To find a rational number between the fractions [tex]\( \frac{2}{13} \)[/tex] and [tex]\( \frac{3}{11} \)[/tex], follow these steps:
1. Convert Fractions to Decimal Form:
- Calculate [tex]\( \frac{2}{13} \)[/tex]:
[tex]\[
\frac{2}{13} \approx 0.15384615384615385
\][/tex]
- Calculate [tex]\( \frac{3}{11} \)[/tex]:
[tex]\[
\frac{3}{11} \approx 0.2727272727272727
\][/tex]
2. Calculate the Midpoint:
- To find a number between these two fractions, take their average:
[tex]\[
\text{midpoint} = \frac{0.15384615384615385 + 0.2727272727272727}{2}
\][/tex]
- Perform the addition:
[tex]\[
0.15384615384615385 + 0.2727272727272727 = 0.4265734265734265
\][/tex]
- Divide by 2 to get the average:
[tex]\[
\text{midpoint} = \frac{0.4265734265734265}{2} \approx 0.21328671328671328
\][/tex]
3. Conclusion:
- The rational number between [tex]\( \frac{2}{13} \)[/tex] and [tex]\( \frac{3}{11} \)[/tex] is approximately [tex]\( 0.21328671328671328 \)[/tex].
Thus, we have:
[tex]\[ \frac{2}{13} \approx 0.15384615384615385 \][/tex]
[tex]\[ \frac{3}{11} \approx 0.2727272727272727 \][/tex]
[tex]\[ \text{A rational number between them is} \approx 0.21328671328671328 \][/tex]
