Is 3/5 greater than 3/4?
Understand the Problem
The question is asking whether the fraction 3/5 is greater than the fraction 3/4, requiring a comparison of the two fractions.
Answer
$\frac{3}{5} < \frac{3}{4}$
Answer for screen readers
The fraction $\frac{3}{5}$ is less than the fraction $\frac{3}{4}$.
Steps to Solve
- Identifying a Common Denominator
To compare the fractions $\frac{3}{5}$ and $\frac{3}{4}$, we need to find a common denominator. The least common multiple (LCM) of the denominators 5 and 4 is 20.
- Converting the Fractions
Next, we convert both fractions to have the common denominator of 20.
For $\frac{3}{5}$: $$ \frac{3}{5} = \frac{3 \times 4}{5 \times 4} = \frac{12}{20} $$
For $\frac{3}{4}$: $$ \frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20} $$
- Comparing the Converted Fractions
Now that both fractions have the same denominator, we can easily compare the numerators.
We have: $$ 12 \quad \text{and} \quad 15 $$
Since $12 < 15$, it follows that: $$ \frac{12}{20} < \frac{15}{20} $$
Thus, we can conclude that: $$ \frac{3}{5} < \frac{3}{4} $$
The fraction $\frac{3}{5}$ is less than the fraction $\frac{3}{4}$.
More Information
When comparing fractions, a common method is to convert them to a common denominator. In this case, both fractions were converted to have the denominator of 20, which made comparison straightforward.
Tips
- Not finding a common denominator: Always ensure both fractions are compared using the same denominator.
- Incorrect conversions: Be careful when multiplying both the numerator and denominator; ensure that the calculation is performed correctly.
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