Question

problem 3 redo - part c
\frac{180}{4} miles in \frac{3}{4} hour
do not include units (miles) in your answer.

Explanation:

Step1: Simplify the distance

Simplify $\frac{180}{4}$ to get $45$. So the distance is $45$ (in the relevant unit) and time is $\frac{3}{4}$ hour.

Step2: Calculate the speed (or the rate we need)

We know that to find the rate (like speed here, but we just need the numerical value from the ratio), we can divide the distance by the time. So we do $45\div\frac{3}{4}$. Dividing by a fraction is multiplying by its reciprocal, so $45\times\frac{4}{3}$.

Step3: Compute the multiplication

$45\times\frac{4}{3}=\frac{45\times4}{3}=\frac{180}{3} = 60$? Wait, no, wait. Wait, actually, the original distance is $\frac{180}{4}$ and time is $\frac{3}{4}$. So the rate is $\frac{\frac{180}{4}}{\frac{3}{4}}$. When dividing fractions, we multiply the numerator by the reciprocal of the denominator: $\frac{180}{4}\times\frac{4}{3}$. The 4s cancel out, so we have $\frac{180}{3}=60$? Wait, no, wait, $\frac{180}{4}$ is 45, and $\frac{3}{4}$ hour. So 45 divided by $\frac{3}{4}$ is 45 times $\frac{4}{3}$ which is (45/3)4 = 154 = 60? Wait, but maybe a simpler way: $\frac{\frac{180}{4}}{\frac{3}{4}}=\frac{180}{4}\times\frac{4}{3}=\frac{180\times4}{4\times3}=\frac{180}{3}=60$. Wait, but let's check again. The problem is maybe asking for the unit rate, like miles per hour? Wait, the problem says "Do not include units (miles) in your answer." So we need to compute $\frac{\frac{180}{4}}{\frac{3}{4}}$. Let's do that:

$\frac{\frac{180}{4}}{\frac{3}{4}}=\frac{180}{4}\times\frac{4}{3}=\frac{180}{3}=60$. Wait, but maybe I misread. Wait, the distance is $\frac{180}{4}$ miles in $\frac{3}{4}$ hour. So to find, say, how many miles per hour? But the problem says "Do not include units". Wait, maybe it's just simplifying the ratio $\frac{\frac{180}{4}}{\frac{3}{4}}$. Let's compute that:

$\frac{\frac{180}{4}}{\frac{3}{4}}=\frac{180}{4}\div\frac{3}{4}=\frac{180}{4}\times\frac{4}{3}= \frac{180\times4}{4\times3}=\frac{180}{3}=60$. Wait, but let's check with the simplified distance. $\frac{180}{4}=45$, time is $\frac{3}{4}$ hour. So 45 miles in $\frac{3}{4}$ hour. So per hour, it's 45 / (3/4) = 60. But maybe the problem is just asking for the value when you simplify the fraction $\frac{\frac{180}{4}}{\frac{3}{4}}$. So the result is 60.

Wait, but let's do it step by step:

Step1: Write the ratio

The ratio is $\frac{\frac{180}{4}}{\frac{3}{4}}$.

Step2: Divide the fractions

To divide two fractions, multiply the numerator by the reciprocal of the denominator:

$\frac{180}{4} \times \frac{4}{3}$

Step3: Simplify

The 4 in the numerator and denominator cancels out:

$\frac{180}{3}$

Step4: Divide 180 by 3

$180 \div 3 = 60$

Answer:

60