Facts on Third Grade Division

The foundations of division are taught in third grade math.

Multiplication and division are usually introduced to students in the third grade. Grasping these new mathematics concepts can be challenging for students. When teaching division, it is helpful to review division's relationship with subtraction and multiplication and cover rules that apply to certain numbers.

Division and Subtraction

The purpose of division is to separate objects into equal groups. The result of dividing objects can be gained by repeated subtraction. For example 18 can be separated into 3 groups of 6. This can be demonstrated when 6 is subtracted from 18 exactly three times, 18-6-6-6=0.

Division and Multiplication

Multiplication and division have an inverse relationship. If numbers are multiplied together to create a product, the product can be divided by either number to determine the solution to a division problem. For example, 5x6=30, so 30/6=5 and 30/5=6. This relationship holds true for any two numbers multiplied together. This rule can also be used to verify answers for division problems.

Rule of One

In multiplication, any number multiplied by 1 remains does not change. For example, 12x1=12. The same rule holds true for division by 1. If any number is separated into equal groups of 1, the number of groups will be equal to the original number. This fact can be proven with subtraction, when 3/1 is shown as 3-1-1-1=0. 1 can be removed from 3 three times.

The Rule of Zero

Numbers can not be successfully divided by 0 because it is not possible to separate an object into zero groups. If the number 0 is divided by another number, the answer is always 0. For example 0/5=0. This corresponds to the relationship between division and multiplication, since 5x0=0.

Division Terms

The numbers in division problems have specific names. The dividend is the number being divided, and this is usually the number with the greatest value. The divisor is the number the dividend is divided by. The quotient is the answer to a division problem - the number of times the divisor goes into the dividend.

Remainders

When divisors do not go evenly into dividends, a remainder is left over. The remainder is a number that can not be divided by the divisor as a whole number. For example, 25 cannot be divided by 8 evenly because there is no multiple of 8 that equals exactly 25. The closest number of times 8 can go into 25 is 3 times, because 8x3=24. The difference between 25 and 24 is one, as 25-24=1. For this problem, the remainder is 1.

References

• AAA Math: Third Grade