Is 1/5 greater than 1/4?
Understand the Problem
The question is asking us to compare two fractions, 1/5 and 1/4, to determine which one is greater.
Answer
$ \frac{1}{4} > \frac{1}{5} $
Answer for screen readers
$ \frac{1}{4} > \frac{1}{5} $
Steps to Solve
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Identify the fractions for comparison We need to compare the two fractions: $ \frac{1}{5} $ and $ \frac{1}{4} $.
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Find a common denominator To compare these fractions easily, we can find a common denominator. The least common denominator (LCD) for 5 and 4 is 20.
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Rewrite the fractions with the common denominator Now we convert both fractions to have the denominator of 20:
For $ \frac{1}{5} $: $$ \frac{1}{5} = \frac{1 \cdot 4}{5 \cdot 4} = \frac{4}{20} $$
For $ \frac{1}{4} $: $$ \frac{1}{4} = \frac{1 \cdot 5}{4 \cdot 5} = \frac{5}{20} $$
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Compare the numerators Now we compare the numerators of the fractions $ \frac{4}{20} $ and $ \frac{5}{20} $. Since 4 is less than 5, we determine that: $$ \frac{4}{20} < \frac{5}{20} $$
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Conclusion Since $ \frac{1}{5} < \frac{1}{4} $, we can conclude that 1/4 is greater than 1/5.
$ \frac{1}{4} > \frac{1}{5} $
More Information
When comparing fractions, it's useful to convert them to a common denominator. This makes it easier to visually compare their sizes.
Tips
- A common mistake is assuming that the first fraction is always greater than the second. It’s crucial to evaluate their values.
- Sometimes, people forget to find a common denominator and compare fractions directly. Always rewrite them when possible.
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