Respuesta :
Common denominator
We want to find a number that is multiple of all the denominators of the fractions we have. For example, in the cases:
[tex]\begin{gathered} \frac{2}{5}+\frac{1}{3} \\ \end{gathered}[/tex]we have two denominators: 5 and 3
And for
[tex]\frac{1}{3}+\frac{3}{12}[/tex]we have 3 and 12
First method
2/5 + 1/3:
We can find a common denominator by simply multiplying all the denominators. In this case the common denominator would be
5 x 3 = 15
then,
[tex]\frac{2}{5}=\frac{2\times3}{5\times3}=\frac{6}{15}[/tex]and
[tex]\frac{1}{3}=\frac{1\times5}{3\times5}=\frac{5}{15}[/tex]then we have that
[tex]\frac{2}{5}+\frac{1}{3}=\frac{6}{15}+\frac{5}{15}[/tex]1/3 + 3/12:
We can find a common denominator by simply multiplying all the denominators. In this case the common denominator would be
3 x 12 = 36
then
[tex]\frac{1}{3}+\frac{3}{12}=\frac{1\times12}{3\times12}+\frac{3\times3}{12\times3}=\frac{12}{36}+\frac{9}{36}[/tex]Second method
1/3 + 3/12:
We can find the denominator by finding the multiples of both denominators:
multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24...
multiples of 12: 12, 24, 36, 48, ...
We find some the numbers that both multiples share:
multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24...
multiples of 12: 12, 24, 36, 48, ...
We choose the first common multiple, and this is the common denominator. In this case it is 12. Since
3 x 4 = 12, then
[tex]\frac{1}{3}+\frac{3}{12}=\frac{1\times4}{3\times4}+\frac{3}{12}=\frac{4}{12}+\frac{3}{12}[/tex]