Year 5 fractions: six questions and the common mistakes

Six questions

1. Write 7 hundredths as a decimal.

   Show the answer to question 1

   Answer: 0.07 (also accept .07)

   Why:

   100 hundredths make one whole, so 7 hundredths = 7 ÷ 100 = 0.07.

   The last digit of 7 goes in the hundredths column, the second place after the point.

   Common mistakes:

   • 0.7: Your digits are right, but in the wrong columns: your answer is 10 times too big.
   • 0.007: Your digits are right, but in the wrong columns: your answer is 10 times too small.

2. Write 2 2/3 as an improper fraction.

   Show the answer to question 2

   Answer: 8/3 · accept equivalent fractions

   Why:

   2 wholes = 2 × 3 = 6 thirds. Add the 2: 8/3.

   Common mistakes:

   • 4/3: It looks as if you added the whole number to the numerator. Each whole is a full set of parts: multiply the whole number by the denominator, then add the numerator.
   • 6/3: That is only the wholes. The fraction part adds its parts too, so add its numerator on.

3. Kai says: 1/2 + 2/6 = 3/8.

   Is Kai right? Write the correct answer, not just yes or no.

   Show the answer to question 3

   Answer: 5/6 · accept equivalent fractions · "No, 5/6" is right too; "No" on its own scores nothing

   Why:

   You cannot add the tops and the bottoms. Make the denominators the same first: 1/2 = 3/6, then 3/6 + 2/6 = 5/6.

   Kai's answer was not right: the correct answer is 5/6.

   Common mistakes:

   • 3/8: It looks as if you added the numerators and added the denominators. First make the denominators the same, then add only the numerators.
   • 3/6: It looks as if you used the numerators before the fractions had the same denominator. Change one fraction first so both are cut into the same pieces.

4. 5/7 × 7 = ?

   Give your answer as a fraction, or as a mixed number or whole number if it is 1 or more.

   Show the answer to question 4

   Answer: 5 (also accept 35/7)

   Why:

   Multiply the numerator only: 5 × 7 = 35, giving 35/7.

   35 ÷ 7 = 5.

   Common mistakes:

   • 35/49: It looks as if you multiplied the denominator as well. Multiplying by a whole number gives more of the same pieces, so only the numerator changes.

5. Write 8 tenths as a decimal.

   Show the answer to question 5

   Answer: 0.8 (also accept .8)

   Why:

   10 tenths make one whole, so 8 tenths = 8 ÷ 10 = 0.8.

   The last digit of 8 goes in the tenths column, the first place after the point.

   Common mistakes:

   • 8: Your digits are right, but in the wrong columns: your answer is 10 times too big.
   • 0.08: Your digits are right, but in the wrong columns: your answer is 10 times too small.

6. Dara says: 4 2/4 is the same as 16/4.

   Is Dara right? Write the correct answer, not just yes or no.

   Show the answer to question 6

   Answer: 18/4 (also accept 9/2) · accept equivalent fractions · "No, 18/4" is right too; "No" on its own scores nothing

   Why:

   4 wholes = 4 × 4 = 16 quarters. Add the 2: 18/4.

   Dara's answer was not right: the correct answer is 18/4.

   Common mistakes:

   • 6/4: It looks as if you added the whole number to the numerator. Each whole is a full set of parts: multiply the whole number by the denominator, then add the numerator.
   • 16/4: That is only the wholes. The fraction part adds its parts too, so add its numerator on.