Lesson 10: Find Missing Side Lengths

Property

Solving a division problem, such as $A \div B = ?$, is the same as finding the unknown factor in the related multiplication equation, $B \times ? = A$.
The quotient of the division is the unknown factor.

Examples

Property

When a whole number (the dividend) cannot be evenly divided by another whole number (the divisor), the result is a quotient and a remainder.
The remainder is the amount left over and must be less than the divisor.
The relationship is:

Examples

• Find $125 \div 4$:

The quotient is $31$ with a remainder of $1$, written as $31 \text{ R}1$.

• Find $347 \div 8$:

The quotient is $43$ with a remainder of $3$, written as $43 \text{ R}3$.

Explanation

To divide whole numbers using long division, follow the divide, multiply, subtract, and bring down steps. If you have a non-zero number left after the final subtraction step and no more digits to bring down, that number is the remainder. The remainder represents the part of the dividend that is left over after creating as many equal groups as possible. Always make sure the remainder is smaller than the divisor.

Property

When the dividend is constant, changing the divisor by a factor causes the quotient to change by the inverse factor.
For example, halving the divisor doubles the quotient, and doubling the divisor halves the quotient.

Examples

Property

A single division equation can represent two different types of problems, depending on whether you are finding the number of groups (quotative division) or the number of objects in each group (partitive division).

Examples