1. Multiplying and Dividing Fractions
Please acknowledge the NCETM in the use of this Presentation

2. Equivalent Fractions
Multiplication preserves the proportional relationships and produces equivalent fractions You have 2 minutes to write down as many equivalent fractions to ½ This activity can become a useful routine to develop fluency.

3. Expectations for multiplication of fractions Y6 POS
multiply simple pairs of proper fractions,
writing the answer in its simplest form (e.g.
× = ) 1 4 2 8
Animated talk through using the bar
Talk through two ways of looking at it.
Start with ¼ and scale it by ½
OR Start with a ½ and find a quarter of it
Select only one of these two models for a schools calculation ploicy
There are two structures for multiplication, repeated addition and scaling, the structure of scaling is required for a secure understanding of multiplication involving fractions.

4. Try These 1 4 X 1 3 1 4 X 2 3 1 4 X 1 4 1 2 X 1 3

5. 1 4 X 1 3 1 12 1 4 X 1 4 1 16 1 4 X 2 3 12 What do you notice? = = =
Notice that you can find the answer by multiplying numerators and denominators. This is a more efficient way to multiply fractions, however the previous strategy of drawing bars supports pupils in appreciation why the product of two fractions is smaller than the starting number 1 4 X 2 3 = 12

6. Expectations for Division of Fractions Y6 POS
divide proper fractions by whole numbers (e.g. ÷ 2 = ) 1 3 6
Animated talk through using the bar
First divide into 1/3 and focus on one of those 1/3 s
Now divide this !/3 into 2 (division by sharing model)
Now divide all of the bar into the same sized equal pieces to check the value of the quotient(the answer to the division)

7. Try these
÷ 2 ÷ 3 1 2 1 3 1 5 2 5

8. What do you notice? 1 2
÷ 2 ÷ 3 x 1 2 1 2 1 3 1 3 1 3 1 5 1 2 1 5
These are equivalent calculations – dividing by 2 is the same as multiplying by a half, dividing by 3 is the same as multiplying by a third, dividing by 7 is the same as multiplying by a seventh
An efficient way for division involving fractions is to multiply by the reciprocal of the divisor – this is an equivalent calculation and easier to perform 2 5 1 2 2 5