1.5 Divide whole numbers

Use division notation

So far we have explored addition, subtraction, and multiplication. Now let’s consider division. Suppose you have the $12$ cookies in [link] and want to package them in bags with $4$ cookies in each bag. How many bags would we need?

You might put $4$ cookies in first bag, $4$ in the second bag, and so on until you run out of cookies. Doing it this way, you would fill $3$ bags.

In other words, starting with the $12$ cookies, you would take away, or subtract, $4$ cookies at a time. Division is a way to represent repeated subtraction just as multiplication represents repeated addition.

Instead of subtracting $4$ repeatedly, we can write

We read this as twelve divided by four and the result is the quotient    of $12$ and $4.$ The quotient is $3$ because we can subtract $4$ from $12$ exactly $3$ times. We call the number being divided the dividend    and the number dividing it the divisor    . In this case, the dividend is $12$ and the divisor is $4.$

In the past you may have used the notation $4\overline{)12}$ , but this division also can be written as $12÷4,12\text{/}4,\frac{12}{4}.$ In each case the $12$ is the dividend and the $4$ is the divisor.

Operation symbols for division

To represent and describe division, we can use symbols and words.

Model division of whole numbers

As we did with multiplication, we will model division using counters. The operation of division helps us organize items into equal groups as we start with the number of items in the dividend and subtract the number in the divisor repeatedly.