Question 2

We will find the sum of fractions by first finding a common denominator.

Step 1 — Sum of $\frac{2}{5} + \frac{3}{10}$

First, let's find the Least Common Multiple (LCM) of the denominators. The denominators are 5 and 10. The LCM of 5 and 10 is 10. Now, we convert each fraction to have a denominator of 10.

$\frac{2}{5} = \frac{2 \times 2}{5 \times 2}$

$= \frac{4}{10}$

Next, we add the fractions with the common denominator.

$\frac{4}{10} + \frac{3}{10} = \frac{4+3}{10}$

$\boxed{\frac{7}{10}}$

Step 2 — Sum of $\frac{7}{12} + \frac{5}{8}$

Let's find the LCM of the denominators. The denominators are 12 and 8. The LCM of 12 and 8 is 24. We convert each fraction to have a denominator of 24.

$\frac{7}{12} = \frac{7 \times 2}{12 \times 2}$

$= \frac{14}{24}$

$\frac{5}{8} = \frac{5 \times 3}{8 \times 3}$

$= \frac{15}{24}$

Now, we add these new fractions.

$\frac{14}{24} + \frac{15}{24} = \frac{14+15}{24}$

$\boxed{\frac{29}{24}}$

Step 3 — Sum of $-\frac{4}{7} + \frac{3}{14}$

Again, we find the LCM of the denominators. The denominators are 7 and 14. The LCM of 7 and 14 is 14. We convert the first fraction to have a denominator of 14.

$-\frac{4}{7} = -\frac{4 \times 2}{7 \times 2}$

$= -\frac{8}{14}$

Now, we add the fractions. Remember the negative sign.

$-\frac{8}{14} + \frac{3}{14} = \frac{-8+3}{14}$

$\boxed{-\frac{5}{14}}$

Answer

(i) $\frac{7}{10}$ (ii) $\frac{29}{24}$ (iii) $-\frac{5}{14}$