Long Division & Remainders Cheat Sheet

Key Facts

• In $156 \div 3 = 52$, the dividend is $156$, the divisor is $3$, and the quotient is $52$.
• The long division steps are divide, multiply, subtract, bring down, and repeat until no digits are left.
• A remainder is what is left after division, as in $17 \div 5 = 3\text{ R }2$.
• The remainder must always be less than the divisor, so in $29 \div 4$, a remainder of $5$ is not allowed.
• Check a division answer using $\text{divisor} \times \text{quotient} + \text{remainder} = \text{dividend}$.
• For $43 \div 6 = 7\text{ R }1$, the check is $6 \times 7 + 1 = 43$.
• If a digit in the dividend cannot be divided yet, write $0$ in the quotient as a placeholder when needed.
• Division and multiplication are inverse operations, so $8 \times 4 = 32$ helps solve $32 \div 8 = 4$.

Vocabulary

Dividend

The dividend is the number being divided, such as $84$ in $84 \div 7$.

Divisor

The divisor is the number you divide by, such as $7$ in $84 \div 7$.

Quotient

The quotient is the answer to a division problem, such as $12$ in $84 \div 7 = 12$.

Remainder

The remainder is the amount left over when the dividend cannot be divided evenly by the divisor.

Placeholder

A placeholder is a $0$ written in the quotient to keep digits in the correct place value.

Check

A check uses multiplication and addition to prove a division answer with $\text{divisor} \times \text{quotient} + \text{remainder}$.