Steven

Steven is cutting construction paper into rectangles for a project. He needs to cut one rectangle that is 9 inches × 14 1/3 inches. He needs to cut another rectangle that is 10 1/2 inches by 10 1/3 inches. How many total square inches of construction paper does Steven need for his project?

Correct answer:

S =  237 ¹⁄₂ = 475/2 in²

Step-by-step explanation:

$$\begin{gathered} a=9\text{in} \\ b=14\frac{1}{3}=14+\frac{1}{3}=\frac{14\cdot 3+1}{3}=\frac{42+1}{3}=\frac{43}{3}\doteq 14.3333\text{in} \\ x=10\frac{1}{2}=10+\frac{1}{2}=\frac{10\cdot 2+1}{2}=\frac{20+1}{2}=\frac{21}{2}=10.5\text{in} \\ y=10\frac{1}{3}=10+\frac{1}{3}=\frac{10\cdot 3+1}{3}=\frac{30+1}{3}=\frac{31}{3}\doteq 10.3333\text{in} \\ {S}_1=a\cdot b=9\cdot \frac{43}{3}=\frac{9\cdot 43}{3}=\frac{387}{3}=129{\text{in}}^2 \\ {S}_2=x\cdot y=\frac{21}{2}\cdot \frac{31}{3}=\frac{21\cdot 31}{2\cdot 3}=\frac{651}{6}=\frac{217}{2}=108.5{\text{in}}^2 \\ S=S_1+S_2=129+\frac{217}{2}=\frac{129\cdot 2}{2}+\frac{217}{2}=\frac{258}{2}+\frac{217}{2}=\frac{258+217}{2}=\frac{475}{2}=\frac{475}{2}{\text{in}}^2=237\frac{1}{2}{\text{in}}^2=237.5{\text{in}}^2 \end{gathered}$$

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