Answer:
[tex]\dfrac{7}{12}[/tex]
Step-by-step explanation:
Method 1
convert the fractions so that their denominators are 12:
[tex]\dfrac12=\dfrac{1 \times 6}{2 \times 6}=\dfrac{6}{12}[/tex]
[tex]\dfrac23=\dfrac{2\times4}{3\times4}=\dfrac{8}{12}[/tex]
From inspection, we can determine that the fraction that lies exactly halfway between [tex]\dfrac{6}{12}[/tex] and [tex]\dfrac{8}{12}[/tex] is [tex]\dfrac{7}{12}[/tex]
Method 2
Find the difference between the fractions and divide by 2:
[tex]\dfrac{\dfrac23-\dfrac12}{2}=\dfrac{1}{12}[/tex]
Add this to the smallest fraction (1/2):
[tex]\dfrac12+\dfrac{1}{12}=\dfrac{7}{12}[/tex]
