Understanding fractions and factors is essential in mathematics. Fractions represent parts of a whole, with numerators and denominators indicating the portions. Factors, including prime numbers, help simplify fractions and find common denominators. These concepts are vital for mathematical problem-solving and have practical applications in various fields such as science and engineering.
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Fractions are mathematical expressions that represent a part of a whole or a ratio between two quantities
Numerator
The numerator 'a' signifies how many parts of the whole are being considered
Denominator
The denominator 'b' indicates the total number of equal parts into which the whole is divided
Fractions can be interpreted as the result of dividing the numerator by the denominator, and mathematical operations with fractions follow specific rules
Factors are numbers that divide another number exactly, without leaving a remainder
Set of Integers
Factors are integral to the study of integers, represented by the symbol ℤ
Prime Numbers
Prime numbers are integers greater than 1 that have no other factors besides 1 and themselves
Factors are crucial for various mathematical procedures, such as simplifying fractions and finding common denominators
Simplifying fractions, also known as reducing fractions, is the process of expressing a fraction in its simplest form by dividing the numerator and the denominator by their greatest common factor (GCF)
Prime factor decomposition is the process of expressing a number as a product of its prime factors
To calculate the HCF of two or more numbers, one must first perform prime factor decomposition for each number and then identify the common prime factors and select the smallest power of these primes that appear in each decomposition
To add or subtract fractions with the same denominator, one combines the numerators and retains the common denominator, while for fractions with different denominators, a common denominator must be found before combining the numerators
Multiplication of fractions involves multiplying the numerators together to find the new numerator and the denominators together to find the new denominator, while division of fractions is performed by multiplying the first fraction by the reciprocal of the second
Mastery of fractions and factors is crucial for solving mathematical problems and for applications in various fields such as science, engineering, and economics
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The symbol for the set of all rational numbers, which includes numbers expressed as fractions, is ______.
ℚ
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Definition of factors
Factors are numbers that divide another number exactly without a remainder.
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Characteristics of prime numbers
Prime numbers are greater than 1 with only two factors: 1 and the number itself.
