+130511 Good Answer, ND......perhaps you're wondering how ND found the common denominator??
Factoring 54, we have 9*6 = 3*3*3*2 = [3^3 * 2]
Factoring 36, we have 6*6= 3*2*3*2 [3^2 * 2^2]
Factoring 162, we have 81*2 = 9*9*2 = 3*3*3*3*2 = [3^4 * 2]
I see we have two different numbers that are used in the factoring process....namely......2 and 3
Take the highest power of each that occur and multiply these together...so we have
[3^4] * [2^2] = 81 * 4 = 324
+3454 First we have to make all the fractions have common deminators.
$${\frac{{\mathtt{1}}}{{\mathtt{54}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{23}}}{{\mathtt{36}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{263}}}{{\mathtt{162}}}}$$
Now I'll multiply the first fraction by 6/6. I'll multiply the second fractions by 9/9, and I'll multiply the last fraction by 2/2. Now we have common denominator!
$${\frac{{\mathtt{6}}}{{\mathtt{324}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{207}}}{{\mathtt{324}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{526}}}{{\mathtt{324}}}}$$
Add them together,
$${\frac{{\mathtt{739}}}{{\mathtt{324}}}}$$
or
$${\mathtt{2}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{91}}}{{\mathtt{324}}}}$$
or
$${\mathtt{2.280\: \!864\: \!197\: \!530\: \!864\: \!2}}$$
+130511 Good Answer, ND......perhaps you're wondering how ND found the common denominator??
Factoring 54, we have 9*6 = 3*3*3*2 = [3^3 * 2]
Factoring 36, we have 6*6= 3*2*3*2 [3^2 * 2^2]
Factoring 162, we have 81*2 = 9*9*2 = 3*3*3*3*2 = [3^4 * 2]
I see we have two different numbers that are used in the factoring process....namely......2 and 3
Take the highest power of each that occur and multiply these together...so we have
[3^4] * [2^2] = 81 * 4 = 324
