Select all ratios equivalent to 1:5.
Understand the Problem
The question is asking to identify which of the given ratios are equivalent to the ratio 1:5. This requires comparing each ratio to see if they simplify or can be converted to the same form as 1:5.
Answer
The ratio equivalent to $1:5$ is $10:50$.
Answer for screen readers
The ratios equivalent to ( 1:5 ) are ( 10:50 ).
Steps to Solve
- Convert the ratio 1:5 to fraction form
The ratio ( 1:5 ) can be expressed as a fraction: $$ \frac{1}{5} $$
- Convert each given ratio to fraction form
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For ( 10:50 ): $$ \frac{10}{50} $$
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For ( 2:3 ): $$ \frac{2}{3} $$
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For ( 9:60 ): $$ \frac{9}{60} $$
- Simplify each fraction
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Simplifying ( \frac{10}{50} ): $$ \frac{10 \div 10}{50 \div 10} = \frac{1}{5} $$
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Simplifying ( \frac{2}{3} ): It is already in simplest form.
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Simplifying ( \frac{9}{60} ): $$ \frac{9 \div 3}{60 \div 3} = \frac{3}{20} $$
- Compare the simplified fractions to ( \frac{1}{5} )
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( \frac{10}{50} = \frac{1}{5} ) (equivalent)
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( \frac{2}{3} \neq \frac{1}{5} ) (not equivalent)
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( \frac{9}{60} = \frac{3}{20} \neq \frac{1}{5} ) (not equivalent)
The ratios equivalent to ( 1:5 ) are ( 10:50 ).
More Information
Understanding ratios and their equivalents is fundamental in mathematics, particularly in proportional reasoning and real-world applications like recipes and scaling.
Tips
- A common mistake is to forget to simplify the fractions properly. Always remember to reduce to the lowest terms for accurate comparison.
