Question

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1. what is the smallest fraction of a full circle that the wagon wheel needs to turn in order to appear the very same as it does now? how many degrees of rotation would that be?
2. what is the smallest fraction of a full circle that the propeller needs to turn in order to appear the very same as it does right now? how many degrees of rotation would that be?
3. what is the smallest fraction of a full circle that the ferris wheel needs to turn in order to appear the very same as it does right now? how many degrees of rotation would that be?

Explanation:

Question 1

Step1: Count the number of equal parts

The wagon wheel is divided into 8 equal parts. So the smallest fraction is $\frac{1}{8}$ (since we need to rotate by 1 part out of 8 to look the same).

Step2: Calculate the degrees of rotation

A full circle is $360^\circ$. To find the degrees for $\frac{1}{8}$ of a circle, we calculate $360^\circ\times\frac{1}{8}$.
$360\div8 = 45$, so $360^\circ\times\frac{1}{8}=45^\circ$.

Step1: Count the number of equal parts

The propeller has 5 equal - angled arms, so the smallest fraction is $\frac{1}{5}$.

Step2: Calculate the degrees of rotation

Using the formula for the angle of rotation: $360^\circ\times\frac{1}{5}$.
$360\div5 = 72$, so $360^\circ\times\frac{1}{5}=72^\circ$.

Step1: Count the number of equal parts

First, we count the number of equal - sized sectors (or the number of "spokes" - like divisions). From the diagram, we can see that there are 18 equal parts. So the smallest fraction is $\frac{1}{18}$.

Step2: Calculate the degrees of rotation

Using the formula $360^\circ\times\frac{1}{18}$.
$360\div18 = 20$, so $360^\circ\times\frac{1}{18}=20^\circ$.

Answer:

Fraction: $\frac{1}{8}$, Degrees: $45^\circ$

Question 2