Final answer:
Emma can drive 1/4 of the distance to work with one gallon of gas.
Step-by-step explanation:
To find out what fraction of the distance Emma can drive to work with one gallon of gas, we need to find the fraction of the distance she can drive with 1/9 gallon of gas and then multiply it by the number of gallons in one gallon.
Emma drives 1/4 of the way to work and uses 1/9 gallon of gas. So, she can drive 1/4 * 1/9 = 1/36 of the distance to work with 1/9 gallon of gas.
To find the fraction of the distance she can drive with one gallon of gas, we multiply 1/36 by the number of gallons in one gallon: 1/36 * 9/1 = 9/36 = 1/4.
Therefore, Emma can drive 1/4 of the distance to work with one gallon of gas.