A fraction is a number that represents a part of a whole or a quantity that is not a whole number. Fractions are typically written in the form of a numerator over a denominator, with a line or a slash separating the two numbers. The numerator represents the number of parts, while the denominator represents the total number of equal parts in the whole.
For example, the fraction 3/4 represents three parts out of a total of four equal parts in the whole.
There are different types of fractions, including:
Proper fraction: a fraction where the numerator is less than the denominator, such as 2/5.
Improper fraction: a fraction where the numerator is greater than or equal to the denominator, such as 7/4.
Mixed number: a whole number and a proper fraction combined, such as 3 1/2.
To add or subtract fractions with the same denominator, simply add or subtract the numerators and keep the denominator the same. For example, to add 1/4 and 2/4, you would add the numerators to get 3/4.
To add or subtract fractions with different denominators, you need to find a common denominator. This can be done by finding the least common multiple (LCM) of the denominators, or by multiplying the denominators together. Once you have a common denominator, you can add or subtract the numerators and simplify the fraction if necessary.
To multiply fractions, multiply the numerators together and then multiply the denominators together. For example, to multiply 1/3 and 2/5, you would multiply 1 x 2 to get 2 for the numerator, and 3 x 5 to get 15 for the denominator, giving you the fraction 2/15.
To divide fractions, you invert the second fraction (flip it upside down) and then multiply the two fractions. For example, to divide 2/3 by 1/4, you would flip the second fraction to get 4/1, and then multiply the two fractions to get 8/3.
It is important to simplify fractions by dividing both the numerator and denominator by their greatest common factor (GCF) if possible. This makes the fraction easier to read and compare to other fractions.