How To Add Fractions Same Denominator

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Fractions are equanimous of a numerator and denominator, and when two fractions take the same number for a denominator, information technology is known as a mutual, or like, denominator. Adding fractions together when they have a common denominator is easy to practice, considering you can only add all the numerators together! The new fraction volition use the aforementioned original denominator, so all you take to worry nigh is calculation the numbers above the line. The same is true for subtracting fractions that accept common denominators. Things go a fiddling trickier when the fractions don't have the same denominator, but they can still exist added or subtracted by finding a mutual denominator first.

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 yous how many parts a whole has been broken into, the numerator tells yous how many pieces of that whole there are.^[i]
- In the fraction ½, for instance, the numerator = 1 and the denominator = 2, and the fraction is half.
2
Decide the denominator. When two or more fractions have a common denominator, it ways 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 example:
- The fractions iii/five and 2/5 take a common denominator of 5.
- The fractions three/8, 5/8, and 17/8 have a common denominator of 8.
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three
Locate the numerators. To add together fractions together when they have a common denominator, you lot just add all the numerators together and rewrite the sum over the original denominator.^[2]
- In the fractions three/5 and 2/5, the numerators are iii and 2.
- In the fractions iii/8, five/8, and 17/viii, the numerators are three, v, and 17.
4

Add together the numerators. In the example of 3/5 + 2/5, add the numerators 3 + 2 = five. In the instance 3/eight + 5/8 + 17/8, add the numerators three + v + 17 = 25
5
Rewrite the fraction with the new numerator. Call back to apply the same common denominator, since the number of parts that the whole is divided into remains the same, and yous are only adding the number of private pieces.
- The fractions 3/5 + 2/5 = v/5
- The fractions 3/viii + 5/viii + 17/8 = 25/viii
6
Solve the fraction if necessary. Sometimes a fraction can exist put into simpler terms, and this includes dividing it to get a number that's non a fraction or decimal. In the example 5/five, this fraction tin be solved hands because any fraction where the numerator and denominator are the same will equal i.^[3] Think near it like a pie that's been cut into three pieces. If you eat all iii pieces of the pie, then you lot've eaten one whole pie.
- Any fraction can exist converted from a fraction by dividing the numerator past the denominator, and you'll frequently end up with a decimal number. For case, v/8 can also be written as 5 ÷ viii, which equals 0.625.
vii
Reduce the fraction if you tin. A fraction is said to be in its simplest form when both the numerator and the denominator don't have whatever common factors they can exist divided by.^[iv]
- For example, in the fraction iii/half-dozen, both the numerator and denominator have a common factor of 3, meaning they tin both be divided by 3 to produce a whole number. Therefore, the fraction 3/half-dozen tin can exist thought of equally iii ÷ 3 / half-dozen ÷ 3 = ½.
8
Catechumen improper fractions to mixed numbers if necessary. When a fraction has a numerator that'south 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 tin be converted into a mixed number, which is a number that has a whole number plus a proper fraction. To convert an improper fraction similar 25/8 to a mixed number, you lot:^[5]
- Carve up the improper fraction's numerator by its denominator to make up one's mind how many whole times 8 goes into 25, where the answer is 25 ÷ eight = 3(.125)
- Determine what's left over. If 8 x iii = 24, decrease that from the original numerator: 25 – 24 = 1, where the difference is the new numerator.
- Rewrite the mixed number. The denominator will exist the same from your original improper fraction, meaning 25/8 can exist rewritten as iii 1/8.

i
Locate the numerators and denominators. For case, look at the equation 12/26 – 4/26 – i/26. In this example:
- The numerators are 12, 4, and 1
- The common denominator is 26
two
Subtract the numerators. Like with add-on, you don't have to worry about doing annihilation to the denominator, so simply discover the difference between the numerators:
- 12 – four – one = 7
- Rewrite the fraction with the new numerator. 12/26 – 4/26 – 1/26 = 7/26.
3
Reduce or solve the fraction if necessary. Similar to adding fractions, when you lot decrease fractions yous can however finish up with:
- An improper fraction that can be converted to a mixed number
- A fraction that can be solved through segmentation
- A fraction that can exist put into a simpler form by finding a common denominator

1
Locate the denominators. Fractions don't always have the same denominators, and in order to add together or subtract those fractions, you lot must start find a mutual denominator. To get-go, locate the denominators in the fractions you're dealing with.
- For instance, in the equation 5/eight + 6/9, the denominators are 8 and 9.
ii
Determine the least common multiple. To observe a common denominator, yous need to find the least mutual multiple of the two numbers, which is the smallest positive number that's a multiple of both original numbers.^[6] To find the least common multiple of 8 and 9, you must starting time go through the multiples of each number:
- The multiples of 8 are: 8, xvi, 24, 32, 40, 48, 56, 64, 72, eighty, 88, 96, 104, etc.
- The multiples of 9 are: 9, xviii, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, etc.
- The least common multiple of 8 and 9 is 72.
iii
Multiply the fractions to achieve the least common multiple. Multiply each denominator by the right number to attain the common denominator. Retrieve that whatever you practise to each denominator, you must also practise 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 five x 9 = 45
- For the fraction 6/9: to attain the common denominator of 72, you multiply 9 x 8. Therefore, yous must likewise multiply the numerator by eight, giving you 6 10 8 = 48^[vii]
4
Rewrite the fractions. The new fraction will have the mutual denominator and the product of the numerators multiplied by the same values:
- The fraction five/8 becomes 45/72, and the fraction 6/9 becomes 48/72.
- Since they at present have a mutual denominator, yous tin add together 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.

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