Fractions
Fractions consist of two basic parts:
- denominator - or bottom number
- numerator - or the top number
Fraction:
a / b (1)
where
a = numerator
b = denominator
- proper fraction - the nominator smaller than the denominator
- improper fraction - the nominator larger than the denominator
- reducible fraction - is a fraction that can be reduced to lower terms
- least common denominator - the smallest denominator value divisible
- mixed number - a combination of a whle number and a fraction
Laws of Fractions
(a / b) + (c / d) = (a d + b c) / (b d) (2)
(a / b) (c / d) = (a c) / (b d) (3)
(a / b) / (c / d) = (a / b) (d / c) (4)
(- a / b) = - (a / b) = a / (- b) (5)
[(a / b) + (c / d)] / [(e / f) + ( g / h)]
= ([(a / b) + (c / d)] / [(e / f) + (g / h)]) ([b d f h] / [b d f h])
= [((a d) + (b c)) f h] / [((e h) + (f g)) b d] (6)
Adding Fractions - Example
(1 / 4) + (3 / 16) + (7 / 8)
= (4 / 4) (1 / 4) + (3 / 16) + (2 / 2) (7 / 8)
= (4 / 16) + (3 / 16) + (14 / 16)
= (4 + 3 + 14) / 16
= 21 / 16
Multiplying Fractions - Example
(3 / 4) (9 / 16)
= ((3) (9)) / ((4) (16))
= 27 / 64
Dividing Fractions - Example
(3 / 4) / (9 / 16)
= ((3) (16)) / ((4) (9))
= 48 / 36
Related Topics
• Mathematics
Mathematical rules and laws - numbers, areas, volumes, exponents, trigonometric functions and more.
Related Documents
Algebraic Expressions
Principal algebraic expressions formulas.
Boolean Algebra
Logic functions where the values of variables are true (1) or false (0).
Complex Numbers
Complex numbers are used in alternating current theory and mechanical vector analysis.
Differential Calculus
Derivatives and differentiation expressions.
Exponents - Powers and Roots
The laws of fractional and integer exponents.
Factorials
The product of all positive integers.
Hyperbolic Functions
Exponential functions related to the hyperbola.
Law of Cosines
One side of a triangle when the opposite angle and two sides are known.
Law of Sines
Calculate the angles in a generic triangle.
Laws of Indices
Simplifying calculations by involving indices.
Logarithms
The rules of logarithms - log10 and loge for numbers ranging 1 to 1000.
Numbers - Squares, Cubes and Roots
Numbers - squares, cubes, square roots and cube roots.
Prime Numbers
Prime numbers up to 1000.
Ratios and Proportions
The relative values between quantities - ratios and proportions.
Standard Differentials and Integrals
Equations for differentials and integrals.
Taylor Series
Function as an infinite sum of terms.
Trigonometric Functions
Sine, cosine and tangent - the natural trigonometric functions.