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Answer:
[tex] \frac{11}{24} [/tex]
Step-by-step explanation:
You first find Sara's number by finding the average of 1/3 and 1/2. To do so, you have to add 1/3 and 1/2 (1/3 + 1/2) and then divide that answer by 2 ((5/6)÷2) to get 5/12 which is Sara's number. Next, you can find Ali's number by finding the average of 5/12 and 1/2. To do so, you have to add 5/12 and 1/2 (5/12 + 1/2) and then divide that answer by 2 ((11/2)÷2) and get 11/24 which is Ali's number. I hope this was helpful!
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]