Question

rica used $3\frac{1}{3}$ gallons of gas on friday and $2\frac{1}{4}$ gallons of gas on saturday. how many more gallons of gas did she use on friday?
write your answer as a mixed number in simplest form.
gallons

Explanation:

Step1: Convert mixed numbers to improper fractions

First, convert \(3\frac{1}{3}\) to an improper fraction. The formula for converting a mixed number \(a\frac{b}{c}\) to an improper fraction is \(\frac{a\times c + b}{c}\). So for \(3\frac{1}{3}\), we have \(a = 3\), \(b = 1\), \(c = 3\). Then \(\frac{3\times3 + 1}{3}=\frac{9 + 1}{3}=\frac{10}{3}\).

Next, convert \(2\frac{1}{4}\) to an improper fraction. Using the same formula, with \(a = 2\), \(b = 1\), \(c = 4\), we get \(\frac{2\times4 + 1}{4}=\frac{8 + 1}{4}=\frac{9}{4}\).

Step2: Find a common denominator and subtract

The denominators are 3 and 4, so the least common denominator (LCD) is \(3\times4 = 12\).

Convert \(\frac{10}{3}\) to a fraction with denominator 12: \(\frac{10}{3}=\frac{10\times4}{3\times4}=\frac{40}{12}\).

Convert \(\frac{9}{4}\) to a fraction with denominator 12: \(\frac{9}{4}=\frac{9\times3}{4\times3}=\frac{27}{12}\).

Now subtract the two fractions: \(\frac{40}{12}-\frac{27}{12}=\frac{40 - 27}{12}=\frac{13}{12}\).

Step3: Convert the improper fraction back to a mixed number

To convert \(\frac{13}{12}\) to a mixed number, divide 13 by 12. 12 goes into 13 once with a remainder of 1. So \(\frac{13}{12}=1\frac{1}{12}\).

Answer:

\(1\frac{1}{12}\)