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 cross-multiply and compare the results.

A fraction A/B is greater than C/D if A/B > C/D, meaning that A*D > B*C when cross-multiplying.

A fraction A/B is less than C/D if A/B < C/D, meaning that A*D < B*C when cross-multiplying.

A common denominator is a shared multiple of the denominators of two or more fractions, allowing for easy comparison or addition.

The least common denominator (LCD) of 5 and 2 is 10. Convert 3/5 to 6/10 and 1/2 to 5/10 to compare.

An equivalent fraction is a fraction that represents the same value as another fraction, achieved by multiplying or dividing both the numerator and denominator by the same non-zero number.

To convert a fraction to a decimal, divide the numerator by the denominator.

An improper fraction has a numerator that is greater than or equal to its denominator, while a mixed number combines a whole number and a proper fraction.

Shaded models visually represent fractions, making it easier to compare their sizes by showing the proportion of the whole that is shaded.