If you can break a fraction into parts, you can put parts together. Adding fractions with the same denominator is counting pieces of the same size.
Idea clave
To add or subtract fractions with the same denominator, add or subtract the numerators and keep the denominator: $\dfrac{1}{5} + \dfrac{2}{5} = \dfrac{3}{5}$ and $\dfrac{7}{8} - \dfrac{3}{8} = \dfrac{4}{8}$.
Por qué funciona
The denominator names the size of the pieces (fifths); the numerator counts them. 1 fifth and 2 fifths make 3 fifths, the same way 1 apple and 2 apples make 3 apples. Putting pieces together does not change their size, so the denominator stays 5.
Ejemplo resuelto: Add
Find $\dfrac{2}{8} + \dfrac{5}{8}$.
- 2 eighths and 5 eighths make 7 eighths.
- The pieces are still eighths.
Respuesta: $\dfrac{7}{8}$
Ejemplo resuelto: Subtract from a whole
Find $1 - \dfrac{3}{8}$.
- Write 1 as eighths: $1 = \dfrac{8}{8}$.
- $\dfrac{8}{8} - \dfrac{3}{8} = \dfrac{5}{8}$.
Respuesta: $\dfrac{5}{8}$
Error común
Adding the denominators too, so $\dfrac{1}{5} + \dfrac{2}{5}$ becomes $\dfrac{3}{10}$. But $\dfrac{3}{10}$ is less than $\dfrac{2}{5}$ alone, so adding cannot give it. The pieces do not shrink when you put them together.