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, called the numerator, tells you how many parts you have. The bottom number, called the denominator, tells you the total number of equal parts the whole is divided into. For example, in the fraction three-fourths, the whole is divided into four equal parts, and we have three of those parts, as shown in our pizza diagram.
In this scene, we'll explore different types of fractions. A proper fraction has a numerator that is less than its denominator, like three-fourths. This means we have 3 parts out of 4 total parts. An improper fraction has a numerator that is greater than or equal to its denominator, like five-thirds. This means we have 5 parts when the whole is divided into 3 parts, which is more than one whole. A mixed number combines a whole number with a proper fraction, like one and two-thirds. This represents one whole plus two-thirds of another whole.
Now let's learn about equivalent fractions. Equivalent fractions are different fractions that represent the same amount or value. To find equivalent fractions, you can multiply or divide both the numerator and denominator by the same number. For example, one-half, two-fourths, three-sixths, and four-eighths are all equivalent fractions. They all represent the same value: 0.5 or 50 percent. As you can see in our visualization, even though these fractions look different, they all represent the same portion of the whole.
Now let's learn how to add and subtract fractions. To add fractions, first find a common denominator. Then convert the fractions to equivalent fractions with that common denominator. Next, add the numerators while keeping the denominator the same. Finally, simplify the result if possible. For example, to add one-fourth plus one-half, we first convert one-half to two-fourths since 4 is our common denominator. Then we add the numerators: 1 plus 2 equals 3, and keep the denominator as 4. So one-fourth plus one-half equals three-fourths. Subtracting fractions follows the same process, except we subtract the numerators instead of adding them.
Let's summarize what we've learned about fractions. A fraction represents a part of a whole, with the numerator on top showing how many parts we have, and the denominator on the bottom showing the total number of equal parts. We explored different types of fractions: proper fractions where the numerator is less than the denominator, improper fractions where the numerator is greater than or equal to the denominator, and mixed numbers which combine a whole number with a proper fraction. We also learned about equivalent fractions, which represent the same value but have different numerators and denominators. To add or subtract fractions, we need to find a common denominator first. Fractions are essential in mathematics and everyday life for representing partial quantities. Understanding fractions helps us solve many real-world problems involving parts of a whole.