The board is a rectangle, so we use the formula of the area of a rectangle to find the answer.
Formula:
[tex]\sf~A=lw[/tex]
Plug in what we know:
[tex]\sf~A=(3\dfrac{1}{5})(3\dfrac{1}{3})[/tex]
Convert both of the fractions into improper fractions.
We do this by multiply the denominator to the whole number, adding it to the numerator(which gives us the numerator), and we keep the denominator.
[tex]\sf3\dfrac{1}{5}\rightarrow\dfrac{5\times3+1}{5}\rightarrow\dfrac{16}{5}[/tex]
[tex]\sf3\dfrac{1}{3}\rightarrow\dfrac{3\times3+1}{3}\rightarrow\dfrac{10}{3}[/tex]
So we have:
[tex]\sf~A=(\dfrac{16}{5})(\dfrac{10}{3})[/tex]
Multiply the numerators and denominators together:
[tex]\sf~A=\dfrac{16\times10}{5\times3}[/tex]
[tex]\sf~A=\dfrac{160}{15}[/tex]
Convert to a mixed number by dividing by hand:
__10
15 | 160
15
10
0
10
The quotient becomes the whole number, the remainder becomes the numerator, and the divisor becomes the denominator.
So we have:
[tex]\sf~A=10\dfrac{10}{15}[/tex]
Now simplify the fraction by dividing the numerator and denominator by 5.
[tex]\sf~A=10\dfrac{10\div5}{15\div5}[/tex]
[tex]\sf~A=\boxed{\sf10\dfrac{2}{3}}[/tex]
