Question 3

We will find the difference between the given fractions.

Step 1 — Subtracting $\frac{1}{4}$ from $\frac{5}{6}$

First, we find the Least Common Multiple (LCM) of the denominators. The denominators are 6 and 4. The LCM of 6 and 4 is 12. Now, we convert both fractions to have a common denominator of 12.

$\frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12}$

$\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}$

Next, we subtract the second fraction from the first.

$\frac{10}{12} - \frac{3}{12}$

$= \frac{10 - 3}{12}$

$\boxed{\frac{7}{12}}$

Step 2 — Subtracting $\frac{3}{4}$ from $\frac{11}{8}$

We find the LCM of the denominators. The denominators are 8 and 4. The LCM of 8 and 4 is 8. We convert the second fraction to have a common denominator of 8.

$\frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8}$

Now, we subtract this from the first fraction.

$\frac{11}{8} - \frac{6}{8}$

$= \frac{11 - 6}{8}$

$\boxed{\frac{5}{8}}$

Step 3 — Subtracting $-\frac{2}{3}$ from $-\frac{7}{9}$

First, we simplify the expression. Subtracting a negative number is the same as adding a positive number.

$-\frac{7}{9} - \left(-\frac{2}{3}\right) = -\frac{7}{9} + \frac{2}{3}$

Next, we find the LCM of the denominators. The denominators are 9 and 3. The LCM of 9 and 3 is 9. We convert the second fraction to have a common denominator of 9.

$\frac{2}{3} = \frac{2 \times 3}{3 \times 3} = \frac{6}{9}$

Now, we add the fractions.

$-\frac{7}{9} + \frac{6}{9}$

$= \frac{-7 + 6}{9}$

$\boxed{-\frac{1}{9}}$

Answer

(i) $\frac{7}{12}$ (ii) $\frac{5}{8}$ (iii) $-\frac{1}{9}$