Skill: Interpret whole-number remainders

When you divide whole numbers, write the result as

$$a=bq+r$$

where:

• $a$ is the total amount, or dividend;
• $b$ is the size of each group, or divisor;
• $q$ is the number of complete groups;
• $r$ is the amount left over.

The remainder must be less than the divisor: $0\le r<b$.

Example: A teacher has $53$ pencils and puts $8$ pencils in each box. How many full boxes can she make, and how many pencils are left?

1. Divide $53$ by $8$:

$$53\div 8=6\text{ remainder }5$$

2. Check the division using the equation:

$$53=8\cdot 6+5$$

3. Interpret the numbers:

   • $6$ is the number of full boxes.
   • $5$ is the number of pencils left over.

So, the teacher can make 6 full boxes with 5 pencils left.

The remainder is not automatically added to the quotient. If the question asked how many boxes are needed to hold all the pencils, the 5 leftover pencils would require one more box, so the answer would be 7 boxes.