Question

melissa used $1 \frac{1}{4}$ gallons of gas on friday and $4 \frac{7}{8}$ gallons of gas on saturday. how many more gallons of gas did she use on saturday?
write your answer as a mixed number in simplest form.
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Explanation:

Step1: Convert mixed numbers to improper fractions

First, convert \(1\frac{1}{4}\) 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 \(1\frac{1}{4}\), we have \(a = 1\), \(b = 1\), \(c = 4\). Then \(\frac{1\times4 + 1}{4}=\frac{5}{4}\).

Next, convert \(4\frac{7}{8}\) to an improper fraction. Here, \(a = 4\), \(b = 7\), \(c = 8\). So \(\frac{4\times8 + 7}{8}=\frac{32 + 7}{8}=\frac{39}{8}\).

Step2: Find a common denominator

The denominators are 4 and 8. The least common denominator of 4 and 8 is 8. So we convert \(\frac{5}{4}\) to a fraction with denominator 8. Multiply the numerator and denominator of \(\frac{5}{4}\) by 2: \(\frac{5\times2}{4\times2}=\frac{10}{8}\).

Step3: Subtract the fractions

Now we subtract the amount used on Friday from the amount used on Saturday. So we calculate \(\frac{39}{8}-\frac{10}{8}\). When subtracting fractions with the same denominator, we subtract the numerators: \(\frac{39 - 10}{8}=\frac{29}{8}\).

Step4: Convert back to a mixed number

Now we convert \(\frac{29}{8}\) to a mixed number. Divide 29 by 8: \(8\times3 = 24\), and \(29-24 = 5\). So \(\frac{29}{8}=3\frac{5}{8}\).

Answer:

\(3\frac{5}{8}\)