The four operations with fractions and decimals

Adding and subtracting fractions

Find a common denominator first — the lowest common multiple is neatest, but any common multiple works. $\tfrac23+\tfrac15=\tfrac{10}{15}+\tfrac{3}{15}=\tfrac{13}{15}$. Never add the denominators.

Multiplying and dividing

Multiply straight across: $\tfrac23\times\tfrac45=\tfrac{8}{15}$. To divide, multiply by the reciprocal: $\tfrac23\div\tfrac45=\tfrac23\times\tfrac54=\tfrac{10}{12}=\tfrac56$. Cancel common factors before multiplying and the numbers stay small.

Mixed numbers

Turn mixed numbers into improper fractions before doing anything: $2\tfrac13=\tfrac73$. Trying to multiply mixed numbers directly is the commonest source of wrong answers in this topic.

Dividing by a decimal

$4{,}8\div0{,}6$: multiply both numbers by $10$ to make the divisor whole — $48\div6=8$. The answer is unchanged because you scaled both sides equally.