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Level Five > Number and Algebra

# Harder Division of Fractions

Specific Learning Outcomes:

Identify highest common factors and least common multiples.

Solve multiplication and division problems that involve fractions.

Description of mathematics:

Number Framework Stage 8

Activity:

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).)

## Multiplying fractions

The purpose of this series of lessons is to develop understanding of the multiplication of fractions.

This unit supports teaching and learning activities in the Student Fractions e-ako 10 and complements the learning activities in Book 7 Teaching Fractions, Decimals and Percentages and in Book 8 Teaching Number Sense and Algebraic Thinking.

This is the fifth in a series of units developing fractional understanding. This unit builds on these previous units of work:

## Little Bites at Big Multiplications and Divisions

Solve multiplication and division problems by splitting factors.

## Folding fractions and decimals

Solve multiplication and division problems that involve decimals.

## Folding fractions and decimals

Solve multiplication and division problems that involve decimals.

## Seed Packets

Solve division problems involving fractions.

Solve simple rate problems using multiplication.