is correct value of expression ![3 \frac{5}{6}=1 \frac{2}{3}+\mathrm{H}](https://tex.z-dn.net/?f=3%20%5Cfrac%7B5%7D%7B6%7D%3D1%20%5Cfrac%7B2%7D%7B3%7D%2B%5Cmathrm%7BH%7D)
<u>Solution:</u>
Given expression is ![3 \frac{5}{6}=1 \frac{2}{3}+\mathrm{H}](https://tex.z-dn.net/?f=3%20%5Cfrac%7B5%7D%7B6%7D%3D1%20%5Cfrac%7B2%7D%7B3%7D%2B%5Cmathrm%7BH%7D)
We have to substitute
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,
![1 \frac{2}{3}+2 \frac{1}{6}](https://tex.z-dn.net/?f=1%20%5Cfrac%7B2%7D%7B3%7D%2B2%20%5Cfrac%7B1%7D%7B6%7D)
Now let us convert the mixed fractions,
![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}](https://tex.z-dn.net/?f=1%20%5Cfrac%7B2%7D%7B3%7D%2B2%20%5Cfrac%7B1%7D%7B6%7D%3D%5Cfrac%7B3%20%5Ctimes%201%2B2%7D%7B3%7D%2B%5Cfrac%7B6%20%5Ctimes%202%2B1%7D%7B6%7D%3D%5Cfrac%7B5%7D%7B3%7D%2B%5Cfrac%7B13%7D%7B6%7D)
On solving we get,
![\frac{5}{3}+\frac{13}{6}=\frac{10+13}{6}=\frac{23}{6}](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B3%7D%2B%5Cfrac%7B13%7D%7B6%7D%3D%5Cfrac%7B10%2B13%7D%7B6%7D%3D%5Cfrac%7B23%7D%7B6%7D)
Thus we have solved R.H.S and got the value ![\frac{23}{6}](https://tex.z-dn.net/?f=%5Cfrac%7B23%7D%7B6%7D)
Now let us solve L.H.S of expression,
![3 \frac{5}{6}=\frac{6 \times 3+5}{6}=\frac{18+5}{6}=\frac{23}{6}](https://tex.z-dn.net/?f=3%20%5Cfrac%7B5%7D%7B6%7D%3D%5Cfrac%7B6%20%5Ctimes%203%2B5%7D%7B6%7D%3D%5Cfrac%7B18%2B5%7D%7B6%7D%3D%5Cfrac%7B23%7D%7B6%7D)
Thus L.H.S and R.H.S are equal
Thus given "H" =
makes the expression true