To compare the fractions [tex]\(\frac{5}{10}\)[/tex] and [tex]\(\frac{2}{4}\)[/tex], let's follow these steps:
1. Simplify the Fractions:
- For the fraction [tex]\(\frac{5}{10}\)[/tex], we can simplify it by finding the greatest common divisor (GCD) of 5 and 10, which is 5. Dividing both the numerator and the denominator by 5, we get:
[tex]\[
\frac{5}{10} = \frac{5 \div 5}{10 \div 5} = \frac{1}{2}
\][/tex]
- For the fraction [tex]\(\frac{2}{4}\)[/tex], we can simplify it by finding the GCD of 2 and 4, which is 2. Dividing both the numerator and the denominator by 2, we get:
[tex]\[
\frac{2}{4} = \frac{2 \div 2}{4 \div 2} = \frac{1}{2}
\][/tex]
2. Compare the Simplified Fractions:
After simplification, we have:
[tex]\[
\frac{1}{2} \quad \text{and} \quad \frac{1}{2}
\][/tex]
Clearly, both fractions are equal. Therefore, the comparison is:
[tex]\[
\frac{1}{2} = \frac{1}{2}
\][/tex]
3. Conclusion:
Since both fractions simplify to the same value, we can conclude:
[tex]\[
\frac{5}{10} = \frac{2}{4}
\][/tex]
Therefore, [tex]\(\frac{5}{10}\)[/tex] is equal to [tex]\(\frac{2}{4}\)[/tex], and we use the symbol [tex]\(=\)[/tex] to denote this equality. Thus,
[tex]\[
\frac{5}{10} = \frac{2}{4}
\][/tex]
