Journey Calculation: Fractions and Distance
This problem requires calculating the total distance of Suhas's journey based on fractions covered by different modes of transport and the remaining distance covered by bicycle.
Steps to Calculate Total Distance
-
Calculate the fraction of the journey covered by train and bus:
Fraction by train = $\frac{5}{12}$
Fraction by bus = $\frac{1}{3}$
Total fraction (train + bus) = $\frac{5}{12} + \frac{1}{3}$
To add these fractions, find a common denominator, which is 12:
Total fraction = $\frac{5}{12} + \frac{1 \times 4}{3 \times 4} = \frac{5}{12} + \frac{4}{12} = \frac{9}{12}$
Simplify the fraction: $\frac{9}{12} = \frac{3}{4}$
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Determine the fraction of the journey covered by bicycle:
The total journey represents 1 whole.
Fraction by bicycle = Total journey - Fraction (train + bus)
Fraction by bicycle = $1 - \frac{3}{4} = \frac{4}{4} - \frac{3}{4} = \frac{1}{4}$
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Calculate the total journey distance:
We are given that the remaining distance covered by bicycle is 36 km.
This means $\frac{1}{4}$ of the total journey is equal to 36 km.
Let the total distance be $D$. Then:
$\frac{1}{4} \times D = 36 \text{ km}$
To find the total distance $D$, multiply the distance by bicycle by 4:
$D = 36 \text{ km} \times 4$
$D = 144 \text{ km}$
Therefore, Suhas traveled a total of 144 km.
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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.
\(\frac{3}{5}\)
