Introduction to Fractions

A fraction is a number representing a part of a whole. This whole may be a single object or a group of objects.

A fraction in which the numerator is smaller than the denominator is termed a proper fraction, while if the numerator is equal to or larger than the denominator, it's referred to as an improper fraction.

Expressions like 541⁄3, 8, or 2⁄795 are categorized as mixed fractions.

There exists a reciprocal conversion between improper and mixed fractions.

Fractions that are equivalent to a given fraction can be derived by multiplying or dividing both its numerator and denominator by a non-zero value.

A fraction is considered to be in its simplest or lowest form when there are no common factors, except 1, shared between its numerator and denominator.

Fractions having identical denominators are classified as like fractions, whereas those with differing denominators are termed unlike fractions.

To compare fractions, they can be transformed into like fractions and then arranged either in ascending or descending order.

Addition or subtraction operations on like fractions involve merely adding or subtracting their numerators.

For unlike fractions, addition or subtraction can be performed after converting them into like fractions.

Fractions with denominators such as 10, 100, etc., can be represented in decimal form, denoted as decimal numbers.

The value of the digit immediately following the decimal point (i.e., tenths place) is 1/10, while that of the subsequent place (i.e., hundredths place) is 1/100, and so forth.

Conversion of fractions to decimals involves representing them with denominators like 10, 100, etc. Similarly, decimals can be converted to fractions by eliminating the decimal points and introducing denominators such as 10, 100, depending on the number of decimal places.

Comparisons between decimal numbers are facilitated by considering their place values, which subsequently enable arranging them in ascending or descending order.

Decimal addition or subtraction necessitates aligning the numbers to ensure they have an equal number of decimal places.

Many practical problems in daily life, such as those involving various units of measurement like money, length, weight, etc., can be effectively solved by first converting them into decimal form and subsequently performing addition or subtraction operations.