Fraction & Mixed Number Calculator

Fractions are fundamental to everyday hands-on work throughout the United States. While decimal notation dominates digital financial ledgers and metric engineering abroad, American residential home construction, cabinetmaking, plumbing, automotive repair, and culinary kitchen baking remain deeply anchored in standard fractional measurements.

This fraction calculator solves everyday fractional arithmetic instantly. Whether you are adding board lengths in a woodshop, scaling down a family baking recipe, or dividing wall framing spacing on a job site, it simplifies fractions to their lowest terms, displays mixed numbers alongside improper fractions, calculates exact decimal equivalents, and provides a transparent step-by-step breakdown.

Understanding American Tape Measure Fractions (Inch Fractions)

In the US customary measurement system, standard tape measures and architectural rulers divide every single inch into binary power-of-two fractional segments:

• Halves (1/2″): The longest center tick mark dividing an inch directly in half (0.500″).
• Quarters (1/4″, 3/4″): The second-longest markings, dividing the inch into 4 quadrants (0.250″ and 0.750″).
• Eighths (1/8″, 3/8″, 5/8″, 7/8″): Common precision marks in residential rough carpentry, framing, and drywall installation (0.125″, 0.375″, 0.625″, 0.875″).
• Sixteenths (1/16″ to 15/16″): Standard precision graduations on job-site tape measures utilized for finish trim carpentry, window casing, and cabinet installation (each 1/16″ represents 0.0625″).
• Thirty-Seconds (1/32″): Found on machinist rules and fine cabinetry layout squares for tight wood joinery and milling tolerances (each 1/32″ represents 0.03125″).

Core Rules of Fraction Arithmetic

1. Adding and Subtracting Fractions (Finding the Common Denominator)

You cannot directly add or subtract fractions with unequal denominators (such as 3/8 + 1/4) because their fractional units represent different physical sizes. You must first find the Least Common Denominator (LCD)—the smallest integer divisible by both denominators.

To add 3/8 + 1/4:

1. The LCD of 8 and 4 is 8.
2. Convert 1/4 to eighths by multiplying numerator and denominator by 2: (1 × 2) / (4 × 2) = 2/8.
3. Add the numerators together while keeping the common denominator: 3/8 + 2/8 = 5/8.

2. Multiplying Fractions (Straight Across)

Multiplying fractions is straightforward: simply multiply the top numerators together to form the new numerator, and multiply the bottom denominators together to form the new denominator.

(a / b) × (c / d) = (a × c) / (b × d)

For example, to take 1/2 of 3/4 of a cup in a recipe: (1 × 3) / (2 × 4) = 3/8 of a cup.

3. Dividing Fractions (Invert and Multiply)

To divide by a fraction, invert the second fraction (flip its numerator and denominator to produce its mathematical reciprocal) and multiply across.

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

For example: (3/4) ÷ (1/2) = (3/4) × (2/1) = 6/4 = 3/2 = 1 1/2.

Converting Between Mixed Numbers and Improper Fractions

A mixed number consists of an integer followed by a proper fraction (such as 3 5/8). An improper fraction is a fraction where the top numerator is equal to or larger than the bottom denominator (such as 29/8).

• Mixed to Improper: Multiply the whole integer by the denominator, add the numerator, and place the result over the original denominator. For 3 5/8: (3 × 8) + 5 = 24 + 5 = 29, yielding 29/8.
• Improper to Mixed: Divide the numerator by the denominator. The whole quotient is your integer, and the remainder forms the new numerator. For 51/8: 51 divided by 8 is 6 with a remainder of 3, yielding 6 3/8.