RemeliaMaths Year 5 Fractions, decimals & %
Year 5 mixed numbers and improper fractions
The objective: Recognise mixed numbers and improper fractions and convert between them.
The explanation, example and questions are the ones Remelia uses in the app; the questions are not taken from any test paper.
The idea
An improper fraction has a top bigger than its bottom. A mixed number splits that into wholes plus a fraction. They are the same amount.
How to do it
- Improper to mixed: divide the top by the bottom. The quotient is the whole number, the remainder is the new top.
- Mixed to improper: multiply the whole number by the denominator, add the numerator.
A worked example
17/5 = 3 r 2 = 3 and 2/5. Backwards: 3 × 5 + 2 = 17, so 17/5.
Watch for
Changing the denominator. It never changes in this conversion.
Try four questions
-
Jonah says: 2 2/9 is the same as 18/9.
Is Jonah right? Write the correct answer, not just yes or no.
Show the answer to question 1
Answer: 20/9 · accept equivalent fractions · "No, 20/9" is right too; "No" on its own scores nothing
Why:
2 wholes = 2 × 9 = 18 ninths. Add the 2: 20/9.
Jonah's answer was not right: the correct answer is 20/9.
-
Which sign goes in the box: <, > or =?
3 1/5 ☐ 32/10
- A =
- B >
- C <
Show the answer to question 2
Answer: A · =
Why:
3 1/5 = 16/5 = 32/10.
Compare 32/10 with 32/10.
So the left side is equal to the right side: =.
-
Which sign goes in the box: <, > or =?
3 1/5 ☐ 31/10
- A =
- B <
- C >
Show the answer to question 3
Answer: C · >
Why:
3 1/5 = 16/5 = 32/10.
Compare 32/10 with 31/10.
So the left side is greater than the right side: >.
-
Which sign goes in the box: <, > or =?
5 8/9 ☐ 53/9
- A =
- B >
- C <
Show the answer to question 4
Answer: A · =
Why:
5 8/9 = 53/9.
Compare 53/9 with 53/9.
So the left side is equal to the right side: =.
Answers
- 1. 20/9 · accept equivalent fractions · "No, 20/9" is right too; "No" on its own scores nothing
- 2. A · =
- 3. C · >
- 4. A · =
The mistakes Remelia names
When a wrong answer to a question like these matches one of these mistakes, the app says what the child seems to have done before they try again.
- Question 1, the answer 4/9: 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.
- Question 1, the answer 18/9: That is only the wholes. The fraction part adds its parts too, so add its numerator on.