Dividing whole numbers
What is division?
Division is the method of breaking up a group of things into equal parts. There are also certain terms related to division.
A few of the terms are:
- Dividend: The number that is being divided.
- Divisor: The number that we divide by.
- Quotient: The result of the division.
- Remainder: If the divisor doesn’t completely divide the dividend, then, the number that is left is called remainder.
So, the general manner in which division is done in math is:
Dividend = Quotient \(\times\) Divisor + Remainder
When do we get a remainder?
In many cases, the divisor may not fully divide the dividend. In such cases, we get a remainder after the division operation.
What is a mixed number?
Mixed numbers, as the name suggests, are a mixture of whole numbers and proper fractions. Mixed numbers are mostly used to express numbers between two whole numbers.
We can use a mixed fraction \(2~\frac{1}{3}\) to represent \(2~+~\frac{1}{3}\), a number between the whole numbers 2 and 3, to make this mixed number easily readable.
\(~1~\frac{3}{5},~9~\frac{6}{7}, ~6~\frac{1}{2}, \) and \(~5~\frac{1}{3}\) are a few examples of mixed fractions.
Example: Find 8425 ÷ 5, and find the product of the quotient and the divisor.
Solution:
We will begin with thousands digit, 8. 8 ÷ 5 will give 1 with remainder 3.
Now, we will bring down 4 to the right of 3.
We will divide 34 by 5 to get 6 with 4 as remainder.
We will bring down 2 to the right of 4.
Now, 42 ÷ 5 will give us 8 with 2 as remainder.
Now, we will bring down 5 to the right of 2. 25 divided by 5 will give us 5.
Thus 8425 ÷ 5 gives us 1685 as the answer.
We have the quotient as 1685 and the divisor is 5. So, the product is:
So we get 8425 as the result, and this is the dividend.
Dividing decimals using models
What is a model?
A model is a grid with 10 columns and 10 rows. So in total we have 100 boxes, which means each box or cell is \(\left(\frac{1}{100}~=~0.01\right)\) or 1 hundredth. Each column or row is \(\left(\frac{1}{10}~=~0.1\right)\) or 1 tenth.
To divide a decimal by a whole number using a model, we first shade the region in the model that represents the dividend (or the decimal. Then we divide this shaded region into an equal number of groups as the divisor. The number of cells or blocks in each group is the quotient.
Division of a decimal by a whole number
We begin by dividing the two numbers just as we divide two whole numbers without taking into account the decimal point. The quotient’s decimal point is then placed above the dividend’s decimal point.
Division of a decimal by another decimal
Both the dividend and the divisor are decimals in this type of division. We have to convert the divisor to a whole number for the division. To do that we multiply both the dividend and divisor by a power of 10 raised to the number of decimal places of the divisor. Then divide the numbers like you would divide two whole numbers. Place the decimal point in the quotient above the dividend’s decimal point.
Solved Examples
Example 1: Divide the decimal value 15.65 by a whole number 5
Solution:
Example 2: 7.10 lb of marbles are owned by a store owner. Calculate the weight of the marbles that each jar contains if she divides the marble into 5 jars?
Solution:
Each jar will contain 1.42 lb of marbles.
Example 3: Divide the decimal value 18.09 by the decimal 0.9.
Solution:
18.09 ÷ 0.9 = \(\frac{18.09}{0.9}\)
The divisor, 0.9 has 1 decimal place. So we multiply the numerator and the denominator by 10
18.09 ÷ 0.9\(~=~\frac{18.09}{0.9}~=~\frac{18.09~\times~ 10}{0.9~\times~ 10}~=~\frac{18.09}{9}\)
Let us use the long division method to find the result.
Example 4: A 1.5-foot piece of sand paper has been given to you. You’re going to cut it into 0.5-foot-long pieces. How many sand paper pieces do you have now?
Solution:
We have to find 1.5 ÷ 0.5
We have to shade 15 columns to represent 1.5 feet. Dividing the model to show groups of 0.5. There are 3 groups of 0.5.
Therefore, 1.5÷ 0.5 = 3. There are 3 pieces of sandpaper.
When dividing decimals, the divisor should be a whole number because it makes the calculation easier and more convenient for students to understand the division process.
We use division in our day-to-day life for various purposes. When we split the bill at a restaurant, we share snacks equally among friends, allot time for studying different subjects, and so on.
The term “rounding off” refers to the process of simplifying a number by keeping its value while bringing it closer to the next number. Finding the approximate value of a given decimal number up to two decimal places is known as rounding to the nearest hundredths.
Base 10 blocks or models as we know, are math manipulatives that are used for building a strong understanding of place value in decimals. They also help in visualising decimals, which helps in creating a strong foundation with regards to decimals.