Question 67

What is the value of $$\frac{75}{28} \times \frac{7}{12} + \left[\frac{5}{12} + \left\{\frac{5}{7} + \left(\frac{8}{12} of \frac{36}{24} - \frac{1}{2}\right)\right\}\right]$$?

Solution

= $$\frac{75}{28} \times \frac{7}{12} + \left[\frac{5}{12} + \left\{\frac{5}{7} + \left(\frac{8}{12} of \frac{36}{24} - \frac{1}{2}\right)\right\}\right]$$

= $$\frac{25}{4}\times\frac{1}{4}+\left[\frac{5}{12}+\left\{\frac{5}{7}+\left(\frac{8}{12}\times\ \frac{36}{24}-\frac{1}{2}\right)\right\}\right]$$

= $$\frac{25}{16}+\left[\frac{5}{12}+\left\{\frac{5}{7}+\left(1-\frac{1}{2}\right)\right\}\right]$$

= $$\frac{25}{16}+\left[\frac{5}{12}+\left\{\frac{5}{7}+\frac{1}{2}\right\}\right]$$

= $$\frac{25}{16}+\left[\frac{5}{12}+\left\{\frac{10+7}{14}\right\}\right]$$

= $$\frac{25}{16}+\left[\frac{5}{12}+\frac{17}{14}\right]$$

= $$\frac{25}{16}+\left[\frac{70+204}{168}\right]$$
= $$\frac{25}{16}+\frac{274}{168}$$
= $$\frac{525+548}{336}$$
= $$\frac{1073}{336}$$

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