Question

During their family vacation, the Lawson family bought 14 2/3
gallons of gasoline for their car. At the end of the trip, they had 5 2/5
gallons left. How much gas did they use during the trip?

Answer 1

To find out how much gasoline the Lawson family used during their trip, we need to subtract the amount of gasoline they had left at the end of the trip from the amount they bought at the beginning of the trip.

First, let's convert the mixed numbers into improper fractions for easier calculation.

1. **Convert \(14 \frac{2}{3}\) to an improper fraction:**
\[
14 \frac{2}{3} = \frac{14 \times 3 + 2}{3} = \frac{42 + 2}{3} = \frac{44}{3}
\]

2. **Convert \(5 \frac{2}{5}\) to an improper fraction:**
\[
5 \frac{2}{5} = \frac{5 \times 5 + 2}{5} = \frac{25 + 2}{5} = \frac{27}{5}
\]

Now we need to subtract the amount of gasoline left from the total amount bought:

\[
\text{Gas used} = \text{Total gas bought} - \text{Gas left} = \frac{44}{3} - \frac{27}{5}
\]

To perform this subtraction, we'll first find a common denominator. The least common multiple of 3 and 5 is 15.

3. **Convert both fractions to have a denominator of 15:**
- For \(\frac{44}{3}\):
\[
\frac{44}{3} = \frac{44 \times 5}{3 \times 5} = \frac{220}{15}
\]
- For \(\frac{27}{5}\):
\[
\frac{27}{5} = \frac{27 \times 3}{5 \times 3} = \frac{81}{15}
\]

4. **Now, subtract the two fractions:**
\[
\frac{220}{15} - \frac{81}{15} = \frac{220 - 81}{15} = \frac{139}{15}
\]

Finally, we can convert \(\frac{139}{15}\) back to a mixed number.

5. **Convert \(\frac{139}{15}\) to a mixed number:**
- Divide 139 by 15. \(15\) goes into \(139\) nine times since \(15 \times 9 = 135\).
- The remainder is \(139 - 135 = 4\).
- Thus, \(\frac{139}{15} = 9 \frac{4}{15}\).

The Lawson family used **9 \( \frac{4}{15} \)** gallons of gasoline during their trip.