Step 1

(a) \(\displaystyle{55}\text{mod}{7}\)

As \(\displaystyle{55}={7}\cdot{7}+{6}\)

So that

\(\displaystyle{55}\text{mod}{7}={6}\text{mod}{7}\)

Step 2

(b) \(\displaystyle-{101}\div{3}\)

As \(\displaystyle-{101}={\left(-{34}\right)}\cdot{3}+{1}\)

So that \(\displaystyle-{101}\div{3}=-{34}\)

(a) \(\displaystyle{55}\text{mod}{7}\)

As \(\displaystyle{55}={7}\cdot{7}+{6}\)

So that

\(\displaystyle{55}\text{mod}{7}={6}\text{mod}{7}\)

Step 2

(b) \(\displaystyle-{101}\div{3}\)

As \(\displaystyle-{101}={\left(-{34}\right)}\cdot{3}+{1}\)

So that \(\displaystyle-{101}\div{3}=-{34}\)