Convert Ratio 1:10 to Percentage: Beverage Distribution Problem

Q: What does the ratio 1:10 actually mean in this problem?

The ratio 1:10 means that for every 1 carbonated drink, there are 10 total beverages in the store. It's showing the relationship between part to whole, not part to part.

Q: Why isn't the answer 1% if the ratio starts with 1?

Great question! The ratio 1:10 means 1 out of 10, which equals $ \frac{1}{10} = 0.1 = 10\% $. The number 1 in the ratio represents parts, not percentage points.

Q: How do I remember to multiply by 100 when converting to percentage?

Remember: Percentage means "per hundred." So $ \frac{1}{10} $ becomes $ \frac{10}{100} $ which is 10 per hundred = 10%!

Q: What if the ratio was 3:10 instead?

Same process! Convert to fraction: $ \frac{3}{10} $, then multiply by 100: $ \frac{3}{10} \times 100 = 30\% $. The denominator stays the same in part-to-whole ratios.

Ratio to Percentage with Beverage Distribution

In a grocery store, the ratio of carbonated drinks to all beverages is $1:10$ ,
what percentage of all beverages are carbonated drinks?

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Step-by-step written solution

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Understand the problem

In a grocery store, the ratio of carbonated drinks to all beverages is $1:10$ ,
what percentage of all beverages are carbonated drinks?

Step-by-step solution

We need to find the percentage of beverages that are carbonated drinks given the ratio $1:10$ .

This ratio $1:10$ indicates that for every 1 part of carbonated drinks, there are 10 parts of all beverages.

Step 1: Express the ratio as a fraction: $\frac{1}{10}$ .
Step 2: Convert the fraction to a percentage by multiplying by 100: $\frac{1}{10} \times 100 = 10\%$ .

Therefore, the percentage of all beverages that are carbonated drinks is $10\%$ .

Final Answer

$10\%$

Key Points to Remember

Essential concepts to master this topic

Rule: Ratio 1:10 means 1 part out of 10 total parts
Technique: Convert $\frac{1}{10}$ to percentage by multiplying by 100
Check: 10% of 100 beverages = 10 carbonated drinks confirms ratio 1:10 ✓

Common Mistakes

Avoid these frequent errors

Confusing ratio parts with percentage directly
Don't think 1:10 means 1%! This ignores that ratios show parts of a whole. The ratio 1:10 means 1 out of 10 total parts, not 1 out of 100. Always convert the ratio to a fraction first, then multiply by 100 for percentage.

Practice Quiz

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What is the ratio between the orange and gray parts in the drawing?

FAQ

Everything you need to know about this question

What does the ratio 1:10 actually mean in this problem?

The ratio 1:10 means that for every 1 carbonated drink, there are 10 total beverages in the store. It's showing the relationship between part to whole, not part to part.

Why isn't the answer 1% if the ratio starts with 1?

Great question! The ratio 1:10 means 1 out of 10, which equals $\frac{1}{10} = 0.1 = 10\%$ . The number 1 in the ratio represents parts, not percentage points.

How do I remember to multiply by 100 when converting to percentage?

Remember: Percentage means "per hundred." So $\frac{1}{10}$ becomes $\frac{10}{100}$ which is 10 per hundred = 10%!

What if the ratio was 3:10 instead?

Same process! Convert to fraction: $\frac{3}{10}$ , then multiply by 100: $\frac{3}{10} \times 100 = 30\%$ . The denominator stays the same in part-to-whole ratios.

Can I check my answer using real numbers?

Absolutely! If there are 100 beverages total and 10% are carbonated, that's 10 carbonated drinks. The ratio would be 10:100, which simplifies to 1:10. Perfect match! ✓

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Convert Ratio 1:10 to Percentage: Beverage Distribution Problem

Ratio to Percentage with Beverage Distribution

❤️ Continue Your Math Journey!

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

What does the ratio 1:10 actually mean in this problem?

Why isn't the answer 1% if the ratio starts with 1?

How do I remember to multiply by 100 when converting to percentage?

What if the ratio was 3:10 instead?

Can I check my answer using real numbers?

🌟 Unlock Your Math Potential

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