Question

1. oliver had an out-of-town company trip last week. before the trip, he noticed that his car was \\(\frac{3}{4}\\) full of gasoline. after the trip, the gas tank was \\(\frac{2}{9}\\) full. what fraction of the gasoline in the car was used during the trip?\
2. oliver spent \\(\frac{1}{3}\\) of his salary for food, \\(\frac{1}{6}\\) for the water and electric bills and \\(\frac{1}{9}\\) for other expenses. the rest went into his savings. what fraction of his salary is used for his expenses? what fraction of his salary went into his savings?\
3. mr. silva owns \\(\frac{4}{5}\\) of the stocks in the company where oliver works. he wants to distribute his company stocks among his 3 children. he gave \\(\frac{3}{10}\\) of the stocks to his eldest child and \\(\frac{1}{4}\\) of the stocks to his youngest child. what part of the stocks will be given to the second child?

Explanation:

Problem 4

Step1: Identify the initial and final fractions

The initial fraction of gasoline is $\frac{3}{4}$, and the final fraction is $\frac{2}{9}$. To find the fraction used, we subtract the final from the initial.

Step2: Find a common denominator

The least common denominator of 4 and 9 is 36. Convert $\frac{3}{4}$ to $\frac{27}{36}$ ($\frac{3\times9}{4\times9}$) and $\frac{2}{9}$ to $\frac{8}{36}$ ($\frac{2\times4}{9\times4}$).

Step3: Subtract the fractions

Subtract the final from the initial: $\frac{27}{36} - \frac{8}{36} = \frac{19}{36}$.

Step1: Find the total fraction for expenses

To find the total fraction used for expenses, add the fractions for food, water/electric, and other expenses. The fractions are $\frac{1}{3}$, $\frac{1}{6}$, and $\frac{1}{9}$.

Step2: Find a common denominator

The least common denominator of 3, 6, and 9 is 18. Convert each fraction: $\frac{1}{3} = \frac{6}{18}$, $\frac{1}{6} = \frac{3}{18}$, $\frac{1}{9} = \frac{2}{18}$.

Step3: Add the fractions

Add them together: $\frac{6}{18} + \frac{3}{18} + \frac{2}{18} = \frac{11}{18}$.

Step4: Find the fraction for savings

Subtract the total expenses from 1 (since 1 represents the whole salary). $1 - \frac{11}{18} = \frac{7}{18}$.

Step1: Identify the total stocks Mr. Silva owns

Mr. Silva owns $\frac{4}{5}$ of the stocks. We need to find the fraction given to the second child by subtracting the fractions given to the eldest and youngest from his total.

Step2: Find a common denominator

First, find the least common denominator for 5, 10, and 4. The LCD is 20. Convert the fractions: $\frac{4}{5} = \frac{16}{20}$, $\frac{3}{10} = \frac{6}{20}$, $\frac{1}{4} = \frac{5}{20}$.

Step3: Subtract the fractions

Subtract the fractions given to the eldest and youngest from his total: $\frac{16}{20} - \frac{6}{20} - \frac{5}{20} = \frac{5}{20} = \frac{1}{4}$.

Answer:

$\frac{19}{36}$

Problem 5