How to Add Fractions With Like Denominators

Step-by-Step Guide

1. 1

   Step 1: Recognize the numerator and denominator.

   There are two parts to all fractions: the numerator, which is the number above the line, and the denominator, which is the number below the line.
   
   While the denominator tells you how many parts a whole has been broken into, the numerator tells you how many pieces of that whole there are.In the fraction ½, for instance, the numerator = 1 and the denominator = 2, and the fraction is one-half.
2. 2

   Step 2: Determine the denominator.

   When two or more fractions have a common denominator, it means they all have the same number as a denominator, or that they all represent wholes that have been broken into the same number of pieces.
   
   Fractions with a common denominator can be added together very easily, and the resulting fraction will have the same denominator as the original fractions.
   
   For instance:
   The fractions 3/5 and 2/5 have a common denominator of
   5.
   
   The fractions 3/8, 5/8, and 17/8 have a common denominator of
   8. , To add fractions together when they have a common denominator, you simply add all the numerators together and rewrite the sum over the original denominator.In the fractions 3/5 and 2/5, the numerators are 3 and
   2.
   
   In the fractions 3/8, 5/8, and 17/8, the numerators are 3, 5, and
   17. , In the example of 3/5 + 2/5, add the numerators 3 + 2 =
   5.
   
   In the example 3/8 + 5/8 + 17/8, add the numerators 3 + 5 + 17 = 25 , Remember to use the same common denominator, since the number of parts that the whole is divided into remains the same, and you are just adding the number of individual pieces.
   
   The fractions 3/5 + 2/5 = 5/5 The fractions 3/8 + 5/8 + 17/8 = 25/8 , Sometimes a fraction can be put into simpler terms, and this includes dividing it to get a number that’s not a fraction or decimal.
   
   In the example 5/5, this fraction can be solved easily because any fraction where the numerator and denominator are the same will equal
   1.Think about it like a pie that’s been cut into three pieces.
   
   If you eat all three pieces of the pie, then you’ve eaten one whole pie.
   
   Any fraction can be converted from a fraction by dividing the numerator by the denominator, and you’ll often end up with a decimal number.
   
   For instance, 5/8 can also be written as 5 ÷ 8, which equals
   0.625. , A fraction is said to be in its simplest form when both the numerator and the denominator don’t have any common factors they can be divided by.For instance, in the fraction 3/6, both the numerator and denominator have a common factor of 3, meaning they can both be divided by 3 to produce a whole number.
   
   Therefore, the fraction 3/6 can be thought of as 3 ÷ 3 / 6 ÷ 3 = ½. , When a fraction has a numerator that’s bigger than the denominator, such as 25/8, this is said to be an improper fraction (the reverse, when the numerator is smaller than the denominator, is a proper fraction).
   
   These can be converted into a mixed number, which is a number that has a whole number plus a proper fraction.
   
   To convert an improper fraction like 25/8 to a mixed number, you:
   Divide the improper fraction’s numerator by its denominator to determine how many whole times 8 goes into 25, where the answer is 25 ÷ 8 = 3(.125) Determine what’s left over.
   
   If 8 x 3 = 24, subtract that from the original numerator: 25 – 24 = 1, where the difference is the new numerator.
   
   Rewrite the mixed number.
   
   The denominator will be the same from your original improper fraction, meaning 25/8 can be rewritten as 3 1/8. , For instance, look at the equation 12/26 – 4/26 – 1/26.
   
   In this example:
   The numerators are 12, 4, and 1 The common denominator is 26 , Like with addition, you don’t have to worry about doing anything to the denominator, so just find the difference between the numerators: 12 – 4 – 1 = 7 Rewrite the fraction with the new numerator. 12/26 – 4/26 – 1/26 = 7/26. , Similar to adding fractions, when you subtract fractions you can still end up with:
   An improper fraction that can be converted to a mixed number A fraction that can be solved through division A fraction that can be put into a simpler form by finding a common denominator , Fractions don’t always have the same denominators, and in order to add or subtract those fractions, you must first find a common denominator.
   
   To start, locate the denominators in the fractions you’re dealing with.
   
   For instance, in the equation 5/8 + 6/9, the denominators are 8 and
   9. , To find a common denominator, you need to find the least common multiple of the two numbers, which is the smallest positive number that’s a multiple of both original numbers.To find the least common multiple of 8 and 9, you must first go through the multiples of each number:
   The multiples of 8 are: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, etc.
   
   The multiples of 9 are: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, etc.
   
   The least common multiple of 8 and 9 is
   72. , Multiply each denominator by the correct number to achieve the common denominator.
   
   Remember that whatever you do to each denominator, you must also do to its numerator.
   
   For the fraction 5/8: to achieve the common denominator of 72, you multiply 8 x
   9.
   
   Therefore, you must also multiply the numerator by 9, giving you 5 x 9 = 45 For the fraction 6/9: to achieve the common denominator of 72, you multiply 9 x
   8.
   
   Therefore, you must also multiply the numerator by 8, giving you 6 x 8 = 48, The new fraction will have the common denominator and the product of the numerators multiplied by the same values:
   The fraction 5/8 becomes 45/72, and the fraction 6/9 becomes 48/72.
   
   Since they now have a common denominator, you can add the fractions 45/72 + 48/72 = 93/72.
   
   Don’t forget to reduce, solve, or convert improper fractions to mixed numbers when applicable and necessary.
3. 3

   Step 3: Locate the numerators.

4. 4

   Step 4: Add the numerators.

5. 5

   Step 5: Rewrite the fraction with the new numerator.

6. 6

   Step 6: Solve the fraction if necessary.

7. 7

   Step 7: Reduce the fraction if you can.

8. 8

   Step 8: Convert improper fractions to mixed numbers if necessary.

9. 9

   Step 9: Locate the numerators and denominators.

10. 10

    Step 10: Subtract the numerators.

11. 11

    Step 11: Reduce or solve the fraction if necessary.

12. 12

    Step 12: Locate the denominators.

13. 13

    Step 13: Determine the least common multiple.

14. 14

    Step 14: Multiply the fractions to achieve the least common multiple.

15. 15

    Step 15: Rewrite the fractions.

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