US Fraction Calculator — Add, Subtract, Multiply & Divide
Free online fraction calculator for students, educators, woodworkers, and professionals. Add, subtract, multiply, and divide proper, improper, and mixed fractions with complete step-by-step mathematical breakdowns, least common denominator (LCD) calculation, and decimal conversions.
US Fraction Arithmetic & Solver
Modify the values below and click Calculate to view your simplified answer and step breakdown.
Educational Purpose Only: This utility is provided for educational, academic, and homework assistance purposes only. All calculations strictly adhere to standard algebraic rules, fraction reduction theorems, and Euclidean GCD algorithms. Verify critical engineering or architectural proportion measurements against official blueprints.
Curriculum Alignment: Aligned with US Common Core Mathematics standards (CCSS.MATH.CONTENT.4.NF, 5.NF) and US High School SAT/ACT math benchmarks.
Common Fractions to Decimals & Percentages Reference Table
Use this quick conversion cheat sheet for everyday US fraction values commonly found in baking, construction, and academic tests.
1. Standard US Fraction Equivalents
| Fraction | Decimal Equivalent | Percentage | Everyday US Example |
|---|---|---|---|
| 1/2 | 0.5 | 50% | Half dollar, half cup, 30 minutes |
| 1/3 | 0.3333... | 33.33% | 1 foot (1/3 of a yard), 1/3 cup |
| 2/3 | 0.6667... | 66.67% | 2 feet (2/3 of a yard), 2/3 cup baking |
| 1/4 | 0.25 | 25% | 1 quarter coin, 15 minutes, 1/4 pounder |
| 3/4 | 0.75 | 75% | Three quarters (75¢), 45 minutes |
| 1/5 | 0.2 | 20% | 20 cents (two dimes) |
| 2/5 | 0.4 | 40% | Two fifths portion |
| 3/5 | 0.6 | 60% | Three fifths portion |
| 4/5 | 0.8 | 80% | Four fifths portion |
| 1/8 | 0.125 | 12.5% | 1 fluid ounce (1/8 cup), 1/8" drill bit |
| 3/8 | 0.375 | 37.5% | 3/8" socket / bolt hardware |
| 5/8 | 0.625 | 62.5% | 5/8" drywall / garden hose diameter |
| 7/8 | 0.875 | 87.5% | 7/8" standard bolt diameter |
| 1/10 | 0.1 | 10% | 1 dime (1/10 of a US dollar) |
| 1/12 | 0.0833... | 8.33% | 1 inch (1/12 of a standard foot) |
| 1/16 | 0.0625 | 6.25% | 1/16" tape measure increment, 1 oz (1/16 lb) |
2. Fundamental Fraction Operations Rules
| Operation | Algebraic Formula | Key Rule |
|---|---|---|
| Addition (+) | a/b + c/d = (ad + bc) / bd |
Find Least Common Denominator (LCD), add numerators, simplify. |
| Subtraction (−) | a/b − c/d = (ad − bc) / bd |
Find LCD, subtract second numerator from first, simplify. |
| Multiplication (×) | a/b × c/d = (a × c) / (b × d) |
Multiply numerators together, multiply denominators together, simplify. |
| Division (÷) | a/b ÷ c/d = a/b × d/c = (a × d) / (b × c) |
Keep-Change-Flip: Multiply by the reciprocal of the divisor. |
Comprehensive Guide to Fraction Operations
A fraction represents a part of a whole number. It consists of two essential components: the numerator (the top number indicating how many equal parts you have) and the denominator (the bottom number indicating the total number of equal parts that form one whole unit).
The Three Types of Fractions
- Proper Fractions: The numerator is strictly smaller than the denominator (e.g.,
3/4,5/8). The numerical value is always between 0 and 1. - Improper Fractions: The numerator is greater than or equal to the denominator (e.g.,
7/4,11/3). The numerical value is equal to or greater than 1. - Mixed Numbers: A combination of a non-zero whole integer and a proper fraction (e.g.,
1 3/4,3 2/3).
How to Add and Subtract Fractions
To add or subtract fractions, they must share the exact same denominator (called a common denominator):
- Find the Least Common Denominator (LCD): Calculate the Least Common Multiple (LCM) of both denominators. For example, for
1/4 + 1/6, the LCM of 4 and 6 is 12. - Convert each fraction: Multiply both numerator and denominator by the factor needed to produce the LCD:
1/4 = 3/12and1/6 = 2/12. - Add or subtract numerators:
3/12 + 2/12 = (3 + 2)/12 = 5/12. - Simplify: Reduce the final fraction to lowest terms by dividing by the Greatest Common Divisor (GCD).
How to Multiply Fractions
Multiplication is the simplest fraction operation because no common denominator is required:
(a/b) × (c/d) = (a × c) / (b × d)
For example: (2/3) × (5/7) = (2 × 5) / (3 × 7) = 10/21.
How to Divide Fractions: The "Keep, Change, Flip" Rule
Dividing by a fraction is mathematically identical to multiplying by its reciprocal:
- Keep: Leave the first fraction unchanged:
3/4. - Change: Change the division symbol (
÷) to multiplication (×). - Flip: Invert the second fraction:
2/5 → 5/2. - Multiply:
(3/4) × (5/2) = 15/8 = 1 7/8.
Frequently Asked Questions (FAQs)
A: Find the Greatest Common Divisor (GCD) of both the numerator and the denominator. Then, divide both numbers by that GCD. For example, in 8/12, the GCD is 4. Dividing both gives (8÷4) / (12÷4) = 2/3.
A: A reciprocal is a fraction turned upside down (swapping the numerator and denominator). For instance, the reciprocal of 3/5 is 5/3. Multiplying any non-zero number by its reciprocal always equals 1.
A: Divide the numerator by the denominator using integer division. The quotient becomes the whole number part, the remainder becomes the new numerator, and the denominator stays identical. For example, 11 ÷ 4 = 2 with a remainder of 3, so 11/4 = 2 3/4.
A: Division by zero is mathematically undefined. A denominator represents the total number of equal parts that constitute a whole. Having zero parts implies dividing into nothingness, which violates algebraic axioms.
A: Standard American tape measures divide each inch into fractional units based on powers of 2: halves (1/2"), quarters (1/4"), eighths (1/8"), sixteenths (1/16"), and thirty-seconds (1/32"). This calculator simplifies hardware and woodworking measurements easily.