In order to add fractions, both fractions must have the same denominator.
A denominator is the lower number of a fraction.
In the fraction [tex] \frac{3}{7} [/tex], the denominator is 7.
In the fraction [tex] \frac{3}{7} [/tex], the denominator is 14.
Since 7 ≠ 14, you must find the LCM (least common multiple) of 7 and 14.
To do this, list the multiples of 7 and 14 separately until you find one that both numbers share.
7 • 1 = 7
7 • 2 = 14
14 • 1 = 14
The LCM of 7 and 14 is 14.
This means that the common denominator that these fractions will be converted to fit will be 14.
Since 7 • 2 = 14, which is what the denominator needs to be, you must also multiply the numerator, or upper number of the fraction, by 2.
3 • 2 = 6
[tex] \frac{3}{7} [/tex] = [tex] \frac{6}{14} [/tex]
[tex] \frac{6}{14} [/tex] and [tex] \frac{5}{14} [/tex] now have common denominators and you can add them together!
To add fractions with common denominators, simply add the numerators and the denominator stays the same.
[tex] \frac{6}{14} [/tex] + [tex] \frac{5}{14} [/tex] = [tex] \frac{6 + 5}{14} [/tex]
6 + 5 = 11
[tex] \frac{11}{14} [/tex] is sum of [tex] \frac{6}{14} [/tex], which is an equivalent fraction to [tex] \frac{3}{7} [/tex], and [tex] \frac{5}{14} [/tex].
Hope this helps!
