Question

Lucas and Henry started a work together. Lucas completed ${\left(\frac{7}{15}\right)}^{th}$ of the whole, whereas, Henry completed ${\left(\frac{23}{50}\right)}^{th}$ of the whole.
did more work.

Answer 1

Let's convert the fractions into their decimal form and compare.

$\left(\frac{7}{15}\right)\to$ Divide $7$ by $15$ using long division.
$\therefore \frac{7}{15}=\mathrm{0.466...}=0.4\overline{6}$
It is a non-terminating and repeating decimal number.

$\left(\frac{23}{50}\right)\to$ Here the denimonator is a factor of power of $10,$ i.e., $100.$

$\Rightarrow 50\times 2=100$
Multiply the numerator and denominator by $2,$ to make the denominator as $100.$

$\frac{23\times 2}{50\times 2}=\frac{46}{100}=0.46$
(by shifting the decimal in the numerator by two places leftward)

$0.4\overline{6}>0.46$
as, $\mathrm{0.466...}>0.46$

$\therefore$ Lucas did more amount of work.