Wigglish sums, products, and quotients

To make a sum using wiggle, write the addends as a string of superdigits, and interpose ${\displaystyle 1}$s as interbases, e.g.

${\displaystyle a+b+c+d = a_1{b}_1{c}_{1}d.}$

Summation is essentially wiggle in base one.

To make a product using wiggle, write the factors as a string of interbases.  Then write ${\displaystyle 1}$ as the first superdigit and ${\displaystyle 0}$s for all remaining superdigits, e.g.

${\displaystyle a b c d = 1_a{0}_b{0}_c{0}_{d}0.}$

To make a quotient using wiggle, treat the numerator and denominator as you would for a fraction, e.g.

${\displaystyle p÷q = p/q = \frac{p}{q} = q \backslash p = 0{;}_{q}p.}$

There is no particularly easy way to represent negation or subtraction in wiggle.