Calculator tool
How this calculator works
Use the explanation to understand the formula, assumptions, and practical limits behind the calculator result.
What Fractions Show
A fraction has a numerator on top and a denominator on the bottom. In , the 3 tells how many parts you have, and the 4 tells how many equal parts make a whole.
How the Main Operations Work
- For addition and subtraction, use a common denominator first.
- For multiplication, multiply tops together and bottoms together.
- For division, multiply by the reciprocal of the second fraction.
A Simple Example
To add , the denominators already match, so add the numerators:
If the denominators differ, convert them to equivalent fractions with a shared denominator before adding.
Why Simplifying Matters
A fraction such as means the same value as , but is easier to read and compare. Simplifying divides the numerator and denominator by their greatest common factor.
Frequently asked questions
How do you find the least common denominator (LCD) of two fractions?
The LCD is the smallest denominator both fractions can share. For example, the LCD of 4 and 6 is 12 because both denominators divide into 12 exactly.
How do you divide fractions — why flip the second fraction?
Dividing by a fraction is the same as multiplying by its reciprocal. For example, .
What does it mean to simplify a fraction to lowest terms?
A fraction is in lowest terms when the numerator and denominator share no common factor larger than 1. Divide both by their GCF to simplify it.
How are fractions used in measurement, cooking, and engineering?
Fractions appear in recipes, measurements, probabilities, construction sizes, and music note lengths because many real quantities are parts of a whole.
