Fractions and Operations Fractions are a special type of number that represents a part of a whole. A fraction is represented by a numerator and a denominator...
Fractions are a special type of number that represents a part of a whole. A fraction is represented by a numerator and a denominator, separated by a line. The numerator represents the number of parts of the whole, while the denominator represents the total number of parts in the entire.
Example: The fraction 1/2 represents two parts of a whole that are taken out. The numerator 1 represents two parts, and the denominator 2 represents four parts in total.
Fractions can be added, subtracted, multiplied, and divided in the same way as whole numbers. However, when adding or subtracting fractions with different denominators, we need to find a common denominator before combining them. The least common multiple (LCM) of the denominators is the lowest common denominator that is divisible by both denominators.
Adding and Subtracting Fractions:
To add fractions with different denominators, we need to find a common denominator and add the numerators together. For example, 1/2 + 1/4 = 3/4.
To subtract fractions with different denominators, we need to first find a common denominator and subtract the numerators together. For example, 3/4 - 1/4 = 2/4.
Multiplying Fractions:
To multiply fractions with different denominators, we need to find the product of the numerators and the product of the denominators. For example, 1/2 x 1/4 = 1/8.
To divide fractions with different denominators, we need to find the reciprocal of the denominator and multiply the numerator and denominator. For example, 1/2 ÷ 1/4 = 2.
Some Important Properties of Fractions:
The sum of two fractions with the same denominator is equal to the denominator of the sum.
The difference between two fractions with the same denominator is equal to the denominator of the difference.
The product of two fractions with the same denominator is equal to the product of the numerators.
The quotient of two fractions with the same denominator is equal to the denominator of the quotient