Fraction Calculator

How you can add, subtract, multiply and divide the fractions manually

You can calculate fractions manually by following simple rules. Addition and subtraction need a common denominator. Multiplication uses the numerators and denominators directly. Division uses the reciprocal of the second fraction. Each answer should be simplified when possible.

How to Add Fractions

Formula

$\frac{a}{b}+\frac{c}{d}=\frac{ad+bc}{bd}$

Step by step guide

1. Find a common denominator for both fractions.
2. Rewrite each fraction with that denominator.
3. Add the numerators and keep the denominator.
4. Simplify the answer if possible.

Practical Example

For $1/3+1/4$, use $12$ as the common denominator. Rewrite the fractions as $4/12+3/12$. Add the numerators: $4+3=7$. The answer is $7/12$.

Keep the denominator unchanged after finding the common denominator. Check that the final fraction uses the simplest form.

How to Subtract Fractions

Formula

$\frac{a}{b}-\frac{c}{d}=\frac{ad-bc}{bd}$

Step by step guide

1. Find a common denominator for both fractions.
2. Rewrite each fraction with that denominator.
3. Subtract the second numerator from the first.
4. Simplify the answer if possible.

Practical Example

For $3/4-1/8$, use $8$ as the common denominator. Rewrite $3/4$ as $6/8$. Then subtract $1/8$: $6/8-1/8=5/8$. The answer is $5/8$.

Keep the denominator unchanged after finding the common denominator. Check the final fraction and reduce it to lowest terms.

How to Multiply Fractions

Formula

$\frac{a}{b}\times\frac{c}{d}=\frac{ac}{bd}$

Step by step guide

1. Multiply the two numerators.
2. Multiply the two denominators.
3. Write the numerator over the new denominator.
4. Simplify the fraction if possible.

Practical Example

For $2/3\times5/7$, multiply the numerators: $2\times5=10$. Multiply the denominators: $3\times7=21$. The answer is $10/21$. No further reduction works.

You can sometimes cancel common factors before multiplying. This keeps the numbers smaller and makes the calculation easier.

How to Divide Fractions

Formula

$\frac{a}{b}\div\frac{c}{d}=\frac{a}{b}\times\frac{d}{c}$

Step by step guide

1. Keep the first fraction unchanged.
2. Change division to multiplication.
3. Flip the second fraction to find its reciprocal.
4. Multiply the fractions and simplify.

Practical Example

For $4/5\div2/3$, keep $4/5$ and flip $2/3$ to $3/2$. Then multiply: $4/5\times3/2=12/10$. Simplify $12/10$ to $6/5$, or $1\frac{1}{5}$.

The reciprocal swaps the numerator and denominator. Never divide by a fraction with zero as its numerator.

Working with Negative Fractions

Negative fractions work like positive fractions, but they carry a minus sign. For example, $-3/4$ means three fourths below zero. Apply normal fraction rules, then keep track of the signs during each operation.

Converting Fractions to Decimals and Percentages

You can convert fractions into decimals and percentages with simple calculations. Divide the numerator by the denominator to find the decimal. Then multiply the decimal by $100$ to find the percentage. For example, $3/4=0.75=75$%.

Fraction to Decimal

Divide the numerator by the denominator.

Formula: $\text{Decimal}=\frac{\text{Numerator}}{\text{Denominator}}$

For $3/4$, calculate $3\div4=0.75$.

Fraction to Percentage

Convert the fraction to a decimal first, then multiply by $100$.

Formula: $\text{Percentage}=\frac{\text{Numerator}}{\text{Denominator}}\times100$

For $3/4$, calculate $3/4\times100=75$%.

Step by step guide

1. Divide the numerator by the denominator.
2. Write the decimal result.
3. Multiply the decimal by $100$.
4. Add the percent sign.