Understanding fractions is key to mastering many mathematical concepts. This overview covers the basics of fraction notation, including the roles of numerators and denominators, and provides step-by-step procedures for multiplying and dividing fractions. Simplification strategies for complex operations and interactions with whole numbers are also discussed, along with methods for converting and calculating with mixed numbers and algebraic fractions.
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A fraction is made up of a numerator and a denominator, representing the number of equal parts and the total number of equal parts, respectively
The denominator of a fraction must never be zero, as division by zero is undefined
Common examples of fractions include \(\dfrac{1}{4}\), \(\dfrac{1}{2}\), and \(\dfrac{3}{4}\)
To multiply fractions, multiply the numerators and denominators separately and simplify the result
The resulting fraction should be simplified by dividing both the numerator and denominator by their greatest common divisor (GCD)
When multiplying \(\dfrac{4}{9}\) by \(\dfrac{3}{5}\), the product is \(\dfrac{12}{45}\), which simplifies to \(\dfrac{4}{15}\) after dividing by their GCD, which is 3
To divide fractions, take the reciprocal of the divisor and multiply it by the dividend
To divide \(\dfrac{4}{5}\) by \(\dfrac{7}{10}\), first find the reciprocal of \(\dfrac{7}{10}\), which is \(\dfrac{10}{7}\), and then multiply to get \(\dfrac{40}{35}\), which simplifies to \(\dfrac{8}{7}\) or \(1\dfrac{1}{7}\)
When multiplying or dividing a fraction by a whole number, convert the whole number to a fraction with a denominator of one and apply the standard rules for fractions
When multiplying or dividing several fractions, it is efficient to simplify the expression by canceling out common factors between numerators and denominators
Mixed numbers must be converted to improper fractions before multiplication or division
Algebraic fractions follow the same rules for multiplication and division as numerical fractions
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In a fraction, the ______ indicates the count of equal parts being taken, while the ______ shows the total equal parts in the whole, which must never be ______.
numerator
denominator
zero
01
Multiplying Numerators
Multiply top numbers of fractions to find new numerator.
02
Multiplying Denominators
Multiply bottom numbers of fractions for new denominator.
