3¼ 1 ½ Adding Fractions and Mixed Numbers
Steps in Adding Fractions 1. Make sure all fractions have the same denominator If not find the Least Common Denominator (by finding the least common multiple of denominators) Then find fractions equivalent to original fractions, but with all having the same denominator. (by multiplying the top and bottom by the same number
Steps in Adding Fractions 2. Once you have common denominators, also called like denominators, add the numerators together Only the numerators of fractions are to be added Denominators are never added together
Steps in Adding Fractions 3. In answer, write the sum of the numerators as your new numerator. Keep the denominator the same
Steps in Adding Fractions 4. Reduce or convert the final answer if necessary Reduce all fractions not in simplest terms Convert any improper fractions to mixed or whole numbers
Common Multiple A number that is a multiple of two or more numbers. Some multiples of 3 & 6 6, 12, 18, 24, 30, 36, 42
Least Common Multiple The smallest common multiple of a set of two or more numbers. 5 = 5, 10, 15, 20, 25, 30 6 = 6, 12, 18, 24, 30, 36
Shortcut for Finding the Least Common Denominator Check to see if the smaller denominator divides evenly into the larger denominator. If it does, use the larger denominator for your LCD or LCM. 1 5 will divide evenly into 10, so 10 is your LCD or LCM. 5 1 + 10
To Add or Subtract Fractions With Unlike Denominators Find the multiples of each denominator. 1 4 = 4, 8, 12, 16, 20, 24 1 + 6 = 6, 12, 18, 24, 30
To Add or Subtract Fractions With Unlike Denominators Find the common multiples of each denominator. 1 4 = 4, 8, 12, 16, 20, 24 1 + 6 = 6, 12, 18, 24, 30
To Add or Subtract Fractions With Unlike Denominators Find the least of the common multiple. 1 4 = 4, 8, 12, 16, 20, 24 1 + 6 = 6, 12, 18, 24, 30
To Add or Subtract Fractions With Unlike Denominators This number is also called the least common denominator. 1 4 = 4, 8, 12, 16, 20, 24 1 + 6 = 6, 12, 18, 24, 30
To Add or Subtract Fractions With Unlike Denominators Rewrite the fractions using the least common denominator or least common multiple. 1 4 12 1 + 12 12
To Add or Subtract Fractions With Unlike Denominators Find the equivalent fractions for 1/4 & 1/12 with 12 as the denominator. You know that 1/12 is equal to 1/12 so Put a 1 over the Bottom 12. 1 4 12 1 1 + 12 12
To Add or Subtract Fractions With Unlike Denominators Find the equivalent fractions for 1/4 & 1/12 with 12 as the denominator. 1 3 is the correct choice. Since you are looking for the equivalent fraction you know the top number must also be multiplied by 3. x 3 = 4 12 x 3= 1 1 + 12 12
To Add or Subtract Fractions With Unlike Denominators Find the equivalent fractions for 1/4 & 1/12 with 12 as the denominator. 1 3 x 3 = To find the top number just multiply 1 x 3 to get your equivalent fraction. 4 12 x 3 = 1 1 + 12 12
To Add or Subtract Fractions With Unlike Denominators Now just add the numerators. 1 3 x 3 = 4 12 Remember when adding fractions you never add the denominators. x 3 = 1 1 + 12 12 4 12
To Add or Subtract Fractions With Unlike Denominators Reduce if needed. 1 3 x 3 = 4 12 x 3 = Check to see if there is a number that goes into both numerator and denominator. 1 1 + 12 12 4 12
To Add or Subtract Fractions With Unlike Denominators Reduce if needed. 1 3 x 3 = 4 12 x 3 = 4 goes into both 4 and 12, so divide both numbers by 4. 1 1 + 12 12 4 12
: : – – To Add or Subtract Fractions With Unlike Denominators Reduce if needed. 1 3 x 3 = 4 12 x 3 = 1 1 + 12 12 Final Answer: 4 4 1 = 12 4 3 =
Adding Mixed Numbers • For adding mixed numbers, steps remain the same, but don’t forget to add the whole numbers as the end step • Also, special circumstances arise when sums end up with whole numbers and improper fractions • For these, you must convert the improper fraction and add it to the whole number
Steps in Adding Mixed Numbers 1. Make sure all fractions have the same denominator • If not find the Least Common Denominator • Then find fractions equivalent to original fractions, but with all having the same denominator.
Steps in Adding Mixed Numbers 2. Once you have common denominators,, add the numerators together 3. In answer, write the sum of the numerators as your new numerator. Keep the denominator the same.
Steps in Adding Mixed Numbers 4. Add the whole numbers. 5. Reduce or convert the final answer if necessary Reduce all fractions not in simplest terms Convert any improper fractions to mixed or whole numbers and add this to the sum of the whole numbers.
