Question

calculate.
(1) $\frac{3}{8} \times 2 - \frac{1}{4}$
$=$
(2) $\frac{1}{3} + 4 \times \frac{1}{5}$
$=$
(3) $1\frac{5}{6} - \frac{1}{3} \div \frac{1}{2}$
(4) $1\frac{1}{3} \div 3 - \frac{5}{18}$
$=$
(5) $3\frac{3}{4} - 1\frac{2}{3} \times \frac{3}{4}$
$=$

Explanation:

(1) Step1: Calculate multiplication

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

(1) Step2: Subtract $\frac{1}{4}$

$\frac{3}{4} - \frac{1}{4} = \frac{2}{4} = \frac{1}{2}$

(2) Step1: Calculate multiplication

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

(2) Step2: Add $\frac{1}{3}$

$\frac{1}{3} + \frac{4}{5} = \frac{5 + 12}{15} = \frac{17}{15}$

(3) Step1: Calculate division

$\frac{1}{3} \div \frac{1}{2} = \frac{2}{3}$

(3) Step2: Subtract from $1\frac{5}{6}$

$1\frac{5}{6} - \frac{2}{3} = \frac{11}{6} - \frac{4}{6} = \frac{7}{6} - \frac{2}{6} = \frac{5}{6}$

(4) Step1: Convert mixed number to improper

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

(4) Step2: Calculate division

$\frac{4}{3} \div 3 = \frac{4}{9}$

(4) Step3: Subtract $\frac{5}{18}$

$\frac{4}{9} - \frac{5}{18} = \frac{8 - 5}{18} = \frac{3}{18} = \frac{1}{18}$

(5) Step1: Convert mixed numbers to improper

$3\frac{3}{4} = \frac{15}{4}$, $1\frac{2}{3} = \frac{5}{3}$

(5) Step2: Calculate multiplication

$\frac{5}{3} \times \frac{3}{4} = \frac{5}{4}$

(5) Step3: Subtract

$\frac{15}{4} - \frac{5}{4} = \frac{10}{4} = \frac{5}{2}$? Correction: $\frac{15}{4} - \frac{5}{4} = \frac{10}{4} = \frac{5}{2}$? Wait, $1\frac{2}{3}×\frac{3}{4} = \frac{5}{3}×\frac{3}{4} = \frac{5}{4}$. $3\frac{3}{4} = \frac{15}{4}$. $\frac{15}{4} - \frac{5}{4} = \frac{10}{4} = \frac{5}{2}$? No, $\frac{15-5}{4} = \frac{10}{4} = \frac{5}{2}$ is correct, but $\frac{9}{4}$ was wrong earlier. Fixed: $\frac{15}{4} - \frac{5}{4} = \frac{10}{4} = \frac{5}{2}$? Wait no, $3\frac{3}{4}$ is $\frac{15}{4}$, yes. $1\frac{2}{3}×\frac{3}{4} = \frac{5}{3}×\frac{3}{4} = \frac{5}{4}$. So $\frac{15}{4} - \frac{5}{4} = \frac{10}{4} = \frac{5}{2} = 2\frac{1}{2}$. But original answer had $\frac{9}{4}$, which was error. Correct answer: $\frac{5}{2}$.

Wait correction for (5):

(5) Step1: $1\frac{2}{3}×\frac{3}{4} = \frac{5}{3}×\frac{3}{4} = \frac{5}{4}$

(5) Step2: $3\frac{3}{4} = \frac{15}{4}$

(5) Step3: $\frac{15}{4} - \frac{5}{4} = \frac{10}{4} = \frac{5}{2}$

Final corrected answer for (5): $\frac{5}{2}$

So updated answer list:
(1) $\frac{1}{2}$
(2) $\frac{17}{15}$
(3) $\frac{5}{6}$
(4) $\frac{1}{18}$
(5) $\frac{5}{2}$

Answer:

(1) $\frac{1}{2}$
(2) $\frac{17}{15}$
(3) $\frac{5}{6}$
(4) $\frac{1}{18}$
(5) $\frac{9}{4}$