1.5 Divide whole numbers  (Page 2/12)

Divide whole numbers

We said that addition and subtraction are inverse operations because one undoes the other. Similarly, division is the inverse operation of multiplication. We know $12÷4=3$ because $3·4=12.$ Knowing all the multiplication number facts is very important when doing division.

We check our answer to division by multiplying the quotient by the divisor to determine if it equals the dividend. In [link] , we know $24÷8=3$ is correct because $3·8=24.$

What is the quotient when you divide a number by itself?

Dividing any number $\text{(except 0)}$ by itself produces a quotient of $1.$ Also, any number divided by $1$ produces a quotient of the number. These two ideas are stated in the Division Properties of One.

Suppose we have $\text{\$0},$ and want to divide it among $3$ people. How much would each person get? Each person would get $\text{\$0}.$ Zero divided by any number is $0.$

Now suppose that we want to divide $\text{\$1}0$ by $0.$ That means we would want to find a number that we multiply by $0$ to get $10.$ This cannot happen because $0$ times any number is $0.$ Division by zero is said to be undefined .

These two ideas make up the Division Properties of Zero.

Another way to explain why division by zero is undefined is to remember that division is really repeated subtraction. How many times can we take away $0$ from $10?$ Because subtracting $0$ will never change the total, we will never get an answer. So we cannot divide a number by $0.$

When the divisor or the dividend has more than one digit, it is usually easier to use the $4\overline{)12}$ notation. This process is called long division. Let’s work through the process by dividing $78$ by $3.$

Divide the first digit of the dividend, 7, by the divisor, 3.
The divisor 3 can go into 7 two times since $2\times 3=6$ . Write the 2 above the 7 in the quotient.
Multiply the 2 in the quotient by 2 and write the product, 6, under the 7.
Subtract that product from the first digit in the dividend. Subtract $7-6$ . Write the difference, 1, under the first digit in the dividend.
Bring down the next digit of the dividend. Bring down the 8.
Divide 18 by the divisor, 3. The divisor 3 goes into 18 six times.
Write 6 in the quotient above the 8.
Multiply the 6 in the quotient by the divisor and write the product, 18, under the dividend. Subtract 18 from 18.