2. ulia has to mow two yards. She will need \( \frac{13}{16} \) gallon of gas to mow the first yard and \( \frac{2}{5} \) gallon to mow the second yard. She has \( 1 \frac{1}{2} \) gallons of gas in her can. Does she have enough to mow both yards? Explain.

To determine if Julia has enough gas, we first need to add the amounts of gas required for both yards: \( \frac{13}{16} \) gallon for the first yard and \( \frac{2}{5} \) gallon for the second yard. First, let's find a common denominator for \( \frac{13}{16} \) and \( \frac{2}{5} \). The least common multiple of 16 and 5 is 80. Therefore, we convert the fractions: \( \frac{13}{16} = \frac{13 \times 5}{16 \times 5} = \frac{65}{80} \) and \( \frac{2}{5} = \frac{2 \times 16}{5 \times 16} = \frac{32}{80} \). Now we add them: \( \frac{65}{80} + \frac{32}{80} = \frac{97}{80} \). This means Julia will need \( \frac{97}{80} \) gallons of gas in total, which is equal to \( 1 \frac{17}{80} \) gallons. Now, let’s convert \( 1 \frac{1}{2} \) gallons into an improper fraction: \( 1 \frac{1}{2} = \frac{3}{2} \) gallons. To convert our gas from gallons into eighths, we can also express this as \( \frac{3 \times 40}{2 \times 40} = \frac{120}{80} \) gallons. Now that we have \( \frac{120}{80} \) gallons, we can compare: Since \( \frac{120}{80} > \frac{97}{80} \), Julia does indeed have enough gas to mow both yards! It looks like it's time to get her mower cranked up and enjoy some quality time outdoors!