how do you add fractions with different denominators
in general, you cannot
you must find a common denominator, then just add the numerators
in general: if b and d have no common factors
a/b + c/d = (ad + bc)/(bd)
otherwise, you should have a method for finding the lowest common denominator.
e.g.
3/5 + 7/25 + 1/3 + 5/27
5 = 5
25 = 5*5
3 = 3
27 = 3*3*3
so LCD = 5*5*3*3*3 = 25*27 = 675
3/5 + 7/25 + 1/3 + 5/27
= 3*135/675 + 7*27/675 +225/675 + 5*25/675
= (404 + 189 + 225 + 125)/675
= 944/675
A / B + C / D
_____
A / B
Multiply numerator and denominator by D
A / B becomes
A ∙ D / B ∙ D
_____
C / D
Multiply numerator and denominator by B
C / D becomes
C ∙ B / B ∙ D
Now:
A / B + C / D = A ∙ D / B ∙ D + C ∙ B / B ∙ D
A / B + C / D = ( A D + C B ) / B D
For example:
1 / 7 + 2 / 3 = ( 1 ∙ 3 + 2 ∙ 7 ) / 7 ∙ 3 = ( 3 + 14 ) / 21 = 17 / 21
all that fancy math provided above is just the steps you need to follow to find a general common denominator.
I agree with oobleck, but i think it is greatest common factor
To add fractions with different denominators, you need to find a common denominator for both fractions. Here's how:
1. Identify the denominators of both fractions.
For example, let's say you have the fractions 1/3 and 1/4.
2. Find the least common multiple (LCM) of the denominators.
For 3 and 4, the LCM is 12.
3. Convert each fraction to have the common denominator.
To do this, you need to multiply the numerator and denominator of each fraction by a value that makes the denominators equal. In this case, you will need to multiply 1/3 by 4/4 and 1/4 by 3/3.
- Multiply the numerator and denominator of 1/3 by 4/4:
(1/3) * (4/4) = 4/12
- Multiply the numerator and denominator of 1/4 by 3/3:
(1/4) * (3/3) = 3/12
4. Now that both fractions have the same denominator, you can add their numerators.
Add the numerators of 4/12 and 3/12:
4/12 + 3/12 = 7/12
So, the sum of 1/3 and 1/4 is 7/12.
It's important to note that once you have a common denominator, you only need to add or subtract the numerators. The denominator remains the same.