Add fractions and mixed numbers with like or unlike denominators. Get instant step-by-step Least Common Denominator (LCD) solutions, equivalent fractions, cross-multiplication proofs, and simplified lowest terms.
Adding fractions requires converting each term to a common denominator before combining numerators. Follow this simple guide to add proper, improper, or mixed fractions:
Input the numerator and denominator for each fraction. If adding mixed numbers like 1 1/2, input 1 in the whole number field.
The calculator finds the Least Common Denominator (LCD) and displays how each fraction is scaled proportionally.
Examine the simplified proper or improper fraction, mixed number equivalent, floating-point decimal, and step-by-step proof.
Combining fractions with completely distinct denominators (like eighths and twelfths) is notoriously error-prone without calculating the Least Common Multiple.
Adding whole parts and fractional parts separately often causes errors when the fractional sum exceeds 1 and requires carrying into the whole integer.
Builders measuring lumber frequently need to add fractional dimensions like 3 5/16 inches + 4 7/8 inches to ensure structural framing alignment.
Solving three or more simultaneous fractions in homework or chemistry formulas without having to manually calculate iterative intermediate sums.
Uses Euclidean prime factor analysis to find the true Least Common Denominator rather than blindly multiplying large numbers together.
Seamlessly add a third fraction with a single click to solve complex multi-term problems without manual recalculation.
Whenever the resulting sum is improper (greater than 1), the tool automatically provides both the reduced improper fraction and mixed number.
Displays the exact scaling multipliers applied to each fraction so students can follow each step of classroom methodology.
Fractions with like denominators can be added directly by summing the numerators:
For fractions with unlike denominators, convert each fraction using the Least Common Denominator (LCD):
The denominators are 3 and 4. The least common multiple is 12. Scale both fractions to have denominator 12:
Like denominators (8). Add whole numbers and numerators: 2 + 1 = 3, and 5/8 + 7/8 = 12/8. Since 12/8 = 1 4/8 = 1 1/2, carry 1 to the whole part:
| Addition Problem | Least Common Denominator | Simplified Sum | Decimal Equivalent |
|---|---|---|---|
| 1/2 + 1/4 | 4 | 3/4 | 0.75 |
| 1/3 + 1/6 | 6 | 1/2 | 0.5 |
| 3/8 + 1/4 | 8 | 5/8 | 0.625 |
| 2/5 + 1/2 | 10 | 9/10 | 0.9 |
Never add denominators together. Think of the denominator as the name of the object (e.g. 2 thirds + 1 third = 3 thirds). When the names differ, you must rename them using equivalent fractions before adding.
When adding tape measure sixteenths and eighths on job sites, double the numerator of the eighths to turn them into sixteenths instantly: 5/8 is 10/16, so 5/8 + 7/16 = 17/16 = 1 1/16 inches without scratch paper.
To add fractions with different denominators, you must first convert them into equivalent fractions that share a common denominator. Find the Least Common Multiple (LCM) of the denominators, scale the numerators proportionally, add the new numerators together while keeping the common denominator, and reduce the final fraction to lowest terms.
The Least Common Denominator (LCD) is the smallest positive integer that is divisible by the denominators of all fractions being added. It is essential because fractions represent parts of equal-sized partitions; you cannot directly combine unequal subdivisions (like thirds and fourths) without converting them to shared equal increments (twelfths).
Yes, for two fractions a/b and c/d, the cross-multiplication formula is (a * d + b * c) / (b * d). This produces a common denominator of (b * d), which is always valid, though it may require simplifying by dividing out common factors if (b * d) is larger than the true Least Common Denominator.
You can either convert all mixed numbers into improper fractions before calculating the common denominator, or you can add the whole numbers together separately and add the fractional parts together separately. If the fractional sum exceeds 1, carry the extra whole number into the integer total.
Leaving an answer as an improper fraction (such as 7/4) is standard and widely preferred in higher mathematics, algebra, and engineering. In everyday contexts or grade-school math, you can convert it to a mixed number by dividing the numerator by the denominator (7 divided by 4 equals 1 with a remainder of 3, or 1 3/4).
