Skill: Interpret remainders

When you divide, the remainder is what is left after making equal groups.

Use the relationship

$$\text{dividend}=(\text{divisor}\times\text{quotient})+\text{remainder}.$$

The remainder must always be smaller than the divisor.

Example: A teacher has 23 markers and puts 5 markers in each box. How many full boxes can she make, and how many markers are left?

1. Divide:

$$23\div 5=4\text{ R }3$$

2. Interpret the answer:

   • The quotient, $4$, means there are 4 full boxes.
   • The remainder, $3$, means 3 markers are left over.

3. Check using the division relationship:

$$23=(5\times4)+3$$

So, there are 4 full boxes and 3 markers left.

The answer changes depending on the question. If every marker must be placed in a box, the 3 leftover markers need another box, so 5 boxes are needed. The remainder is not automatically added to the quotient; its meaning depends on the situation.