The rules
Addition and subtraction
You need a common denominator first: a/b ± c/d = (a×d ± c×b) / (b×d), then simplify.
Multiplication
Straightforward — multiply across: a/b × c/d = (a×c) / (b×d)
Division
Flip the second fraction and multiply: a/b ÷ c/d = (a×d) / (b×c)
Simplifying
Divide both numerator and denominator by their highest common factor. 18/24 has an HCF of 6, giving 3/4.
Worked examples
| Problem | Working | Answer |
|---|---|---|
| 2/3 + 1/4 | (2×4 + 1×3) / 12 = 11/12 | 11/12 = 0.917 |
| 5/6 − 1/3 | (5×3 − 1×6) / 18 = 9/18 | 1/2 = 0.5 |
| 3/4 × 2/5 | 6/20 | 3/10 = 0.3 |
| 3/4 ÷ 2/5 | (3×5)/(4×2) = 15/8 | 1⅞ = 1.875 |
Common fractions as decimals and percentages
| Fraction | Decimal | Percent |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333… | 33.33% |
| 1/4 | 0.25 | 25% |
| 2/3 | 0.667… | 66.67% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 1/8 | 0.125 | 12.5% |
| 5/8 | 0.625 | 62.5% |
Where fractions turn up in real life
- Cooking — halving or doubling a recipe means multiplying every fraction.
- Construction and carpentry — measurements in inches are commonly written in eighths and sixteenths.
- Land records — shares in ancestral property are often expressed as fractions.
- Exam marks — converting a raw score to a percentage is a fraction operation.
- Time — three quarters of an hour is 45 minutes.
Common mistakes
- Adding numerators and denominators straight across. 1/2 + 1/3 is not 2/5.
- Forgetting to simplify the final answer.
- Flipping the wrong fraction when dividing — invert the second one, not the first.
- Leaving a mixed number unconverted before multiplying. 2½ must become 5/2 first.
Frequently Asked Questions
How do I add fractions with different denominators?
Convert both to a common denominator, add the numerators, then simplify. For 2/3 + 1/4 the common denominator is 12, giving 8/12 + 3/12 = 11/12.
Why can't I just add numerators and denominators?
Because the denominator tells you the size of each part. 1/2 + 1/3 is 5/6, not 2/5, which would be smaller than either fraction.
How do I divide fractions?
Flip the second fraction and multiply. 3/4 ÷ 2/5 becomes 3/4 × 5/2 = 15/8.
How do I simplify a fraction?
Divide the numerator and denominator by their highest common factor. 18/24 divided by 6 gives 3/4.
How do I convert a mixed number?
Multiply the whole number by the denominator and add the numerator. 2½ becomes (2 × 2 + 1) / 2 = 5/2.
How do I turn a fraction into a percentage?
Divide the numerator by the denominator and multiply by 100. 3/8 is 0.375, which is 37.5%.
Mixed numbers ke saath kaam
2¾ jaise mixed number ko pehle improper fraction banana padta hai:
2¾ → (2 × 4) + 3 = 11, isliye 11/4
Ulta karne ke liye numerator ko denominator se divide kariye: 11 ÷ 4 = 2 bachta hai 3, matlab 2¾.
| Mixed | Improper | Decimal |
|---|---|---|
| 1½ | 3/2 | 1.5 |
| 2¾ | 11/4 | 2.75 |
| 3⅓ | 10/3 | 3.333… |
| 5⅝ | 45/8 | 5.625 |
Do fractions mein kaunsa bada hai
Denominator bada hone ka matlab fraction bada nahi hota — 1/8 asal mein 1/3 se chhota hai.
Tulna karne ka seedha tareeka: cross-multiply kariye. 3/5 aur 4/7 mein — 3 × 7 = 21 aur 4 × 5 = 20. Pehla bada hai, isliye 3/5 > 4/7.
Ya dono ko decimal bana lijiye: 3/5 = 0.6 aur 4/7 = 0.571. Wahi jawab.
More questions
Mixed number ko improper fraction kaise banayein?
Whole number ko denominator se multiply kariye, numerator jod dijiye, denominator wahi rakhiye. 2¾ ka matlab (2×4)+3 = 11/4.
Kaunsa fraction bada hai, ye kaise pata karein?
Cross-multiply kariye — pehle ka numerator doosre ke denominator se, aur ulta. Jiska guna bada aaye, wo fraction bada hai.
Rozmarra mein fractions
Fractions sirf exam ki cheez nahi — roz kaam aate hain:
- Rasoi — recipe aadhi karni ho to ¾ cup ka aadha ⅜ cup hota hai. Aur ⅜ cup lagbhag 6 badi chammach hai.
- Napai — carpenter aur mistri inch ke ½, ¼, ⅛ mein kaam karte hain. ⅝ inch aur 0.625 inch ek hi cheez hai.
- Batwara — 3 logon mein 2 pizza baantne par har ek ko ⅔ milta hai.
- Chhoot — "⅓ off" ka matlab 33.33% chhoot.
- Samay — ¾ ghanta yaani 45 minute.
¾ cup ka aadha kitna hota hai?
⅜ cup, jo lagbhag 6 badi chammach ke barabar hai.
⅝ inch decimal mein kitna hota hai?
0.625 inch. Numerator ko denominator se divide karke decimal nikal jaata hai.
Related calculators and guides
Disclaimer. This calculator provides estimates for general guidance only and is not financial, tax or legal advice. Rates, rules and limits change, and your own situation may differ. Please verify current figures with the relevant authority or a qualified professional before acting on them.