Complex expr with fractions

Find 1½ of 16 ÷2⅓+(2¼ of ⅑). Use the correct order of operations. The order is PEMDAS: Parentheses, Exponents, Multiplication, Division (from left to right), addition, and Subtraction (from left to right).

Correct answer:

x =  10 ¹⁵⁄₂₈ = 295/28

Step-by-step explanation:

$$\begin{gathered} a=1\frac{1}{2}=1+\frac{1}{2}=\frac{1\cdot 2+1}{2}=\frac{2+1}{2}=\frac{3}{2}=1\frac{1}{2}=1.5 \\ b=a\cdot 16=\frac{3}{2}\cdot 16=\frac{3\cdot 16}{2}=\frac{48}{2}=24 \\ c=2\frac{1}{3}=2+\frac{1}{3}=\frac{2\cdot 3+1}{3}=\frac{6+1}{3}=\frac{7}{3}=2\frac{1}{3}\doteq 2.3333 \\ d=2\frac{1}{4}=2+\frac{1}{4}=\frac{2\cdot 4+1}{4}=\frac{8+1}{4}=\frac{9}{4}=2\frac{1}{4}=2.25 \\ e=1/9=\frac{1}{9}\doteq 0.1111 \\ f=d\cdot e=\frac{9}{4}\cdot \frac{1}{9}=\frac{9\cdot 1}{4\cdot 9}=\frac{9}{36}=\frac{1}{4}=0.25 \\ g=b/c=24/\frac{7}{3}=24:\frac{7}{3}=24\cdot \frac{3}{7}=\frac{24\cdot 3}{7}=\frac{72}{7}\doteq 10.2857 \\ x=g+f=\frac{72}{7}+\frac{1}{4}=\frac{288}{28}+\frac{7}{28}=\frac{288+7}{28}=\frac{295}{28}=10\frac{15}{28}=10.5357 \end{gathered}$$

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