Fractions exercises

Express all answers in their lowest forms and in mixed numbers where necessary.
  1. Find two other fractions equivalent to each of these
    a) 2/3 b) 3/7 c) 3/4 d) 2/9 e)13/7

  2. Express the following fractions in their lowest forms using equivalent fractions.
    a) 6/9 b) 12/15 c) 28/36 d) 16/28 e) 21/33

  3. Add the following fractions
    a) 1/4+1/2 b) 4/7+2/14 c) 5/6+2/9 d) 1/2+5/17 e) 3/5+3/4

  4. Work out the following fractions
    a) 1/4 of 36 b) 2/7 of 14 c) 5/9 of 27 d) 1/2 of 5/7 e) 3/7 of 5/6
    f) 1/6 of 3/8 g) 5/8 of 2/9 h) 1 3/4 of 24 (convert to improper fractions first)
    i) 2 1/2 of 5/4 j) 3/7 of 4 1/5
  5. a) Continue this pattern up to 10 and 10/9
    2 + 2/1 = 4
    3 + 3/2 = 9/2 =
    4 + 4/3 = 19/3 =
    etc...

    b) Now continue this pattern up to 10 and 10/9 again.
    2 × 2/1 = 4
    3 × 3/2 = 9/2 =
    4 × 4/3 = 19/3 =
    etc...

    c) What do you notice?

  6. a) Now continue this sequence up to 10 and 10/11
    1 - 1/2 = 1/2
    2 - 2/3 = 4/3 = 1 1/3
    3 - 3/4 = 9/4 =
    etc...

    b) Now repeat the sequence up to 10 and 10/11 but this time, replace the - with a x.

    c) What do you notice? Can explain or prove that this works with all positive numbers using algebra?

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