Skip to main content
Speclore

Fractions Addition Subtraction

Reference data and engineering information about fractions addition subtraction for mathematics applications.

fractionsadditionsubtraction

Overview

Engineering reference data for Fractions Addition Subtraction in mathematics.

Key Formulas

Quadratic Formula

x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Roots of ax² + bx + c = 0.

Pythagorean Theorem

c2=a2+b2c^2 = a^2 + b^2

Right triangle relationship.

Circle Area

A=πr2A = \pi r^2

Area of a circle.

Logarithm

log⁡b(x)=ln⁡(x)ln⁡(b)\log_b(x) = \frac{\ln(x)}{\ln(b)}

Change of base formula.

Variables

Symbol Description Unit
π\pi Pi 3.14159...
ee Euler's number 2.71828...

Fraction Operations Guide

Adding Fractions

To add fractions, first find a common denominator:

ab+cd=a⋅d+c⋅bb⋅d\frac{a}{b} + \frac{c}{d} = \frac{a \cdot d + c \cdot b}{b \cdot d}

For mixed numbers, convert to improper fractions first: abc=a⋅c+bca \frac{b}{c} = \frac{a \cdot c + b}{c}

Example from content: 234+4382\frac{3}{4} + 4\frac{3}{8}

  1. Convert to common denominator (LCD=8): 268+4382\frac{6}{8} + 4\frac{3}{8}
  2. Add whole numbers: 2+4=62 + 4 = 6
  3. Add fractions: 68+38=98=118\frac{6}{8} + \frac{3}{8} = \frac{9}{8} = 1\frac{1}{8}
  4. Combine: 6+118=7186 + 1\frac{1}{8} = 7\frac{1}{8}

Subtracting Fractions

ab−cd=a⋅d−c⋅bb⋅d\frac{a}{b} - \frac{c}{d} = \frac{a \cdot d - c \cdot b}{b \cdot d}

When subtracting mixed numbers where the fractional part of the minuend is smaller:

  1. Borrow 1 from the whole number: 1=denominatordenominator1 = \frac{\text{denominator}}{\text{denominator}}
  2. Add to the fractional part
  3. Subtract

Example from content: 634−4386\frac{3}{4} - 4\frac{3}{8}

  1. Convert 6346\frac{3}{4} to 6686\frac{6}{8}
  2. Subtract: 668−438=2386\frac{6}{8} - 4\frac{3}{8} = 2\frac{3}{8}

Least Common Denominator (LCD)

The LCD is the smallest common multiple of denominators. For denominators 4 and 8:

  • Multiples of 4: 4, 8, 12, 16, 20...
  • Multiples of 8: 8, 16, 24...
  • LCD = 8

Key Definitions

Numerator: Top number in a fraction (parts we have) Denominator: Bottom number (total equal parts) Proper Fraction: Numerator < Denominator (38\frac{3}{8}) Improper Fraction: Numerator ≥ Denominator (138\frac{13}{8}) Mixed Number: Whole number + proper fraction (2342\frac{3}{4})

Conversion Examples

From the extracted content:

  • 91389\frac{13}{8} → 9⋅8+138=858=1058\frac{9 \cdot 8 + 13}{8} = \frac{85}{8} = 10\frac{5}{8}
  • 31211631\frac{21}{16} → 31⋅16+2116=51716=32516\frac{31 \cdot 16 + 21}{16} = \frac{517}{16} = 32\frac{5}{16}

References