Answer:
[tex]\Large\textsf{$7\frac{17}{18}$ m$^2$}[/tex]
Step-by-step explanation:
The area of a rectangle is the product of its length and width.
Given that the length of the rectangle is 4¹/₃ meters and its width is 1⁵/₆ meters, then the expression for its area is:
[tex]4\frac13 \times 1\frac56[/tex]
First, convert the mixed numbers into improper fractions by multiplying the whole number by the denominator of the fraction, adding this to the numerator of the fraction, and placing the answer over the denominator:
[tex]\dfrac{4\times 3+1}{3}\times \dfrac{1 \times 6+5}{6}\\\\\\\dfrac{12+1}{3}\times \dfrac{6+5}{6}\\\\\\\dfrac{13}{3}\times \dfrac{11}{6}[/tex]
Now, multiply the numerators and denominators:
[tex]\dfrac{13 \times 11}{3 \times 6}\\\\\\\dfrac{143}{18}[/tex]
When we divide 143 by 18, we get 7 remainder 17, so we can rewrite the numerator 143 as 7 × 18 + 17:
[tex]\dfrac{7 \times 18+17}{18}[/tex]
Separate the fractions:
[tex]\dfrac{7 \times 18}{18}+\dfrac{17}{18}[/tex]
This simplifies to:
[tex]7}+\dfrac{17}{18}[/tex]
[tex]7\frac{17}{18}[/tex]
Therefore, the area of the rectangle is:
[tex]\Large\textsf{Area = $7\frac{17}{18}$ m$^2$}[/tex]
