[tex]\mathrm{H}=2 \frac{1}{6}[/tex] is correct value of expression [tex]3 \frac{5}{6}=1 \frac{2}{3}+\mathrm{H}[/tex]
Solution:
Given expression is [tex]3 \frac{5}{6}=1 \frac{2}{3}+\mathrm{H}[/tex]
We have to substitute [tex]2\frac{1}{6}[/tex] for H
We have to substitute the value into the given expression and determine whether the given value of "H" makes the sentence true
On substituting given value of H in equation (1) and solving Right Hand Side, we get,
[tex]1 \frac{2}{3}+2 \frac{1}{6}[/tex]
Now let us convert the mixed fractions,
[tex]1 \frac{2}{3}+2 \frac{1}{6}=\frac{3 \times 1+2}{3}+\frac{6 \times 2+1}{6}=\frac{5}{3}+\frac{13}{6}[/tex]
On solving we get,
[tex]\frac{5}{3}+\frac{13}{6}=\frac{10+13}{6}=\frac{23}{6}[/tex]
Thus we have solved R.H.S and got the value [tex]\frac{23}{6}[/tex]
Now let us solve L.H.S of expression,
[tex]3 \frac{5}{6}=\frac{6 \times 3+5}{6}=\frac{18+5}{6}=\frac{23}{6}[/tex]
Thus L.H.S and R.H.S are equal
Thus given "H" = [tex]2\frac{1}{6}[/tex] makes the expression true
