1 / 56

KS3 Mathematics

KS3 Mathematics. N6 Calculating with fractions. N6 Calculating with fractions. Contents. N6.2 Finding a fraction of an amount. N6.1 Adding and subtracting fractions. N6.3 Multiplying fractions. N6.4 Dividing by fractions. Fraction counter. Adding and subtracting simple fractions. 3 + 1.

ruth-richardson
Download Presentation

KS3 Mathematics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. KS3 Mathematics N6 Calculating with fractions

  2. N6 Calculating with fractions Contents N6.2 Finding a fraction of an amount N6.1 Adding and subtracting fractions N6.3 Multiplying fractions N6.4 Dividing by fractions

  3. Fraction counter

  4. Adding and subtracting simple fractions 3 + 1 3 1 4 5 5 5 5 When fractions have the same denominator it is quite easy to add them together and to subtract them. For example, + = = We can show this calculation in a diagram: + =

  5. Adding and subtracting simple fractions 7 – 3 4 – 8 8 3 1 7 2 8 8 1 = = = 2 Fractions should always be cancelled down to their lowest terms. We can show this calculation in a diagram: = –

  6. Adding and subtracting simple fractions + + 1 3 4 1 7 9 3 9 9 9 1 + 7 + 4 12 1 1 9 9 1 = = = = 3 Top-heavy or improper fractions should be written as mixed numbers. Again, we can show this calculation in a diagram: = + +

  7. Adding and subtracting simple fractions 1 1 3 4 4 4 1 1 2 2 What is + ? + = + =

  8. Adding and subtracting simple fractions 3 1 3 4 4 4 1 1 2 2 1 What is + ? + = + =

  9. Adding and subtracting simple fractions 3 3 1 8 8 8 1 1 2 2 What is – ? – = – =

  10. Fractional magic square

  11. Fractions with common denominators 11 11 4 4 5 12 12 12 12 12 5 11 + 4 + 5 8 2 1 1 20 12 12 12 3 12 Fractions are said to have a common denominator if they have the same denominator. For example, , and all have a common denominator of 12. We can add them together: = + + = = =

  12. Fractions with different denominators 1 1 What is + ? 2 3 2 5 3 + 2 3 6 6 6 6 Fractions with different denominators are more difficult to add and subtract. For example, We can show this sum using diagrams: + = + = =

  13. Using diagrams 2 9 15 11 4 15 – 4 18 18 18 18 5 6 What is – ? – = – = =

  14. Using diagrams 3 What is + ? 4 12 15 27 7 1 12 + 15 20 20 20 20 20 3 5 + = + = = =

  15. Using diagrams 1 4 7 1 10 25 14 25 – 14 11 20 20 20 20 What is – ? – = – = =

  16. Using a common denominator 3 5 7 1 3 1 + What is + ? 4 12 9 4 1 4 1) Write any mixed numbers as improper fractions. = 2) Find the lowest common multiple of 4, 9 and 12. The multiples of 12 are: 12, 24, 36 . . . 36 is the lowest common denominator.

  17. Using a common denominator 5 7 1 1 3 1 + What is + ? 12 9 4 9 4 ×3 ×4 ×9 5 10 82 63 4 15 12 18 36 36 36 36 36 36 36 36 ×9 ×3 ×4 5 2 2 63 + 4 + 15 36 3) Write each fraction over the lowest common denominator. 63 4 15 = = = 4) Add the fractions together. = + + = = =

  18. Adding and subtracting fractions

  19. Using a calculator It is also possible to add and subtract fractions using the key on a calculator. a a b b c c we can key in For example, to enter 4 8 = Pressing the key converts this to: 4 8 The calculator displays this as:

  20. Using a calculator 2 4 3 5 a a b b + c c 2 3 + = 5 4 15 7 1 We write this as To calculate: using a calculator, we key in: The calculator will display the answer as:

  21. Fraction Puzzle

  22. Drag and drop fraction sum

  23. Fraction cards

  24. N6 Calculating with fractions Contents N6.1 Adding and subtracting fractions N6.2 Finding a fraction of an amount N6.3 Multiplying fractions N6.4 Dividing by fractions

  25. Finding a fraction of an amount 2 2 What is of £18? 3 3 of £18 We can see this in a diagram: = £18 ÷ 3 × 2 = £12

  26. Finding a fraction of an amount What is of £20? 7 10 7 of £20 10 Let’s look at this in a diagram again: = £20 ÷ 10 × 7 = £14

  27. Finding a fraction of an amount 5 1 5 What is of £24? 6 6 6 of £24 = of £24 × 5 = £24 ÷ 6 × 5 = £4 × 5 = £20

  28. Finding a fraction of an amount To find of an amount we can multiply by 4 and divide by 7. 4 4 1 7 7 7 36 5 kg = kg 7 What is of 9 kg? We could also divide by 7 and then multiply by 4. 4 × 9 kg = 36 kg 36 kg ÷ 7 =

  29. Finding a fraction of an amount 2 3 multiply by the numerator and divide by the denominator of 18 litres When we work out a fraction of an amount we For example, = 18 litres ÷ 3 × 2 = 6 litres × 2 = 12 litres

  30. Finding a fraction of an amount 2 5 To find of an amount we need to add 1 times the amount to two fifths of the amount. 1 2 2 2 5 5 5 of 3.5 m = 1 so, of 3.5 m = 1 What is of 3.5m? 1 × 3.5 m = 3.5 m and 1.4 m 3.5 m + 1.4 m = 4.9 m

  31. MathsBlox

  32. N6 Calculating with fractions Contents N6.1 Adding and subtracting fractions N6.2 Finding a fraction of an amount N6.3 Multiplying fractions N6.4 Dividing by fractions

  33. Counting on and back using fractions

  34. Multiplying fractions by integers 1 3 1 1 1 3 1 What is 8 × ? 4 4 2 2 4 4 4 1 1 1 1 1 1 1 1 4 4 4 4 4 4 4 4 1 1 1 We can illustrate this calculation on a number line: 0 1 2

  35. Multiplying fractions by integers 3 What is 12 × ? 4 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 3 1 1 6 3 7 2 4 5 1 3 3 1 1 1 8 1 4 2 4 4 4 4 2 2 4 Again, we can illustrate this calculation on a number line: 0 3 6 9

  36. Multiplying fractions by integers 1 1 2 1 2 2 1 What is 9 × ? 3 3 3 3 3 3 3 1 1 1 1 1 1 1 1 1 3 3 3 3 3 3 3 3 3 2 1 2 1 Let’s use a number line again: 0 1 2 3

  37. Multiplying fractions by integers 1 3 1 4 4 3 8 × = 2 9 × = 3 12 × = 9 So, and What do you notice?

  38. Multiplying fractions by integers 1 1 1 4 4 4 8 × × 8 8 ÷ 4 of 8 Following the rules of arithmetic, we know that, In maths the word ‘of’ means ‘times’. = = = These are equivalent calculations.

  39. Equivalent calculations 3 3 3 of 20 × 20 5 5 5 1 3 × of 20 5 20 × 20 × 3 ÷ 5 20 ÷ 5 × 3 3 ÷ 5 × 20 Means the same as:

  40. Multiplying fractions by integers 4 9 54 × When we multiply a fraction by an integer we: multiply by the numerator and divide by the denominator For example, = 54 ÷ 9 × 4 = 6 × 4 = 24

  41. Multiplying fractions by integers 4 5 5 7 7 7 What is 12 × ? 12 × 60 = 7 8 = = 12 × 5 ÷ 7 = 60 ÷ 7

  42. Using cancellation to simplify calculations 7 7 7 What is 16 × ? 12 12 12 We can write 16 × as: 16 × 1 3 9 1 = 3 4 28 = 3

  43. Using cancellation to simplify calculations 8 8 What is × 40? 25 25 We can write × 40 as: 8 40 25 1 × 5 12 4 = 5 8 64 = 5

  44. Multiplying a fraction by a fraction 3 3 2 4 8 8 5 5 = × 40 3 = 10 What is × ? To multiply two fractions together, multiply the numerators together and multiply the denominators together: 3 12 10

  45. Multiplying a fraction by a fraction 12 5 5 4 What is × ? 25 6 5 35 12 × = 6 25 5 2 = Start by writing the calculation with any mixed numbers as improper fractions. To make the calculation easier, cancel any numerators with any denominators. 7 2 14 1 5

  46. Multiplying fractions mentally

  47. N6 Calculating with fractions Contents N6.1 Adding and subtracting fractions N6.2 Finding a fraction of an amount N6.4 Dividing by fractions N6.3 Multiplying fractions

  48. Multiplying and dividing fractions

  49. Dividing an integer by a fraction 1 1 1 3 3 3 What is 4 ÷ ? 4 ÷ means, “How many thirds are there in 4?” 4 ÷ = 12 Here are 4 rectangles: Let’s divide them into thirds.

  50. Dividing an integer by a fraction 2 2 2 What is 4 ÷ ? 5 5 5 4 ÷ means, “How many two fifths are there in 4?” 4 ÷ = 10 Here are 4 rectangles: Let’s divide them into fifths, and count the number of two fifths.

More Related