Comparing Fractions

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 compare two fractions, you can find a common denominator, convert them to equivalent fractions, and then compare the numerators, or you can convert them to decimal form.

Two fractions are equal if they represent the same part of a whole, meaning their cross-products are equal (a/b = c/d if a*d = b*c).

To convert a fraction to an equivalent fraction, multiply or divide both the numerator and the denominator by the same non-zero integer.

The least common denominator is the smallest multiple that is common to the denominators of two or more fractions, used to compare or add fractions.

To add fractions with different denominators, first find the least common denominator, convert each fraction to an equivalent fraction with that denominator, and then add the numerators.

A proper fraction is a fraction where the numerator is less than the denominator, indicating a value less than one.

An improper fraction is a fraction where the numerator is greater than or equal to the denominator, indicating a value equal to or greater than one.

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

To convert an improper fraction to a mixed number, divide the numerator by the denominator to find the whole number, and use the remainder as the new numerator over the original denominator.