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Fractions

Adding and subtracting fractions Adding fractions with different denominators Multiplying fractions by integers Multiplying a fraction by a fraction Dividing a fraction by a fraction. Fractions. Adding and subtracting fractions. 3 + 1. 3. 1. 4. 5. 5. 5. 5.

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Fractions

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  1. Adding and subtracting fractions Adding fractions with different denominators Multiplying fractions by integers Multiplying a fraction by a fraction Dividing a fraction by a fraction Fractions

  2. Adding and subtracting 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, + = =

  3. Adding and subtracting fractions 7 – 3 4 – 8 8 1 7 3 2 8 8 When fractions have the same denominator it is quite easy to add them together and to subtract them. 1 = = = 2 Fractions should always be cancelled down to their lowest terms.

  4. Adding and subtracting fractions + + 1 3 4 1 7 3 9 9 9 9 1 + 7 + 4 12 1 1 9 9 1 = = = = 3

  5. Adding fractions with different denominators 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.

  6. Adding fractions with different denominators 5 7 1 1 3 1 + What is + ? 12 4 9 9 4 ×4 ×9 ×3 5 63 82 10 4 15 12 36 18 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.

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

  8. 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

  9. 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

  10. Dividing a fraction by a fraction 4 2 2 5 2 5 2 4 5 3 4 3 3 4 5 3 ÷ × × This is the reciprocal of . = 12 4 5 5 = 6 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. can be written as 10

  11. Multiplying and dividing by fractions When we multiply by a fraction we: multiply by the numerator and divide by the denominator When we divide by a fraction we: divide by the numerator and multiply by the denominator Multiplying and dividing are inverse operations.

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