply by the reciprocal when dividing fractions? Why is: 2 3  3 4 3 2 x 3 4 = ? How many 1 3 in a whole? 3 1 3 the reciprocal of How many 2 3 in a whole? 2 3 the reciprocal of 3 2 How many 2 3 3 4 in ? It must be ¾ of the number that are in a whole. Specific Case 1 3 4 x 3 2 =

9. Why 2 Why do we multiply by the reciprocal when dividing fractions? Why is: 4 5  3 8 5 4 x 3 8 = ? How many 1 5 in a whole? 5 1 5 the reciprocal of How many 4 5 in a whole? 4 5 the reciprocal of 5 4 How many 4 5 3 8 in ? It must be 3/8 of the number that are in a whole. Specific Case 2 3 8 x 5 4 =

10. General Why do we multiply by the reciprocal when dividing fractions? How many 1 d in a whole? d 1 d the reciprocal of How many c d in a whole? c d the reciprocal of d c How many c d a b in ? It must be a/b of the number that are in a whole. c d  a b d c x a b = General Case a b x d c =

11. Worksheet 1 Answer the following questions: 3 4  3  3 2 3  5  5 5 6  2  2 1 5  5  5 1 6  6  6 5 8  4  4 3 4  4  4 7 10  8  8 5 12  3  3 a b c d e f g h i

12. Workshe et2 Answer the following questions: 3 4 3  a 2 3 5  1 3 2  1 5 7  5 8 6  4 5 7  1 11 11  1 6 9  7 8 4  b c d e f g h i

13. Workshe et3 Answer the following questions: 1 3  3 4 1 8  6 7 2 3  1 8 1 4  2 9 3 4  7 10 9  5 6 1 2  13 15 2 3  1 12 2 15  19 20 a b c d e f g h i