a fraction represents a part of a hole or a part of a set every fraction has a numerator and a denominator the numerator stands for the number of parts being considered the denominator stands for the number of equal parts that make up the whole this pie is divided into 12 equal parts marcel and his friend each ate three pieces of pie what fraction of the pie did the two boys eat the denominator is the total number of pieces that make up the pie twelve again the numerator is the number of parts being considered in this case the numerator is six since each of the two boys ate three pieces of pie the boys ate six twelfths or one half of the pie one half of this pizza is highlighted one third of this pizza is highlighted one fourth of this pizza is highlighted what do you notice as the denominator gets bigger it represents a smaller part of the pizza one half of an object is a bigger portion than one-fourth of the same object think of the horizontal line between the numerator and denominator as the words out of for instance this fraction means one out of two this fraction means three out of four this fraction means seven out of eight [Music] a great way to compare fractions is by using fraction strips is two-thirds greater than less than or equal to one-fourth two-thirds is greater than one-fourth which is greater one-half or two-fourths [Music] one-half and two-fourths are equal so they are called equivalent fractions fraction strips can also help you put fractions in order list these fractions from least to greatest three-fourths two-fifths three-tenths and three-eighths the fraction with the least value is three-tenths three-eighths is slightly greater than three-tenths two-fifths has a value greater than both three-tenths and three-eighths three-fourths is greater than all three fractions the fractions ordered from least to greatest are three-tenths three-eighths two-fifths and three-fourths you can reduce a fraction to its simplest form by finding the greatest common factor of the numerator and the denominator common factors of two numbers are factors that are the same for both numbers the greatest common factor of two numbers is the largest number that is a factor of both what is the simplest form of 18 24 first find the factors of the two numbers then look for the common factors 1 2 3 and 6 are common factors of 18 and 24. the greatest common factor is 6. divide both the numerator and the denominator of the fraction 18 24 by 6. 18 divided by six equals three twenty-four divided by six equals four the simplest form of eighteen twenty-fourths is three-fourths a mixed number is a number that includes both a whole number part and a fraction part two and three-fifths five and one-fourth and seven and four-fifths are examples of mixed numbers an improper fraction is a fraction whose numerator is greater than its denominator three halves is an example of an improper fraction here are three half pizzas when two halves are put together they make a whole pizza three halves of pizza is the same as one and one-half pizzas one and one-half is a mixed number the next time you eat a piece of pizza or a slice of pie think of fractions consider how fractions represent a part of a hole or a part of a set and remember that they can be compared ordered and simplified