Welcome to our lesson on fractions. A fraction represents a part of a whole. It consists of two numbers separated by a line. The top number is called the numerator, which tells us how many parts we have. The bottom number is called the denominator, which tells us the total number of equal parts the whole is divided into. Remember, the denominator cannot be zero. In this example, we have a pizza divided into 8 equal slices, with 3 slices highlighted. This represents the fraction three-eighths.
Let's explore the different types of fractions. Fractions can be classified into three main types. First, we have proper fractions, where the numerator is less than the denominator. Examples include three-fourths, two-fifths, and one-half. In a proper fraction, we're dealing with less than one whole unit. Next, we have improper fractions, where the numerator is greater than or equal to the denominator. Examples include five-thirds, seven-fourths, and eleven-fifths. Improper fractions represent one or more whole units. Finally, we have mixed numbers, which combine a whole number with a proper fraction. Examples include one and two-thirds, two and three-fourths, and four and one-fifth. Mixed numbers are another way to express improper fractions.
Now let's learn about equivalent fractions. Equivalent fractions represent the same value but have different numerators and denominators. To create equivalent fractions, you can multiply or divide both the numerator and denominator by the same number. For example, one-half is equivalent to two-fourths, three-sixths, and four-eighths. Similarly, two-thirds is equivalent to four-sixths, six-ninths, and eight-twelfths. In our visual representation, you can see that one-half, two-fourths, and three-sixths all represent the same portion of the whole, even though they use different numbers. When working with fractions, it's often helpful to simplify them by dividing both the numerator and denominator by their greatest common factor.