Adding and Subtracting Fractions - Word Problems

A fraction represents a part of a whole and is expressed as a ratio of two integers, with a numerator (top number) and a denominator (bottom number).

To add fractions with like denominators, you simply add the numerators and keep the denominator the same. For example, 1/4 + 2/4 = (1+2)/4 = 3/4.

To add fractions with unlike denominators, first find a common denominator, convert the fractions, and then add the numerators. For example, to add 1/3 and 1/4, the common denominator is 12: (1/3 = 4/12) + (1/4 = 3/12) = 7/12.

To subtract fractions, if they have like denominators, subtract the numerators and keep the denominator the same. If they have unlike denominators, find a common denominator, convert the fractions, and then subtract the numerators.

A mixed number is a whole number combined with a proper fraction, such as 2 1/2.

To convert an improper fraction to a mixed number, divide the numerator by the denominator. The quotient is the whole number, and the remainder over the original denominator is the fraction. For example, 9/4 = 2 1/4.

Finding a common denominator is essential when adding or subtracting fractions with unlike denominators, as it allows you to combine the fractions accurately.

To simplify a fraction, divide both the numerator and the denominator by their greatest common divisor (GCD). For example, to simplify 8/12, divide both by 4 to get 2/3.

Fractions can be interpreted as division; for example, the fraction 3/4 represents 3 divided by 4.

To solve word problems involving fractions, identify the quantities involved, determine the operations needed (addition, subtraction, etc.), and translate the problem into a mathematical expression.