Final answer:
Aisha can use 1/8 of a tank of gas per day for 6 days, having only 3/4 of a tank available. This is calculated by dividing the total gas she has by the number of days it needs to last and simplifying the resulting fraction.
Step-by-step explanation:
Aisha is planning to fill her car with gas and only has enough money to buy 3/4 of a tank. She needs the gas to last for 6 days. To find the fraction of a tank she can use each day, you divide the fraction of the gas she can purchase by the number of days the gas needs to last.
The calculation is as follows:
- Fraction of a tank available: 3/4
- Number of days the gas needs to last: 6
- Daily fraction of gas: (3/4) ÷ 6
To simplify this, you first convert the mixed number to an improper fraction:
- (3/4) ÷ 6 = (3/4) ÷ (6/1)
- Next, multiply by the reciprocal of 6/1, which is 1/6:
- (3/4) ÷ (6/1) = (3/4) × (1/6)
- Finally, multiply the numerators and denominators:
- 3 × 1 = 3 and 4 × 6 = 24, so the fraction is 3/24.
- Reduce the fraction by dividing both numerator and denominator by their greatest common divisor, which is 3:
- 3 ÷ 3 = 1 and 24 ÷ 3 = 8
- So the simplest form of the fraction is 1/8.
Aisha can use 1/8 of a tank of gas per day to ensure she has enough gas to last for 6 days.