Do these ratios form a proportion?
18 cellos : 40 basses
9 cellos : 20 basses
yes

Question

Do these ratios form a proportion? 18 cellos : 40 basses 9 cellos : 20 basses yes

UpStudy AI · Accepted Answer

Yes, the ratios you've provided do form a proportion. Here's why:

### Given Ratios:
1. **18 cellos : 40 basses**
2. **9 cellos : 20 basses**

### To Determine if They Form a Proportion:
A proportion exists if the two ratios are equivalent, meaning the cross-products are equal.

Let's convert the ratios to fractions and compare them:

1. **First Ratio:**  
   $$\frac{18 \text{ cellos}}{40 \text{ basses}}$$  
   Simplifying this fraction by dividing both numerator and denominator by 2:  
   $$\frac{18 ÷ 2}{40 ÷ 2} = \frac{9}{20}$$

2. **Second Ratio:**  
   $$\frac{9 \text{ cellos}}{20 \text{ basses}} = \frac{9}{20}$$

### Comparison:
- **First Ratio Simplified:** $$\frac{9}{20}$$
- **Second Ratio:** $$\frac{9}{20}$$

Since both simplified ratios are equal ($$\frac{9}{20} = \frac{9}{20}$$), the original ratios **18 cellos : 40 basses** and **9 cellos : 20 basses** do indeed form a proportion.

### Cross-Product Verification:
Alternatively, you can use the cross-multiplication method to verify:

$$
18 \times 20 = 360 \
40 \times 9 = 360 \
$$

Since both cross-products are equal ($$360 = 360$$), the ratios are proportional.

**Conclusion:**  
Yes, **18 cellos : 40 basses** and **9 cellos : 20 basses** form a proportion because they simplify to the same ratio or have equal cross-products.
Yes, the ratios 18 cellos : 40 basses and 9 cellos : 20 basses form a proportion.

Do these ratios form a proportion?
18 cellos : 40 basses
9 cellos : 20 basses
yes

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