The missing fraction is 7/9
The given equation is:
[tex]\frac{3}{4}+\frac{1}{2}+\frac{2}{9}+x=\frac{9}{4}[/tex]
This can be simplified as:
[tex]\frac{27+18+8+36x}{36} =\frac{9}{4} \\\\\frac{53+36x}{36} =\frac{9}{4}[/tex]
Cross multiply
[tex]9(36)=4(53+36x)\\\\324=212+144x\\\\144x=324-212\\\\144x=112\\\\x=\frac{112}{144} \\\\x=\frac{7}{9}[/tex]
Therefore, the missing value is [tex]\frac{7}{9}[/tex]
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