Fractional Calculation: Finding 40% of a Number
Let the unknown number be represented by '$x$'.
Step 1: Formulate the Equation
The problem states that "Two-fifth of seven-seventeenth of three-fifth of a number is 84". This translates to the following equation:
$ \frac{2}{5} \times \frac{7}{17} \times \frac{3}{5} \times x = 84 $
Step 2: Calculate the Product of Fractions
Multiply the given fractions together:
$ \frac{2 \times 7 \times 3}{5 \times 17 \times 5} = \frac{42}{425} $
The equation simplifies to:
$ \frac{42}{425} \times x = 84 $
Step 3: Solve for the Number (x)
To isolate '$x$', rearrange the equation:
$ x = 84 \times \frac{425}{42} $
Perform the calculation:
$ x = 2 \times 425 $
$ x = 850 $
The value of the number is 850.
Step 4: Calculate 40% of the Number
The final step is to find 40% of the number '$x$' (which is 850).
Convert 40% to a decimal or fraction: $40\% = \frac{40}{100} = 0.4$.
Calculate 40% of 850:
$ 0.4 \times 850 $
Alternatively, using fractions:
$ \frac{40}{100} \times 850 = \frac{2}{5} \times 850 $
$ = \frac{2 \times 850}{5} = 2 \times 170 $
$ = 340 $
Thus, 40% of the number is 340.
Similar Questions
- $1.236576576...$
can be written in the form of: - What is the sum of $\frac{1}{3}$, $\frac{4}{3}$ and $\frac{3}{4}$?
- Four persons A, B, C and D completed a task in $\frac{2}{3} \text{ h}, \frac{3}{4} \text{ h}, \frac{4}{5} \text{ h}$ and $\frac{1}{5} \text{ h}$ respectively. Who among the following took the highest amount of time to complete the task?
- The value of $\frac{4}{3} + \left( \frac{1}{1 + \frac{5}{6}} \right) - \frac{5}{4}$ is
What is the value of
$\frac{7}{9} - \frac{11}{12} + \frac{13}{16} - \frac{1}{8}$?
- How much does one need to add to $\frac{1}{2}$ to get $2$?
- The sum of the numerator and denominator of a fraction is 11. If the numerator is decreased by 1, the fraction becomes $\frac{1}{4}$. Find the fraction.
- If the numerator of a fraction is increased by 30% and its denominator is decreased by 35%, the value of the fraction becomes $\frac{3}{15}$. Find the original fraction.
- A beautician's income includes her salary and the tips she gets for her services. During a particular week, if her tips were $\frac{5}{4}$ of her salary, then what fraction of her income came from the tips?
- What smallest fraction should be added to $3\frac{2}{3} + 6\frac{7}{12} + 4\frac{9}{36} + 5 + 7\frac{1}{12}$ to make the sum a whole number?
Important Questions from Fractions
5 \(\frac{3}{4}\) + x + 2 \(\frac{1}{2}\) = 10 \(\frac{1}{8}\) Find the value of x.
Simplify the expression 441 ÷ \(\left[270 \div \frac{3}{7}+\left(17\div \frac{1}{3}\right)-\left(8\frac{1}{2}-\frac{5}{2}\right)\right]\)
Number 0.232323 can be written in rational form as:
Solve: \(\frac{1}{2}\) [{-2(2 + 3)*20}/2]
Match the following.
Column I
Column II
a.
Equivalent fraction of \(\frac{7}{12}\) is
i.
Proper fraction
b.
Equivalent fraction of \(\frac{9}{15}\) is
ii.
Improper fraction
c.
\(\frac{7}{11}\) is
iii.
\(\frac{21}{36}\)
d.
\(\frac{19}{5}\) is
iv.
\(\frac{3}{5}\)
