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A compound fraction is a fraction of a fraction, or any number of fractions connected with the word of, [22] [23] corresponding to multiplication of fractions. To reduce a compound fraction to a simple fraction, just carry out the multiplication (see § Multiplication).
Multiplication is an arithmetic operation in which two numbers, called the multiplier and the multiplicand, are combined into a single number called the product. [50] [d] The symbols of multiplication are , , and *.
In academic literature, when inline fractions are combined with implied multiplication without explicit parentheses, the multiplication is conventionally interpreted as having higher precedence than division, so that e.g. 1 / 2n is interpreted to mean 1 / (2 · n) rather than (1 / 2) · n.
Note also how multiplication by zero causes a reduction in dimensionality, as does multiplication by a singular matrix where the determinant is 0. In this process, information is lost and cannot be regained. For real and complex numbers, which includes, for example, natural numbers, integers, and fractions, multiplication has certain properties:
The topic of Egyptian fractions has also seen interest in modern number theory; for instance, the Erdős–Graham problem [9] and the Erdős–Straus conjecture [10] concern sums of unit fractions, as does the definition of Ore's harmonic numbers. [11] A pattern of spherical triangles with reflection symmetry across each triangle edge.
Multiplication is often defined for natural numbers, then extended to whole numbers, fractions, and irrational numbers. However, abstract algebra has a more general definition of multiplication as a binary operation on some objects that may or may not be numbers. Notably, one can multiply complex numbers, vectors, matrices, and quaternions.
The percent value can also be found by multiplying first instead of later, so in this example, the 50 would be multiplied by 100 to give 5,000, and this result would be divided by 1,250 to give 4%. To calculate a percentage of a percentage, convert both percentages to fractions of 100, or to decimals, and multiply them. For example, 50% of 40% is:
In mathematics, a product is the result of multiplication, or an expression that identifies objects (numbers or variables) to be multiplied, called factors.For example, 21 is the product of 3 and 7 (the result of multiplication), and (+) is the product of and (+) (indicating that the two factors should be multiplied together).
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