Sure, let's go through this step-by-step to find out what fraction of Rohit's pocket money is left after spending on various items.
1. Determine the fractions spent:
- On a science fiction book: [tex]\( \frac{2}{5} \)[/tex]
- On a newspaper: [tex]\( \frac{1}{6} \)[/tex]
- On recreation: [tex]\( \frac{2}{15} \)[/tex]
2. Find a common denominator:
To add these fractions together, we need a common denominator. The denominators are 5, 6, and 15. The least common multiple (LCM) of these numbers is 30.
3. Convert each fraction to have the common denominator of 30:
- For [tex]\( \frac{2}{5} \)[/tex]:
[tex]\[
\frac{2}{5} = \frac{2 \times 6}{5 \times 6} = \frac{12}{30}
\][/tex]
- For [tex]\( \frac{1}{6} \)[/tex]:
[tex]\[
\frac{1}{6} = \frac{1 \times 5}{6 \times 5} = \frac{5}{30}
\][/tex]
- For [tex]\( \frac{2}{15} \)[/tex]:
[tex]\[
\frac{2}{15} = \frac{2 \times 2}{15 \times 2} = \frac{4}{30}
\][/tex]
4. Add the fractions together:
[tex]\[
\frac{12}{30} + \frac{5}{30} + \frac{4}{30} = \frac{12 + 5 + 4}{30} = \frac{21}{30}
\][/tex]
5. Simplify the total fraction spent:
[tex]\(\frac{21}{30}\)[/tex] simplifies to [tex]\(\frac{7}{10}\)[/tex].
6. Subtract the spent fraction from the whole:
Since the whole pocket money is represented by 1 (or 1/1 as a fraction), subtracting [tex]\( \frac{7}{10} \)[/tex] from 1 gives:
[tex]\[
1 - \frac{7}{10} = \frac{10}{10} - \frac{7}{10} = \frac{3}{10}
\][/tex]
7. Determine the fraction left:
The fraction of pocket money left is [tex]\(\frac{3}{10}\)[/tex].
After verification, the fraction of Rohit's pocket money that is left is indeed [tex]\( 0.30000000000000004 \)[/tex], or [tex]\(\frac{3}{10}\)[/tex] when represented as a fraction.
