Fraction worksheets
Fractions make sense with pictures: a pizza cut into four shows what 1/4 and 3/4 mean. Then move on to simplifying and calculating.
How to make the worksheet
Choose the type of fraction task and the level. Sheets suit ages 9 to 15.
Simplifying and expanding
Expand by multiplying numerator and denominator by the same number: 2/3 = 4/6 = 8/12. Simplify by dividing both by the same number: 6/8 = 3/4. The value never changes — the pieces just become more and smaller, or fewer and bigger.
Worked example step by step
1/2 + 1/3: the denominators differ, so find a common denominator – 6. 1/2 = 3/6 and 1/3 = 2/6. 3/6 + 2/6 = 5/6. Only add the numerators; the denominator shows the size of the pieces and stays the same. As a mixed number: 7/4 = 1 3/4.
Common mistakes and how to fix them
The classic mistake is 1/2 + 1/3 = 2/5 — adding both numerators and denominators. Draw two pizzas to show the answer must be more than a half. Another is thinking 1/8 is bigger than 1/4 because 8 is bigger: the bigger the denominator, the smaller the pieces.
What suits which grade?
Grade 3: halves, quarters and thirds with pictures. Grade 4: tenths and comparing simple fractions. Grade 5: mixed numbers and adding with like denominators. Grade 6: unlike denominators and fraction–decimal–percent links. Grades 7–9: all four operations.