Year 6 fractions: six questions and the common mistakes

Six questions

1. 5/8 and 11/12 are to be written with the same denominator.

   What is the lowest denominator you can use?

   Show the answer to question 1

   Answer: 24

   Why:

   Multiples of 12: 12, 24.

   24 is the first that 8 also goes into: 5/8 = 15/24 and 11/12 = 22/24.

   8 × 12 = 96 works too, but it is not the lowest.

   Common mistakes:

   • 96: That is a common denominator, but not the lowest. Multiplying the denominators always gives one; look for a smaller number that both denominators go into.

2. 3/5 + 2/3 = ?

   Give your answer in its simplest form.

   Show the answer to question 2

   Answer: 1 4/15 (also accept 19/15)

   Why:

   Common denominator: 15.

   3/5 = 9/15 and 2/3 = 10/15.

   Add: 19/15 = 1 4/15.

   Common mistakes:

   • 5/8: It looks as if you added the numerators and added the denominators. First make the denominators the same, then add only the numerators.

3. 5/7 ÷ 5 = ?

   Give your answer in its simplest form.

   Show the answer to question 3

   Answer: 1/7

   Why:

   Dividing by 5 makes each piece 5 times smaller, so the denominator gets 5 times bigger: 5/35 = 1/7.

   Common mistakes:

   • 25/7: It looks as if you multiplied instead of dividing. Dividing a fraction by a whole number makes it smaller: the pieces get smaller, so the denominator gets bigger.

4. Write 33/50 as a decimal.

   Show the answer to question 4

   Answer: 0.66

   Why:

   A fraction is a division: 33 ÷ 50 = 0.66.

   Common mistakes:

   • 33.50: It looks as if you wrote the numerator, a point, then the denominator. A fraction is a division: the numerator divided by the denominator. A fraction less than one whole is a decimal less than 1.

5. Work out 810.7 ÷ 100.

   Show the answer to question 5

   Answer: 8.107

   Why:

   Move every digit 2 places to the right: 810.7 ÷ 100 = 8.107.

   Common mistakes:

   • 81.07: Your digits are right, but in the wrong columns: your answer is 10 times too big.
   • 0.8107: Your digits are right, but in the wrong columns: your answer is 10 times too small.
   • 810.7: Your digits are right, but in the wrong columns: your answer is 100 times too big.
   • 0.08107: Your digits are right, but in the wrong columns: your answer is 100 times too small.

6. A jug holds 2 5/8 litres of juice.

   Theo pours out 1 1/6 litres.

   How much juice is left in the jug?

   Give your answer as a mixed number or a fraction, in its simplest form.

   Show the answer to question 6

   Answer: 1 11/24 litres (also accept 35/24)

   Why:

   As improper fractions over 24: 63/24 and 28/24.

   Take away: 35/24, or 1 11/24.

   Common mistakes:

   • 70/48: That is the right amount, but not in its simplest form yet. Divide the numerator and the denominator by a number that goes into both, until none does.