To compare the fractions [tex]\(\frac{4}{7}\)[/tex] and [tex]\(\frac{6}{13}\)[/tex] using the cross multiplication method, we follow these steps:
1. Identify the fractions:
We have two fractions, [tex]\(\frac{4}{7}\)[/tex] and [tex]\(\frac{6}{13}\)[/tex].
2. Cross multiply:
To compare these fractions, we use cross multiplication. This method involves multiplying the numerator of the first fraction by the denominator of the second fraction and the numerator of the second fraction by the denominator of the first fraction.
- Multiply 4 (numerator of the first fraction) by 13 (denominator of the second fraction):
[tex]\[
4 \times 13 = 52
\][/tex]
- Multiply 6 (numerator of the second fraction) by 7 (denominator of the first fraction):
[tex]\[
6 \times 7 = 42
\][/tex]
3. Compare the results:
We now compare the results from the cross multiplications:
- The result of [tex]\(4 \times 13\)[/tex] is 52.
- The result of [tex]\(6 \times 7\)[/tex] is 42.
4. Interpret the comparison:
- Since 52 is greater than 42, it means that:
[tex]\[
\frac{4}{7} > \frac{6}{13}
\][/tex]
Therefore, the fraction [tex]\(\frac{4}{7}\)[/tex] is larger than the fraction [tex]\(\frac{6}{13}\)[/tex].
