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# Fractions

## Law of 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)

(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

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Principal algebraic expressions formulas.
• ### Boolean Algebra

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• ### Complex Numbers

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• ### 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.

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## Citation

• The Engineering ToolBox (2018). Fractions. [online] Available at: https://www.engineeringtoolbox.com/fractions-d_2098.html [Accessed Day Month Year].

Modify the access date according your visit.

7.8.15

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