Fractions represent parts of a whole and are fundamental to mathematics, engineering, culinary recipes, and competitive exams (CBSE, ICSE, SSC, Banking, and JEE). Our free Fraction Calculator allows you to add, subtract, multiply, and divide any two fractions or mixed numbers instantly, showing simplified lowest terms, mixed fraction notation, and decimal equivalents.
Types of Fractions Explained
1. Proper Fraction
Numerator smaller than denominator. Value < 1. Example: 3/4, 5/8.
2. Improper Fraction
Numerator ≥ denominator. Value ≥ 1. Example: 7/4, 11/5.
3. Mixed Fraction
Whole number + proper fraction. Example: 1 ¾ = 7/4.
4. Like vs Unlike
Like: same denominator (3/7 & 5/7). Unlike: different denominators.
Find the Greatest Common Factor (GCF / HCF) of numerator and denominator, then divide both. Use our GCF Calculator to verify.
Frequently Asked Questions
How do you add fractions with different denominators?
To add fractions with unlike denominators, find the Least Common Multiple (LCM) of the denominators to create a common base. Convert both fractions into equivalent fractions with this common denominator, add the numerators together while keeping the denominator identical, and simplify the result to lowest terms.
How do I calculate mixed fractions online?
To calculate mixed fractions online, first convert each mixed number into an improper fraction by multiplying the whole number by the denominator and adding the numerator. Next, perform the operation (+, −, ×, or ÷) using common denominators, and finally reduce the resulting fraction to lowest terms or convert back to a mixed number.
How do you divide two fractions using the Keep-Change-Flip rule?
To divide fractions, Keep the first fraction unchanged, Change the division symbol to multiplication, and Flip the second fraction upside down (its reciprocal). Then multiply the numerators straight across and the denominators straight across, simplifying if possible.
How do you multiply fractions by whole numbers?
Write the whole number as a fraction with a denominator of 1 (for example, 5 becomes 5/1). Then multiply the numerators together and the denominators together: (3/4) × 5 = (3 × 5) / (4 × 1) = 15/4 = 3 ¾.
What is the difference between proper and improper fractions?
A proper fraction has a numerator that is strictly less than its denominator (like 3/5), representing a value less than 1. An improper fraction has a numerator equal to or greater than its denominator (like 7/4), representing a value equal to or greater than 1.
How do you simplify a fraction to its lowest terms?
Find the Greatest Common Factor (GCF / HCF) of the numerator and denominator, then divide both numbers by that GCF. For example, in 18/24, the GCF is 6. Dividing both by 6 yields the simplified lowest term 3/4.
What is a common denominator and how do you find it?
A common denominator is a shared multiple of the denominators of two or more fractions. The best common denominator is the Least Common Denominator (LCD), which is found by calculating the Least Common Multiple (LCM) of the denominators.
How do you convert an improper fraction into a mixed number?
Divide the numerator by the denominator. The whole number quotient becomes the whole part of the mixed number, the remainder becomes the new numerator, and the denominator stays the same. For example, 17 ÷ 5 = 3 with remainder 2, yielding 3 ⅖.
Can fractions have negative values?
Yes. If either the numerator or the denominator is negative, the entire fraction is negative: -a/b = a/-b = -(a/b). If both numerator and denominator are negative, the signs cancel out, making the fraction positive.
How are fractions used in Indian competitive exams like SSC and Banking?
Fractions appear heavily in SSC CGL, IBPS PO, SBI Clerk, and CAT exams in simplification, ratio & proportion, and time & work topics. Practising with a step-by-step fraction calculator builds speed and accuracy for these exams.
What is the difference between LCM and GCF in fractions?
LCM (Least Common Multiple) is used to find a common denominator when adding or subtracting fractions. GCF (Greatest Common Factor) is used to simplify fractions to lowest terms. Both are essential tools in fraction arithmetic.
➗Fractions, Decimals & Arithmetic Cluster
Related Calculators & Recommended Tools
Fraction operations with simplification, percentages, rounding modes, long division with remainders, and ratios. Use these interconnected tools to verify results and explore alternative calculation scenarios:
Fractions are a core topic in the CBSE and ICSE curriculum from Class 4 onwards, and form a significant portion of India's major competitive examinations.
Where Fractions Appear in Indian Exams
SSC CGL / CHSL: Simplification, ratio & proportion, percentage conversion
IBPS PO / SBI Clerk: Quantitative Aptitude — data interpretation with fractions
CAT / XAT: Arithmetic — fractions in time-speed-distance, work problems
CBSE Class 6–8: Operations on fractions, equivalent fractions, mixed numbers
