Write this ratio as a fraction in simplest form without any units. 16 quarts to 9 gallons
The Correct Answer and Explanation is:
Correct Answer:
49\dfrac{4}{9}94
Explanation:
To write the ratio 16 quarts to 9 gallons as a fraction in simplest form, you need both quantities to have the same unit. Since 1 gallon equals 4 quarts, we will convert 9 gallons into quarts.
Step 1: Convert gallons to quarts
9 gallons×4=36 quarts9 \text{ gallons} \times 4 = 36 \text{ quarts}9 gallons×4=36 quarts
Now the ratio is:16 quarts36 quarts\frac{16 \text{ quarts}}{36 \text{ quarts}}36 quarts16 quarts
Since the units are the same, they cancel out. So we are left with:1636\frac{16}{36}3616
Step 2: Simplify the fraction
To simplify the fraction, find the greatest common factor (GCF) of 16 and 36.
- Factors of 16: 1, 2, 4, 8, 16
- Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
- Greatest common factor: 4
Now divide both numerator and denominator by 4:16÷436÷4=49\frac{16 ÷ 4}{36 ÷ 4} = \frac{4}{9}36÷416÷4=94
So, the ratio 16 quarts to 9 gallons written as a fraction in simplest form is:49\boxed{\frac{4}{9}}94
Summary:
To compare two quantities with different units, always convert them to the same unit. In this case, we converted gallons to quarts. After canceling the units and simplifying the fraction using the GCF, the final answer is 4 over 9, with no units included. This approach helps maintain accuracy and ensures the result is presented in the correct mathematical form.
