A fraction represents parts of a whole. It shows how many equal parts we have out of the total number of equal parts. Fractions are written with a numerator on top and a denominator on the bottom. The numerator tells us how many parts we have, and the denominator tells us how many equal parts make up the whole. For example, three-fourths means we have 3 parts out of 4 equal parts, and two-fifths means we have 2 parts out of 5 equal parts.
Every fraction has two main parts. The numerator is the top number that shows how many parts we have. The denominator is the bottom number that shows the total number of equal parts. The fraction bar separates these two important numbers. For example, in three-fourths, 3 is the numerator showing we have 3 parts, and 4 is the denominator showing there are 4 total equal parts. In two-fifths, we have 2 parts out of 5 total parts. In seven-eighths, we have 7 parts out of 8 total parts.
There are three main types of fractions. Proper fractions have a numerator smaller than the denominator, so their value is less than one. Examples include two-thirds and four-fifths. Improper fractions have a numerator equal to or greater than the denominator, so their value is one or greater. Examples include five-thirds and seven-fourths. Mixed numbers combine a whole number with a proper fraction, like one and three-fourths. Improper fractions can be converted to mixed numbers and vice versa. For example, five-thirds equals one and two-thirds.
Fractions appear everywhere in daily life. When eating pizza, we might have three-eighths of a pizza. In cooking, recipes call for measurements like one-half cup of flour or three-fourths teaspoon of salt. Time is often expressed in fractions - a quarter hour equals fifteen minutes, and a half hour equals thirty minutes. Money uses fractions too - a quarter is one-fourth of a dollar, equal to twenty-five cents. Understanding fractions helps us navigate these everyday situations with confidence.
Equivalent fractions represent the same value but look different. The rule for creating equivalent fractions is to multiply or divide both the numerator and denominator by the same number. For example, one-half equals two-fourths, three-sixths, and four-eighths. Even though the number of parts changes, the shaded area remains exactly the same. This happens because when we multiply one-half by two-over-two, we get two-fourths. Similarly, multiplying by three-over-three gives us three-sixths, and multiplying by four-over-four gives us four-eighths. Understanding equivalent fractions is essential for adding, subtracting, and comparing fractions.