Answer:
[tex]\dfrac{11}{24}[/tex]
Step-by-step explanation:
Let S be Sara's number.
To find the average of two numbers, we add them together and divide the result by 2. Therefore, if Sara's number is the average of 1/3 and 1/2, then:
[tex]S=\dfrac{\frac13+\frac12}{2}[/tex]
To add two fractions with different denominators, convert each fraction to an equivalent fraction with a common denominator. The least common multiple (LCM) of the two denominators is 6, so:
[tex]S=\dfrac{\frac{1\cdot 2}{3\cdot 2}+\frac{1\cdot 3}{2\cdot 3}}{2} \\\\\\ S=\dfrac{\frac{2}{6}+\frac{3}{6}}{2}[/tex]
Now, add the numerators while keeping the common denominator the same:
[tex]S=\dfrac{\frac{2+3}{6}}{2} \\\\\\ S=\dfrac{\frac{5}{6}}{2}[/tex]
Finally, apply the fraction rule (a/b)/c = a/(bc):
[tex]S=\dfrac{5}{6\cdot 2} \\\\\\ S=\dfrac{5}{12}[/tex]
Therefore, Sara's number is 5/12.
Let A be Ali's number.
Given that Ali's number is the average of Sara's number (5/12) and 1/2, then:
[tex]A=\dfrac{\frac{5}{12}+\frac{1}{2}}{2} \\\\\\ A=\dfrac{\frac{5}{12}+\frac{1\cdot 6}{2\cdot 6}}{2} \\\\\\ A=\dfrac{\frac{5}{12}+\frac{6}{12}}{2} \\\\\\ A=\dfrac{\frac{5+6}{12}}{2} \\\\\\ A=\dfrac{\frac{11}{12}}{2} \\\\\\ A=\dfrac{11}{12 \cdot 2} \\\\\\ A=\dfrac{11}{24}[/tex]
Therefore, Ali's number is:
[tex]\LARGE\boxed{\boxed{\dfrac{11}{24}}}[/tex]
