Overview
Division is the inverse of multiplication. If a times b equals c, and b is not equal to zero, then c divided by b equals a. Also, for any real number a not equal to zero, a times 1/a equals 1.
Division
Division is one of the four basic arithmetic operations. It is usually the last one to be taught, because solving division problems can involve addition, subtraction, and multiplication. Suppose the problem is 36 divided by 4. The answer, 9, is a math fact, because 9 times 4 is 36. It can be solved by using the definition of division, as 36/4 =9. It can be solved by subtraction, as 36 – 4 = 32 – 4 = 28 – 4 = 24 – 4 = 20 – 4 = 16 – 4 = 12 – 4 = 8 – 4 = 4 – 4 = 0. The number 4 was subtracted 9 times from 36. To check division, students can multiply the quotient by the divisor, or add the divisor repeatedly.
Measurement Model for Division
Suppose you had 100 movie tickets and you wanted to give 4 free tickets to as many people as possible who were waiting in line outside a theatre. One way that could be done is to measure sets of 4 tickets and give them to the first people in line until there were no more left. In this case, 100 is the dividend, 4 is the divisor, and dividing 100/4, gives 25 groups of 4 tickets each. The first 25 people in line get 4 free movie tickets.
Partitive Model for Division
Similarly, suppose the 100 movie tickets were divided into 4 equal parts. How many tickets would be in each set? The quotient would be the same, 25, but this time the divisor 4 represents the number of equal parts. Even though the numbers are the same in both models, the concepts are a little different.
Hands-On Illustrations
Many hands-on models for division exist, such as dividing beans or cubes into groups, or using the abacus to illustrate division by measurement. When students number off in groups of 4 to take part in activities or register for one of 5 home rooms, they illustrate the partitive model.
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