A fraction is equivalent to 0·375. If 5 is added to its numerator and 8 to its denominator, the resulting fraction is \( \frac{1}{2} \). What is the original fraction ?
\( \frac{3}{8} \)
Since \( 0.375 = \frac{3}{8} \), let the fraction be \( \frac{3k}{8k} \).
Given \( \frac{3k + 5}{8k + 8} = \frac{1}{2} \), so \( 2(3k + 5) = 8k + 8 \).
\( 6k + 10 = 8k + 8 \Rightarrow 2k = 2 \Rightarrow k = 1 \), so the fraction is \( \frac{3}{8} \).
Check: \( \frac{3 + 5}{8 + 8} = \frac{8}{16} = \frac{1}{2} \) and \( \frac{3}{8} = 0.375 \).
Hence, \( \frac{3}{8} \).
Similar Questions
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Important Questions from Fractions
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.
\(\frac{3}{5}\)
Among the fractions \(\frac{7}{12}\) , \(\frac{8}{15}\) , \(\frac{17}{24}\) and \(\frac{13}{18}\) , which is the smallest?
