To handle a large number of us will turn to handle string.

In the code below you noticed method was needed str.insert(int post, int n, int ch); n times to insert the character ch in the string str at position pos;
There are also 2 Other methods are :
str.insert(int post, char * s); insert s (array of characters ending '') at position pos of str;
str.insert(int post, string s); insert string s (string) the position of the string str pos;

#include <string>
#include <iostream>

using namespace std;

int stringToNum(char c)		// chuyen char sang so
{
	return c - '0';
}

char numToString(int n)		// chuyen so sang char
{
	return (char)(n+48);
}

void chuanHoa(string &a, string &b)	// lam 2 xau co do dai bang nhau
{
	int l1 = a.length(), l2 = b.length();
	if (l1 >= l2)
	{
		b.insert(0, l1-l2, '0');	// chen vao dau cua b cac ky tu '0'
	}
	else
	{
		a.insert(0, l2-l1, '0');	// chen vao dau cua a cac ky tu '0'
	}
}

string sum(string a, string b)	// tong 2 so
{
	string s = "";
	chuanHoa(a,b);		// chuan hoa
	int l = a.length();
	
	int temp = 0;
	for (int i=l-1; i>=0; i--)	// duyet va cong
	{
		temp = stringToNum(a[i]) + stringToNum(b[i]) + temp;	// tinh tong tung doi mot
		s.insert(0,1,numToString(temp%10));			// gan phan don vi vao
		temp = temp/10;		// lay lai phan hang chuc
	}
	if (temp>0)	// neu hang chuc > 0 thi them vao KQ
	{
		s.insert(0,1,numToString(temp));
	} 
	return s;
}

// nhan so co 1 chu so voi so co nhieu chu so (VD 4 va 7826), lam tuong tu nhu phep cong
string nhanNho(char a, string b)	
{
	string s = "";
	int temp = 0;
	for (int i=b.length()-1; i>=0; i--)		
	{
		temp = stringToNum(a) * stringToNum(b[i]) + temp;
		s.insert(0,1,numToString(temp%10));
		temp = temp/10;
	}
	
	if (temp>0)
	{
		s.insert(0,1,numToString(temp));
	} 
	return s;
}

string nhan(string a, string b)		// nhan 2 so lon
{
	string s = "";
	int l = a.length();
	string s1[l];
	
	for (int i=l-1; i>=0; i--)	// nhan tung chu so cua a voi b sau do cong don vao
	{
		s1[i] = nhanNho(a[i], b);	// nhan tung so cua a voi b
		s1[i].insert(s1[i].length(), l-i-1, '0');	
		s = sum(s, s1[i]);	// cong don theo cach cong so lon
	}
	return s;
}

int main(int argc, char **argv)
{
	string a, b, s;

	cout<<"Nhap a va b"<<endl;
	
	getline(cin, a);
	getline(cin, b);
	
	s = sum(a,b);
	cout<<"Tong cua a va b : "<<s<<endl;
	
	s = nhan(a,b);
	cout<<"Tich cua a va b : "<<s<<endl;
	
	return 0; 
}