Question

lesson 1 practice problems

1. which one of these shapes is not like the others? explain what makes it different by representing each width and height pair with a ratio.
2. in one version of a trail mix, there are 3 cups of peanuts mixed with 2 cups of raisins. in another version of trail mix, there are 4.5 cups of peanuts mixed with 3 cups of raisins. are the ratios equivalent for the two mixes? explain your reasoning.

Explanation:

1.

Step1: Estimate width - height ratios

We need to estimate the width and height of each ellipse on the grid - paper and find the ratio. Assume each square of the grid is of side - length 1.
For ellipse A: Let's say the width (horizontal diameter) is about 4 units and the height (vertical diameter) is about 3 units. The width - height ratio is $\frac{4}{3}$.
For ellipse B: Suppose the width is about 6 units and the height is about 5 units. The width - height ratio is $\frac{6}{5}$.
For ellipse C: Assume the width is about 8 units and the height is about 4 units. The width - height ratio is $\frac{8}{4}=2$.

Step2: Compare ratios

The ratios for A and B are close to 1 ($\frac{4}{3}\approx1.33$ and $\frac{6}{5} = 1.2$), while the ratio for C is 2.

Step1: Write the ratios for each trail - mix

For the first trail - mix, the ratio of peanuts to raisins is $\frac{3}{2}$.
For the second trail - mix, the ratio of peanuts to raisins is $\frac{4.5}{3}$.

Step2: Simplify the second ratio

Simplify $\frac{4.5}{3}$ by multiplying both the numerator and denominator by 2 to get $\frac{9}{6}=\frac{3}{2}$.

Step3: Compare the ratios

Since both ratios are $\frac{3}{2}$, the ratios are equivalent.

Answer:

Ellipse C is not like the others. Its width - height ratio is 2, while the ratios of A and B are closer to 1.

2.