How do you add or subtract fractions with different denominators?

To add or subtract fractions with different denominators, first find the Least Common Denominator (LCD) using the Least Common Multiple (LCM) of the denominators. Next, convert each fraction to an equivalent fraction with that LCD, add or subtract the numerators while keeping the common denominator, and finally reduce the resulting fraction to lowest terms using the Greatest Common Divisor (GCD).

What is the difference between proper, improper, and mixed fractions?

A proper fraction has a numerator smaller than its denominator (e.g., 3/4). An improper fraction has a numerator greater than or equal to its denominator (e.g., 7/4). A mixed number combines a non-zero integer with a proper fraction (e.g., 1 3/4).

How do you multiply and divide fractions?

To multiply fractions, multiply the numerators together and the denominators together (a/b × c/d = (a×c)/(b×d)). To divide fractions, multiply the first fraction by the reciprocal (the inverted form) of the second fraction (a/b ÷ c/d = a/b × d/c = (a×d)/(b×c)).

How do you simplify a fraction to its lowest terms?

To simplify a fraction, compute the Greatest Common Divisor (GCD) of both the numerator and denominator using the Euclidean algorithm, then divide both numbers by that GCD. When the GCD is 1, the fraction is in simplest form.

How do you convert a fraction to a decimal and percentage?

Divide the numerator by the denominator using long division (e.g., 5 ÷ 8 = 0.625). To express it as a percentage, multiply the decimal by 100 and append '%' (0.625 × 100 = 62.5%).

Fraction Calculator — Free Step-by-Step Mixed Number & Math Solver

Quick Summary

Bottom Line: The MakerHub Fraction Calculator delivers instant, exact mathematical results for proper fractions, improper fractions, and mixed numbers. Every computation includes full step-by-step working, Least Common Denominator (LCD) resolution, Greatest Common Divisor (GCD) reduction, and interactive pie & bar diagrams.

Mastering Fraction Arithmetic: The Complete Guide

To add or subtract fractions with different denominators, convert them to equivalent fractions with a shared common denominator using LCM. To multiply, multiply numerators together and denominators together. To divide, multiply by the reciprocal of the second fraction.

Understanding the Least Common Denominator (LCD)

The LCD is the smallest positive integer that is divisible by all denominators in your equation. Using the LCD keeps numbers as small and manageable as possible before simplifying.

Addition & Subtraction

a/b ± c/d = (a·d ± b·c) / (b·d)

Find common denominator with LCM, scale numerators, combine, and reduce with GCD.

Multiplication

(a/b) × (c/d) = (a·c) / (b·d)

Multiply top by top and bottom by bottom directly, then simplify to lowest terms.

Division (Invert & Multiply)

(a/b) ÷ (c/d) = (a/b) × (d/c) = (a·d) / (b·c)

Flip the second fraction upside down (reciprocal) and multiply across.

Simplification (Euclidean GCD)

a/b = (a ÷ GCD) / (b ÷ GCD)

Divide both terms by their Greatest Common Divisor to yield irreducible lowest terms.

Common Fraction ↔ Decimal ↔ Percentage Quick Reference

Fraction	Decimal	Percentage	Common Usage
1/2	0.5	50%	Half, recipes
1/4	0.25	25%	Quarter, time
3/4	0.75	75%	Three quarters
1/3	0.3333...	33.33%	Thirds
2/3	0.6667...	66.67%	Two thirds
1/8	0.125	12.5%	Carpentry, rulers
5/8	0.625	62.5%	Socket sizes

Fraction Calculator & Math Solver

Step-by-Step Calculation

Find the Least Common Denominator (LCD)

Add Numerators

Convert to Mixed Number

Mastering Fraction Arithmetic: The Complete Guide

Understanding the Least Common Denominator (LCD)

Common Fraction ↔ Decimal ↔ Percentage Quick Reference

Frequently Asked Questions