understanding ratio concepts
complete each problem about ratio relationships.
ms. cama helps the school tennis club. she has a bin of tennis balls and tennis rackets. in the bin, there are 5 tennis balls and 3 tennis rackets. draw a model to show the ratio of tennis balls to tennis rackets.
write the following ratios:
tennis balls to tennis rackets
tennis balls to total pieces of tennis equipment
christian has a collection of 18 shark teeth. he identified them as 6 tiger shark teeth, 8 sand shark teeth, and the rest as bull shark teeth.
what does the ratio 6:8 represent in this situation?
what does the ratio 4:18 represent in this situation? explain your reasoning. include a model in your explanation.
how do you describe different types of part - to - whole ratios?

Question

Accepted Answer

### First Problem (Tennis Equipment Ratios)
# Explanation:
## Step 1: Analyze Tennis Balls to Rackets Ratio
From the problem, we know the number of tennis balls and tennis rackets. Let's assume the number of tennis balls is 5 and rackets is 3 (from the handwritten numbers, but we'll use the ratio concept). The ratio of tennis balls to tennis rackets is the number of tennis balls divided by the number of tennis rackets, so if there are $ 5 $ tennis balls and $ 3 $ rackets, the ratio is $ 5:3 $.
## Step 2: Analyze Tennis Balls to Total Equipment Ratio
First, find the total number of tennis equipment. Total = tennis balls + tennis rackets. If tennis balls = $ 5 $ and rackets = $ 3 $, total = $ 5 + 3 = 8 $. So the ratio of tennis balls to total equipment is $ 5:8 $.
# Answer:
Tennis balls to tennis rackets: $ 5:3 $
Tennis balls to total tennis equipment: $ 5:8 $

### Second Problem (Shark Teeth Ratios)
#### What does $ 6:8 $ represent?
# Brief Explanations:
We know Christian has 6 tiger shark teeth, 8 sand shark teeth, and the rest are bull shark teeth. The ratio $ 6:8 $ compares the number of tiger shark teeth (6) to the number of sand shark teeth (8). So it represents the ratio of the number of tiger shark teeth to the number of sand shark teeth.
# Answer:
The ratio $ 6:8 $ represents the ratio of the number of tiger shark teeth to the number of sand shark teeth.

#### What does $ 4:18 $ represent? (First, find the number of bull shark teeth: Total teeth = 18, tiger = 6, sand = 8, so bull = $ 18 - 6 - 8 = 4 $)
# Brief Explanations:
The total number of shark teeth is 18, and the number of bull shark teeth is 4. So the ratio $ 4:18 $ represents the ratio of the number of bull shark teeth to the total number of shark teeth. To explain, we can model it as a part - whole relationship: out of 18 total teeth, 4 are bull shark teeth.
# Answer:
The ratio $ 4:18 $ represents the ratio of the number of bull shark teeth to the total number of shark teeth.

### Third Problem (How to Use Part - to - Part and Part - to - Whole Ratios)
# Brief Explanations:
- **Part - to - Part Ratios**: These compare two different parts of a whole. For example, in the shark teeth problem, the ratio of tiger shark teeth to sand shark teeth ($ 6:8 $) is a part - to - part ratio. We use them to show the relationship between two distinct groups within the whole set.
- **Part - to - Whole Ratios**: These compare one part of the whole to the entire whole. For example, the ratio of bull shark teeth to total shark teeth ($ 4:18 $) or the ratio of tennis balls to total tennis equipment ($ 5:8 $) are part - to - whole ratios. We use them to show the proportion of a specific part relative to the entire group.
# Answer:
Part - to - part ratios (e.g., $ 6:8 $ for shark teeth) compare two different parts of a whole, showing the relationship between two distinct subgroups. Part - to - whole ratios (e.g., $ 4:18 $ for shark teeth or $ 5:8 $ for tennis equipment) compare one part to the entire whole, showing the proportion of a part relative to the total group.

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QUESTION IMAGE

Question

Explanation:

First Problem (Tennis Equipment Ratios)

Step 1: Analyze Tennis Balls to Rackets Ratio

Step 2: Analyze Tennis Balls to Total Equipment Ratio

Answer:

Second Problem (Shark Teeth Ratios)

What does \( 6:8 \) represent?