Dividing fractions is probably the most difficult idea students will have encountered in all their experiences with number. It requires careful teaching by the teacher and clever thinking by the students.

Using Number Properties

Problem: “Juanita has 7/8 of a cake. She cuts pieces of 2/9 in size to put in packets for  her guests.  How many packets of cake will she make?” Write 7/8 ÷ 2/9 on the board.

Discuss why it is hard to compare 7/8 and 2/9. (Answer: They have different names or  denominators, eighths and ninths.)

“How could you convert them into like fractions?” (Answer: The lowest common  multiple of 8 and 9 is 72, so you could convert eighths and ninths into “seventy-twoths”. So 7/8 = 63/72 and 2/9 = 16/72.)

How would you work out 63/72 ÷ 16/72? (Answer: 63/72 ÷ 16/72 = 63 ÷ 16 = or 3 15/16.)

Examples: Find 2/3 ÷ 4/7
2/7 ÷ 11/3
10/11 ÷ 9/4
5/6 ÷ 7/10

Problem: “Summarise the answers above in a table that discusses a quick way of dividing fractions.”

(Answer: Flipping the second fraction and multiplying always works. So, for example  7/8 ÷ 2/9 = 7/8 x 9/2 = 63/16.)

Examples: Find: 2/3 ÷ 4/7
2/7 ÷ 11/3
10/11 ÷ 9/4
5/6 ÷ 7/10...

Understanding Number Properties:

What letters replace the question marks? a/b ÷c/d = (? x ?)/(? x ?)
(Answer: (a x d)(b x c).)