Note
Studied by 172 peoplefe Fractions represent a part of a whole and are expressed as two numbers separated by a slash. The number above the line is called the numerator, and the number below is the denominator. Fractions can be classified into several categories:
Proper Fractions
These are fractions where the numerator is less than the denominator (e.g., 3/4, 2/5).
Improper Fractions
In these fractions, the numerator is greater than or equal to the denominator (e.g., 5/4, 2/2).
Mixed Numbers
A combination of a whole number and a proper fraction (e.g., 1 1/2, 3 2/3).
Equivalent Fractions
These are different fractions that represent the same value (e.g., 1/2 is equivalent to 2/4).
Like Fractions
Fractions that have the same denominator (e.g., 1/4 and 3/4).
Unlike Fractions
Fractions with different denominators (e.g., 1/3 and 1/4).To add or subtract unlike fractions, convert them to like fractions first.
Operations with Fractions:
Addition and Subtraction
To add or subtract fractions, if they have like denominators, simply add or subtract the numerators and keep the denominator the same.
For unlike fractions, find a common denominator, convert the fractions, then perform the operation.
Multiplication
Multiply the numerators together and the denominators together to get the result (e.g., (1/2) * (3/4) = (13)/(24) = 3/8).
Division
To divide by a fraction, multiply by its reciprocal (e.g., (1/2) ÷ (3/4) = (1/2) * (4/3) = 4/6 = 2/3 after simplification).
Simplifying Fractions:This involves dividing the numerator and denominator by their greatest common divisor (GCD) to reduce the fraction to its simplest form (e.g., 6/8 can be simplified to 3/4).
Applications of Fractions:Fractions are used in many areas, such as cooking (e.g., 1/2 cup), measurements (e.g., 1/4 inch), and financial calculations (e.g., splitting bills). Understanding fractions is essential for real-world application and further mathematical learning, including topics like ratios, proportions, and algebraic expressions.