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How to Do Fractions Without A Scientific Calculator

Reviewed by Calculator Editorial Team

Fractions are a fundamental part of mathematics, and while scientific calculators can handle them, there are several methods you can use to perform fraction calculations without one. This guide will walk you through the essential operations: addition, subtraction, multiplication, division, simplification, and conversion of fractions.

Adding Fractions

Adding fractions requires a common denominator. Here's how to do it:

  1. Find the least common denominator (LCD) of the two fractions.
  2. Convert each fraction to have the LCD as its denominator.
  3. Add the numerators together.
  4. Simplify the resulting fraction if possible.

Formula: a/b + c/d = (a×d + b×c)/(b×d)

Example: 1/4 + 1/6

  1. LCD of 4 and 6 is 12.
  2. Convert: 1/4 = 3/12, 1/6 = 2/12.
  3. Add: 3/12 + 2/12 = 5/12.

Subtracting Fractions

Subtracting fractions is similar to adding them, but you subtract the numerators instead.

  1. Find the LCD of the two fractions.
  2. Convert each fraction to have the LCD as its denominator.
  3. Subtract the numerators.
  4. Simplify the resulting fraction if possible.

Formula: a/b - c/d = (a×d - b×c)/(b×d)

Example: 3/4 - 1/6

  1. LCD of 4 and 6 is 12.
  2. Convert: 3/4 = 9/12, 1/6 = 2/12.
  3. Subtract: 9/12 - 2/12 = 7/12.

Multiplying Fractions

Multiplying fractions is straightforward: multiply the numerators together and the denominators together.

  1. Multiply the numerators.
  2. Multiply the denominators.
  3. Simplify the resulting fraction if possible.

Formula: (a/b) × (c/d) = (a×c)/(b×d)

Example: 2/3 × 3/4

  1. Multiply numerators: 2 × 3 = 6.
  2. Multiply denominators: 3 × 4 = 12.
  3. Result: 6/12, which simplifies to 1/2.

Dividing Fractions

Dividing fractions involves multiplying by the reciprocal of the second fraction.

  1. Find the reciprocal of the second fraction (flip numerator and denominator).
  2. Multiply the first fraction by this reciprocal.
  3. Simplify the resulting fraction if possible.

Formula: (a/b) ÷ (c/d) = (a×d)/(b×c)

Example: 3/4 ÷ 2/3

  1. Reciprocal of 2/3 is 3/2.
  2. Multiply: 3/4 × 3/2 = 9/8.

Simplifying Fractions

Simplifying fractions involves reducing them to their simplest form by dividing numerator and denominator by their greatest common divisor (GCD).

  1. Find the GCD of the numerator and denominator.
  2. Divide both the numerator and denominator by the GCD.

Formula: a/b simplified = (a ÷ GCD(a,b))/(b ÷ GCD(a,b))

Example: 8/12

  1. GCD of 8 and 12 is 4.
  2. Divide: 8 ÷ 4 = 2, 12 ÷ 4 = 3.
  3. Result: 2/3.

Converting Fractions

You can convert fractions to decimals or percentages using simple division.

Fraction to Decimal

  1. Divide the numerator by the denominator.

Formula: a/b = a ÷ b

Example: 3/4 = 3 ÷ 4 = 0.75

Fraction to Percentage

  1. Divide the numerator by the denominator.
  2. Multiply by 100 and add the % symbol.

Formula: a/b = (a ÷ b) × 100%

Example: 3/4 = 0.75 × 100% = 75%

FAQ

What is the easiest way to add fractions?
Find the least common denominator (LCD), convert each fraction to have the LCD as its denominator, add the numerators, and simplify if possible.
How do I simplify a fraction?
Find the greatest common divisor (GCD) of the numerator and denominator, then divide both by the GCD.
Can I divide fractions without a calculator?
Yes, multiply the first fraction by the reciprocal of the second fraction.
What's the difference between improper and proper fractions?
A proper fraction has a numerator smaller than its denominator (e.g., 3/4), while an improper fraction has a numerator larger than or equal to its denominator (e.g., 5/2).
How do I convert a fraction to a percentage?
Divide the numerator by the denominator to get a decimal, then multiply by 100 and add the % symbol.