Grade 6, Fractions, decimals and percents
Improper fractions and mixed numbers
Change improper fractions to mixed numbers and back, then compare them.
Three levels
One skill, rising difficulty
Each sheet carries one level. The three are the same skill at rising difficulty, each named for what it practises.
- Level 1: Improper to mixed
- Write each improper fraction as a mixed number.
- Level 2: Mixed to improper
- Write each mixed number as an improper fraction.
- Level 3: Compare
- Write <, > or = in the circle.
Worked example
How the sheet explains it
The helper printed at the top of each sheet: one solved example and the steps a student follows, before the first question. Every number sentence in it is proven by the same checker as the answer key.
Level 1: Improper to mixed
17/5 = 3 2/5
- Divide the top by the bottom. The answer is the whole number and the remainder is the new top number.
- 17 ÷ 5 is 3 with 2 left over: 5 × 3 + 2 = 17.
- Keep the bottom number, 5. So 17/5 = 3 2/5.
Level 2: Mixed to improper
2 3/4 = 11/4
- Each whole is 4 fourths: 2 × 4 = 8.
- Add the top number: 8 + 3 = 11, so 2 3/4 = 11/4.
Level 3: Compare
2 3/5 > 12/5
- Write the mixed number as a fraction: 2 × 5 + 3 = 13, so 2 3/5 = 13/5.
- Same bottom number: 13 > 12, so 2 3/5 > 12/5.
- A whole number works the same way: 3 = 15/5 because 3 × 5 = 15.
Goes with
Reference sheets
One-page helpers a student keeps beside this sheet:
- Fractions
Every reference, facts and support sheet is listed in the worksheet catalogue.
In the BC curriculum
Content standards
The British Columbia content standard this skill is written for, by the codes used across this site:
- bc.math.6.c.5
The wording of each standard is on the Province's mathematics curriculum page.
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