To Change a Mixed Number to an Improper Fraction Starter To Change a Mixed Number to an Improper Fraction 1. Whole number x Denominator 2. Add numerator to make NEW numerator 3. Denominator stays the same

We are Learning to…… Divide Fractions

Dividing an integer by a fraction 1 3 What is 4 ÷ ? 1 3 4 ÷ means, “How many thirds are there in 4?” Here are 4 rectangles: We could also think of this as, ‘What number times 1/3 will give us an answer of 4?’ or, ‘If we divided four apples into thirds, how many pieces would we have?’ Reveal the rectangles and ask pupils to count the number of thirds in four or deduce the number by working out 4 × 3, 3 thirds in each whole one. Dividing by a third is equivalent to multiplying by three. Stress that when we divide a whole number by a fraction less than one, the result will be a larger number. Let’s divide them into thirds. 4 ÷ = 12 1 3

Dividing an integer by a fraction 2 5 What is 4 ÷ ? 2 5 4 ÷ means, “How many two fifths are there in 4?” Here are 4 rectangles: We could also think of this as, ‘what number times 2/5 will give us an answer of 4?’ Reveal the rectangles and ask pupils to deduce the number of fifths in 4 by working out 4 × 5, five fifths in each whole one. So how many two fifths are there in four whole ones? Click to count the number of two fifths, 10. We could have worked this out by dividing the number of fifths, 20, by two to get 10. What is 2/5 × 10? or 2/5 of 10? This is four, so we know we are correct. Let’s divide them into fifths, and count the number of two fifths. 4 ÷ = 10 2 5

Dividing an integer by a fraction 3 4 What is 6 ÷ ? 3 4 6 ÷ means, ‘How many three quarters are there in six?’ 6 ÷ = 6 × 4 1 4 = 24 So, 6 ÷ = 24 ÷ 3 3 4 Go through each step in the calculation. Establish that when we divide a whole number by a fraction, we multiply by the denominator and divide by the numerator. = 8 We can check this by multiplying. 8 × = 8 ÷ 4 × 3 3 4 = 6

Dividing a fraction by a fraction 1 8 What is ÷ ? 2 means, ‘How many eighths are there in one half?’ 1 8 ÷ 2 Here is of a rectangle: 1 2 Reveal the shape divided into eighths and ask pupils how many eighths there are in one half. Reveal the calculation and the answer 4. State that dividing by 1/8 is equivalent to multiplying by 8. When we divide by a fraction we multiply by denominator and divide by the numerator. Now, let’s divide the shape into eighths. 1 8 ÷ 2 = 4

Dividing a fraction by a fraction 2 3 4 5 What is ÷ ? To divide by a fraction we multiply by the denominator and divide by the numerator. Swap the numerator and the denominator and multiply. 4 5 2 3 ÷ 5 4 2 3 × can be written as Explain that when we are dividing by a fraction we can write an equivalent calculation by swapping the numerator and the denominator around (turning the fraction upside-down) and multiplying. This works because when we multiply by a fraction we multiply by the numerator and divide by the denominator. Multiplying by a fraction is straight forward because we simply multiply the numerators together and multiply the denominators together. 5 4 2 3 × = 10 12 = 5 6

Dividing a fraction by a fraction 3 3 5 6 7 What is ÷ ? Start by writing as an improper fraction. 3 5 3 5 = 18 5 3 18 5 ÷ 6 7 = 18 5 × 7 6 Point out that cancelling before we multiply make the calculation easier. If we did not cancel at this stage we would have to cancel later on. 1 = 21 5 = 1 5 4

Dividing fractions

To succeed at this lesson today you need to… 1. As with multiplying you first have to convert any mixed numbers into improper fractions 2. INVERT the dividing fraction (turn it upside down) and change the division sign to multiplication 3. Do the multiplication Intermediate Page 188 Ex 11M

Homework 1.  3 1/7 ÷ 2 5/14 2.  3 1/5 ÷ 1 7/25 3.  2 4/7 ÷ 1 5/7 4.  1 19/26 ÷ 1 2/13 5.  1 2/17 ÷ 1 25/51