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Find the area of a rectangle with a length of 5(1)/(3) inches and a width of (2)/(3) inches. (A) (9)/(16)ln^(2) (B) (16)/(9)in^(2) (C) (32)/(9)in^(2) (D) (5)/(2)in^(2)

Find the area of a rectangle with a length of 513 5 \frac{1}{3} inches and a width of 23 \frac{2}{3} inches \newline(A) 916in2\frac{9}{16} \mathrm{in}^{2}\newline(B) 169in2\frac{16}{9} \mathrm{in}^{2} \newline(C) 329in2 \frac{32}{9} \mathrm{in}^{2} \newline(D) 52in2 \frac{5}{2} \mathrm{in}^{2}

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Full solution

Q. Find the area of a rectangle with a length of 513 5 \frac{1}{3} inches and a width of 23 \frac{2}{3} inches \newline(A) 916in2\frac{9}{16} \mathrm{in}^{2}\newline(B) 169in2\frac{16}{9} \mathrm{in}^{2} \newline(C) 329in2 \frac{32}{9} \mathrm{in}^{2} \newline(D) 52in2 \frac{5}{2} \mathrm{in}^{2}
  1. Convert to Improper Fraction: Convert the mixed number for the length to an improper fraction.\newlineThe length of the rectangle is 5135\frac{1}{3} inches, which can be converted to an improper fraction by multiplying the whole number by the denominator and adding the numerator, then placing the result over the original denominator.\newline513=(5×3+1)/3=(15+1)/3=1635\frac{1}{3} = \left(5 \times 3 + 1\right)/3 = \left(15 + 1\right)/3 = \frac{16}{3} inches.
  2. Identify Rectangle Width: Identify the width of the rectangle.\newlineThe width of the rectangle is given as 23\frac{2}{3} inch, which is already in fraction form.
  3. Calculate Area: Calculate the area of the rectangle.\newlineThe area of a rectangle is found by multiplying the length by the width.\newlineArea = (length)×(width)=(163)×(23) (\text{length}) \times (\text{width}) = \left(\frac{16}{3}\right) \times \left(\frac{2}{3}\right) inches2^2.
  4. Perform Multiplication: Perform the multiplication to find the area.\newlineArea = (163)×(23)=(16×23×3)=329(\frac{16}{3}) \times (\frac{2}{3}) = (\frac{16 \times 2}{3 \times 3}) = \frac{32}{9} inches2^2.

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