Fraction Calculator
Arithmetic, Fractions
What is a fraction
Definition: A fraction shows part of a whole. The top number (numerator) counts parts, and the bottom number (denominator) tells how many equal parts make one whole.
Formula: $$\frac{a}{b}+\frac{c}{d}=\frac{ad+bc}{bd},\quad \frac{a}{b}-\frac{c}{d}=\frac{ad-bc}{bd}$$ $$\frac{a}{b}\cdot\frac{c}{d}=\frac{ac}{bd},\quad \frac{a}{b}\div\frac{c}{d}=\frac{a}{b}\cdot\frac{d}{c}$$
Intro: Use this fraction calculator to add, subtract, multiply, or divide fractions. MathGPT shows clear Grade 5–6 steps, simplifies the result, and can convert to a mixed number.
Accepted fraction forms
- Proper fraction: $\frac{2}{5}$
- Improper fraction: $\frac{9}{4}$ ( $can\;convert\;to\;2\frac{1}{4}$ )
- Mixed number: $1\frac{3}{8}$ ( $equals\;\frac{11}{8}$ )
- Whole number: $7$ ( $treat\;as\;\frac{7}{1}$ )
How this calculator works
- Enter your two fractions (you can also type mixed numbers like
1 1/4). - Choose an operation: Add, Subtract, Multiply, or Divide.
- MathGPT converts mixed numbers to improper fractions when needed.
- For add/subtract, we find a common denominator, combine numerators, then simplify.
- For multiply/divide, we multiply across (and flip the second fraction for division), then simplify.
Worked example
- Add $\dfrac{3}{4} + \dfrac{2}{3}$.
- Find a common denominator. For $4$ and $3$, the common denominator is $12$.
- Rewrite each fraction with denominator $12$: $$\dfrac{3}{4}=\dfrac{9}{12},\quad \dfrac{2}{3}=\dfrac{8}{12}.$$
- Add the numerators: $$\dfrac{9}{12}+\dfrac{8}{12}=\dfrac{17}{12}.$$
- This is an improper fraction. Convert to a mixed number: $$\dfrac{17}{12}=1\dfrac{5}{12}.$$
- Final answer: $$\dfrac{17}{12}\;\text{(or)}\;1\dfrac{5}{12}.$$
- Subtract $\dfrac{5}{6} - \dfrac{1}{4}$.
- Find a common denominator for $6$ and $4$. The common denominator is $12$.
- Rewrite the fractions: $$\dfrac{5}{6}=\dfrac{10}{12},\quad \dfrac{1}{4}=\dfrac{3}{12}.$$
- Subtract the numerators: $$\dfrac{10}{12}-\dfrac{3}{12}=\dfrac{7}{12}.$$
- $$\dfrac{7}{12}$$ is already simplified because $7$ and $12$ have no common factor greater than $1$.
- Final answer: $$\dfrac{7}{12}.$$
- Multiply $\dfrac{2}{5} \times \dfrac{15}{8}$.
- Multiply across: $$\dfrac{2}{5}\times\dfrac{15}{8}=\dfrac{2\cdot 15}{5\cdot 8}=\dfrac{30}{40}.$$
- Simplify by dividing top and bottom by $10$: $$\dfrac{30}{40}=\dfrac{3}{4}.$$
- Final answer: $$\dfrac{3}{4}.$$
- Divide $\dfrac{3}{7} \div \dfrac{2}{9}$.
- Division by a fraction means multiply by the reciprocal: $$\dfrac{3}{7}\div\dfrac{2}{9}=\dfrac{3}{7}\times\dfrac{9}{2}.$$
- Multiply across: $$\dfrac{3}{7}\times\dfrac{9}{2}=\dfrac{3\cdot 9}{7\cdot 2}=\dfrac{27}{14}.$$
- Convert to a mixed number: $$\dfrac{27}{14}=1\dfrac{13}{14}.$$
- Final answer: $$\dfrac{27}{14}\;\text{(or)}\;1\dfrac{13}{14}.$$
- Add $1\dfrac{1}{4} + \dfrac{2}{3}$.
- Convert the mixed number to an improper fraction: $$1\dfrac{1}{4}=\dfrac{5}{4}.$$
- Find a common denominator for $4$ and $3$: $12$.
- Rewrite: $$\dfrac{5}{4}=\dfrac{15}{12},\quad \dfrac{2}{3}=\dfrac{8}{12}.$$
- Add: $$\dfrac{15}{12}+\dfrac{8}{12}=\dfrac{23}{12}.$$
- Convert to a mixed number: $$\dfrac{23}{12}=1\dfrac{11}{12}.$$
- Final answer: $$\dfrac{23}{12}\;\text{(or)}\;1\dfrac{11}{12}.$$
- Simplify $\dfrac{18}{24}$.
- Find the greatest common factor of $18$ and $24$. It is $6$.
- Divide top and bottom by $6$: $$\dfrac{18}{24}=\dfrac{18\div 6}{24\div 6}=\dfrac{3}{4}.$$
- Final answer: $$\dfrac{3}{4}.$$
FAQs
Do I always need a common denominator?
You need a common denominator for adding and subtracting. You do not need it for multiplying or dividing.
How do I simplify a fraction?
Divide the numerator and denominator by the same number (a common factor) until no bigger common factor exists.
How do I turn an improper fraction into a mixed number?
Divide the numerator by the denominator. The quotient is the whole number, and the remainder becomes the new numerator over the same denominator.
What does it mean to divide by a fraction?
To divide by a fraction, multiply by its reciprocal (flip the second fraction).
Why choose MathGPT?
- Get clear, step-by-step solutions that explain the “why,” not just the answer.
- See the rules used at each step (power, product, quotient, chain, and more).
- Optional animated walk-throughs to make tricky ideas click faster.
- Clean LaTeX rendering for notes, homework, and study guides.
More ways MathGPT can help
- Ask follow-up questions if a step is confusing and get a clearer explanation.
- Practice mode generates similar fraction problems for Grade 5–6.
- Create flashcards for fraction rules (common denominators, simplify, mixed numbers). ( Flashcards )
- Try Kids Mode for beginner-friendly wording, or Advanced Mode for faster steps. ( Kids Mode )
- Generate a video walkthrough you can rewatch before a test. ( Generate a video )
- Use the MathGPT Discord bot for quick help from your phone. ( MathGPT Discord bot )