Question

chapter 2: ratios, rates, and proportional reasoning practice test
phase 1: easy levels (questions 1-6)
focus: writing ratios, simplifying ratios, and finding basic unit rates.

1. a mountain bike gear has a front chainring with 32 teeth and a rear cog with 16 teeth. write the ratio of front teeth to rear teeth in simplest fractional form.

1. a box of lawn fertilizer contains \\(3\text{ kg}\\) of nitrogen and \\(1\text{ kg}\\) of phosphorus. what is the two-term ratio of nitrogen to the total mass of the fertilizer?

1. if a cyclist travels \\(30\text{ km}\\) in \\(2\text{ hours}\\) at a constant speed, what is their unit rate in kilometers per hour (\\(\text{km}/\text{h}\\))?

1. a local store sells a 3-pack of mechanical pencils for \\(\\$6.00\\). what is the unit price per pencil?

1. complete the equivalent ratio to find the missing value of \\(x\\):

\\3 : 5 = 12 : x\\

1. a recipe for mixing a specific shade of green paint calls for 2 parts blue paint to 5 parts yellow paint. if you use 10 buckets of yellow paint, how many buckets of blue paint do you need?

Explanation:

Calculate ratio of front teeth to rear teeth

$$ \text{Ratio} = \frac{32}{16} = \frac{2}{1} $$

Calculate ratio of nitrogen to total mass

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Calculate unit rate in kilometers per hour

$$ \text{Unit Rate} = \frac{30\text{ km}}{2\text{ hours}} = 15\text{ km/h} $$

Calculate unit price per pencil

$$ \text{Unit Price} = \frac{\$6.00}{3} = \$2.00 $$

Solve for equivalent ratio value x

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Solve for required buckets of blue paint

$$
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$$

Answer:

No.	Answer
2	\(3 : 4\)
3	\(15\text{ km/h}\)
4	\(\$2.00\)
5	\(x = 20\)
6	\(4\text{ buckets}\)