Summarize:

The top number of a fraction is known as the numerator and represents how many parts of the whole you have. The bottom number of the fraction is the denominator, which is the number of parts that would equal the whole. If the numerator is smaller than the denominator, then it is a proper fraction. If the numerator was greater than the denominator, then the fraction is improper.  For example, in the fraction ½, the 1 is the numerator and 2 is the denominator. You can also write fractions on a single line, like 4/5. The number on the left is always the numerator and the number on the right is the denominator. Equivalent fractions are the same amount but written with different numerators and denominators. If you want to make a fraction that’s equivalent to the one you have, multiply the numerator and denominator by the same number and write the result as your new fraction.  For example, if you want to make an equivalent fraction to 3/5, you can multiply both numbers by 2 to make the fraction 6/10. In a real-world example, if you have 2 equal slices of pizza and you cut one of them in half, the two halves are still the same amount as the other full slice. Many times, you’ll be asked to write a fraction in its simplest terms. If you have larger numbers in the numerator and denominator, look for a common factor that each number shares. Divide the numerator and denominator separately by the factor you found to reduce the fraction to an easier number to read. For example, if you have the fraction 2/8, both the numerator and denominator are divisible by 2. Divide each number by 2 to get 2/8 = 1/4. Improper fractions are when the numerator is larger than the denominator. To simplify an improper fraction, divide the numerator by the denominator to find a whole number and a remainder. Write the whole number first, and then make a new fraction where the numerator is the remainder you found and the denominator is the same. For example, if you want to simplify 7/3, divide 7 by 3 to get the answer 2 with a remainder of 1. Your new mixed number will look like 2 ⅓. When you want to use a mixed number in an equation, it’s easiest to change it back to an improper fraction so you can easily do the math. To convert the mixed number back to a fraction, multiply the whole number by the denominator. Add the result to the numerator to finish your equation. For example, if you want to convert 5 ¾ to an improper fraction, multiply 5 x 4 = 20. Add 20 to the numerator to get the fraction 23/4.
Identify the numerator and denominator. Know fractions are equal if you multiply the numerator and denominator by the same number. Simplify fractions by dividing the numerator and denominator by a common multiple. Convert improper fractions to mixed numbers if the numerator is greater than the denominator. Change mixed numbers into fractions when you need to use them in equations.