Question

How do you evaluate \[\dfrac{5.7\times 5.3}{6}\]\[?\]

Answer 1

Hint: To simplify the given problem first we can remove the decimal from 5.7 and 5.3 to get rational numbers like \[\dfrac{57}{10}\] and \[\dfrac{53}{10}\], then the denominator becomes \[6\times 10\times 10\] which is 600 and numerator becomes \[57\times 53\] which is 3021 then we can divide the numerator by the denominator to end up with the solution required.

Complete step by step solution:
From the given problem we have \[\dfrac{5.7\times 5.3}{6}\]
So we can write 5.7 as \[5.7\times \dfrac{10}{10}\] = \[\dfrac{57}{10}\]
Similarly we get 5.3 as \[5.3\times \dfrac{10}{10}\] = \[\dfrac{53}{10}\]
So,
\[\dfrac{5.7\times 5.3}{6}\]
\[\Rightarrow \] \[\dfrac{1}{6}\times \dfrac{57}{10}\times \dfrac{53}{10}\]
\[\Rightarrow \] \[\dfrac{57\times 53}{6\times 10\times 10}\]
When we multiply 57 and 53 we get the product as below,
\[57\times 53=3021\]
Likewise when we multiply 6, 10 and 10 we get,
 \[6\times 10\times 10=600\]
\[\Rightarrow \dfrac{3021}{600}\]
As this is a fraction we can simplify this by dividing numerator 3021 by the denominator 600 to get the required solution.
\[600\overset{5.035}{\overline{\left){\begin{align}
  & 3021 \\
 & \underline{3000} \\
 & 002100 \\
 & \underline{001800} \\
 & 0003000 \\
 & \underline{0003000} \\
 & 0000000 \\
\end{align}}\right.}}\]
So from this division we get \[\dfrac{3021}{600}\] = 5.035
So the given problem is simplified as above to obtain the answer as mentioned,
\[\dfrac{5.7\times 5.3}{6}\]= 5.035

Note: This problem can also be solved using various others methods, one of them is without making the decimals in numerator to fractions by directly multiplying the fractions to get a decimal number and then converting it to fraction followed with the division of numerator by denominator. The important point here is to multiply the numbers with simple multiplication to get the products of the numbers. The division of numbers is known to divide the obtained fraction to the simplified form of the problem.