Question

a biking track has a length of 4480 feet (ft). how long is this in miles (mi)? first fill in the blank on the left side of the equation using one of the ratios. then write your answer on the right side of the equation. ratios: 5280 ft / 1 mi, 1 mi / 5280 ft, 1 mi / 1760 yd, 1760 yd / 1 mi, 1 yd / 36 in, 36 in / 1 yd. 4480 ft / 1 × blank = blank mi

Explanation:

Step1: Identify conversion ratio

We know that 1 mile = 5280 feet, so the ratio to convert feet to miles is $\frac{1\ \text{mi}}{5280\ \text{ft}}$.

Step2: Set up the equation

Multiply the given length in feet by the conversion ratio: $\frac{4480\ \text{ft}}{1} \times \frac{1\ \text{mi}}{5280\ \text{ft}}$.

Step3: Simplify the calculation

Simplify the fraction: $\frac{4480}{5280} = \frac{28}{33} \approx 0.848$ (or keep it as a fraction, but let's compute the decimal). Wait, actually, $4480\div5280=\frac{448}{528}=\frac{28}{33}\approx0.848$? Wait, no, wait 4480 divided by 5280: divide numerator and denominator by 160: 4480÷160=28, 5280÷160=33. So 28/33 ≈0.848? Wait, no, wait 5280 feet is 1 mile. So 4480 ft (1 mi / 5280 ft) = 4480/5280 mi. Let's simplify: divide numerator and denominator by 160: 4480÷160=28, 5280÷160=33. So 28/33 ≈0.848? Wait, no, 4480 divided by 5280: let's divide numerator and denominator by 80: 4480÷80=56, 5280÷80=66. Then divide by 2: 28/33 ≈0.848? Wait, maybe I made a mistake. Wait 5280 feet is 1 mile. So 4480 ft is how many miles? Let's do 4480 ÷ 5280. Let's divide numerator and denominator by 160: 4480/160=28, 5280/160=33. So 28/33 ≈0.848? Wait, no, 28 divided by 33 is approximately 0.848? Wait, 330.8=26.4, 330.84=27.72, 330.848=27.984, which is close to 28. So yes. But let's check the calculation again. The equation is 4480 ft (1 mi / 5280 ft) = (4480/5280) mi = 28/33 mi ≈0.848 mi. Wait, but maybe the problem expects a fraction or a decimal. Let's compute 4480 ÷ 5280. Let's divide numerator and denominator by 160: 4480 ÷ 160 = 28, 5280 ÷ 160 = 33. So 28/33 is the exact value, which is approximately 0.848. But let's see the ratio. The correct ratio to use is $\frac{1\ \text{mi}}{5280\ \text{ft}}$ because we want to cancel out feet and get miles. So the blank should be filled with $\frac{1\ \text{mi}}{5280\ \text{ft}}$, and then the calculation is 4480 1 / 5280 = 4480/5280 = 28/33 ≈0.848. Wait, but maybe I miscalculated. Wait 5280 feet is 1 mile. So 4480 feet is 4480/5280 miles. Let's simplify that fraction: divide numerator and denominator by 160: 4480 ÷ 160 = 28, 5280 ÷ 160 = 33. So 28/33 ≈0.848. So the first blank (the ratio) is $\frac{1\ \text{mi}}{5280\ \text{ft}}$, and the answer is 28/33 or approximately 0.848. Wait, but let's check the numbers again. 4480 and 5280. Let's divide numerator and denominator by 80: 4480 ÷80=56, 5280 ÷80=66. Then divide by 2: 28/33. Yes. So the ratio to use is $\frac{1\ \text{mi}}{5280\ \text{ft}}$, and then the calculation is 4480 * 1 / 5280 = 28/33 ≈0.848.

Answer:

The ratio to fill in the blank is $\frac{1\ \text{mi}}{5280\ \text{ft}}$, and the length in miles is $\frac{28}{33} \approx 0.848$ (or as a fraction $\frac{28}{33}$). So the blank on the left is $\boldsymbol{\frac{1\ \text{mi}}{5280\ \text{ft}}}$ and the answer on the right is $\boldsymbol{\frac{28}{33}}$ (or approximately $\boldsymbol{0.848}$) mi.