Question

(5) $9\frac{1}{4}-1\frac{2}{3}-\frac{5}{6}$
=
(7) $6\frac{5}{12}-1\frac{1}{2}-\frac{1}{6}$
=
(6) $4\frac{1}{12}-1\frac{2}{3}-1\frac{1}{6}$
=
(8) $3\frac{5}{6}-1\frac{3}{4}-1\frac{1}{2}$
=

Explanation:

(a) Step1: Convert mixed numbers to improper fractions

$3\frac{1}{2} = \frac{7}{2}$, $1\frac{3}{4} = \frac{7}{4}$

(a) Step2: Find common denominator (4)

$\frac{7}{2} = \frac{14}{4}$, $\frac{2}{4}$ remains

(a) Step3: Subtract left to right

$\frac{14}{4} - \frac{7}{4} - \frac{2}{4} = \frac{14-7-2}{4} = \frac{5}{4}$

(a) Step4: Convert to mixed number

$\frac{5}{4} = 1\frac{1}{4}$

(b) Step1: Convert mixed numbers to improper fractions

$4\frac{9}{12} = \frac{57}{12}$, $1\frac{1}{4} = \frac{5}{4}$, $\frac{1}{6} = \frac{1}{6}$

(b) Step2: Find common denominator (12)

$\frac{5}{4} = \frac{15}{12}$, $\frac{1}{6} = \frac{2}{12}$

(b) Step3: Subtract left to right

$\frac{57}{12} - \frac{15}{12} - \frac{2}{12} = \frac{57-15-2}{12} = \frac{40}{12}$

(b) Step4: Simplify fraction

$\frac{40}{12} = \frac{10}{3} = 3\frac{1}{3}$

(c) Step1: Convert mixed numbers to improper fractions

$4\frac{1}{12} = \frac{49}{12}$, $1\frac{2}{3} = \frac{5}{3}$, $1\frac{1}{6} = \frac{7}{6}$

(c) Step2: Find common denominator (12)

$\frac{5}{3} = \frac{20}{12}$, $\frac{7}{6} = \frac{14}{12}$

(c) Step3: Subtract left to right

$\frac{49}{12} - \frac{20}{12} - \frac{14}{12} = \frac{49-20-14}{12} = \frac{15}{12}$

(c) Step4: Simplify fraction

$\frac{15}{12} = \frac{5}{4} = 1\frac{1}{4}$

(d) Step1: Convert mixed numbers to improper fractions

$3\frac{5}{6} = \frac{23}{6}$, $1\frac{3}{4} = \frac{7}{4}$, $1\frac{1}{2} = \frac{3}{2}$

(d) Step2: Find common denominator (12)

$\frac{23}{6} = \frac{46}{12}$, $\frac{7}{4} = \frac{21}{12}$, $\frac{3}{2} = \frac{18}{12}$

(d) Step3: Subtract left to right

$\frac{46}{12} - \frac{21}{12} - \frac{18}{12} = \frac{46-21-18}{12} = \frac{7}{12}$

Answer:

(a) $1\frac{1}{4}$
(b) $3\frac{1}{3}$
(c) $1\frac{1}{4}$
(d) $\frac{7}{12}$