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

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.

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.

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

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

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)

Try these ÷ 2 ÷ 3 1 2 1 3 1 5 2 5

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