Question

What are the answers to all these problems?

Answer 1

I'll show you a couple of examples, since all the exercises are to be done in the same way.

The point is that we can only sum two fractions if they have the same denominator. So, for example, we can sum

$\dfrac{3}{8} + \dfrac{2}{8} = \dfrac{3+2}{8} = \dfrac{5}{8}$

So, we first need to transform the two fractions so that they have the same denominators. A fraction can be transformed by multiplying both numerator and denominator by the same number. By doing so, you write another fraction with the same value as the original.

Let's deal with the first sum: we have 1/3 + 3/5. We transform the fraction as follows:

$\dfrac{1}{3} \to \dfrac{1\cdot 5}{3\cdot 5} = \dfrac{5}{15}$

$\dfrac{3}{5} \to \dfrac{3\cdot 3}{5\cdot 3} = \dfrac{9}{15}$

And now we can sum them:

$\dfrac{1}{3} + \dfrac{3}{5} = \dfrac{5}{15} + \dfrac{9}{15} = \dfrac{14}{15}$