A primary class mathematics teacher gave his students the following problem to solve :

“How many classes of 28 pupils would be needed for a school of 616 pupils ?”

One of the student solved the problem in the following way :

1 Class=28 Pupils
10 →  2 8 0
10 →  2 8 0
      5 6 0
2  →    5 6  →  10 +10+2=22 Classes
      6 1 6

Which of the following is most appropriate for the algorithm used by the student ?

Correct Option: The student has used the distributive law of division across addition to solve the problem

Step-by-Step Explanation:

1. Understanding the Given Problem:

The problem asks to calculate the number of classes required for 616 pupils, given that 1 class contains 28 pupils.

Standard mathematical operation required:

$\text{Number of classes}=\frac{616}{28}$

2. Analyzing the Student's Method:

The student broke down the total number of pupils (616) into smaller parts using chunks of classes:

• 10 classes = 280 pupils

• 10 classes = 280 pupils

Combining these two gives 20 classes = 280 + 280 = 560 pupils.

• 2 classes = 56 pupils

Adding this to 560 gives 560 + 56 = 616 pupils.

Thus, total classes = 10 + 10 + 2 = 22 classes.

3. Identifying the Mathematical Property/Algorithm:

Mathematically, the student expressed 616 as a sum of parts:

$616=280+280+56$

Then divided each part by 28:

$\frac{616}{28}=\frac{280+280+56}{28}$

Applying division individually to each term inside the sum:

$\frac{616}{28}=\frac{280}{28}+\frac{280}{28}+\frac{56}{28}$

$\frac{616}{28}=10+10+2=22$

This process of distributing the divisor across a sum of terms in the dividend is known as the distributive law of division across addition, or partial quotients algorithm.