 WME@Kimpton Middle

## Dividing Integers To ask What is 10 divided by 2? is the same as asking What times 2 equals 10?. We know

10 ÷ 2 = 5 because 5 × 2 = 10

In other words

15 ÷ 5 = ? really asks ? × 5 = 15

When we divide a number by another, the answer is called the quotient of the two numbers.

Based on this understanding, do these problems.

```14 ÷ 2 =

-14 ÷ 2 =

18 ÷ -2 =

-18 ÷ -2 =
```

Division is the inverse operation of multiplication because if you divide by a number then multiply by that number you have done nothing.

(10 ÷ 2) × 2 = 10

(10 × 2) ÷ 2 = 10

You can also think of 21 ÷ 7 as asking How many 7's are there in 21?. Sometimes an integer does not divide another evenly. 19 ÷ 7 is an example. We can fit 2 7's in 19 easily, but we can't fit 3 7's. In this case we say the quotient is 2 with a remainder of 5.

19 ÷ 7 = (14 + 5) ÷ 7 = 14 ÷ 7 + 5 ÷ 7 = 2 + 5/7

In general we have Keep in mind that the remainder must be smaller than the divisor in absolute values. If the remainder is zero, then the divisor is a factor of the dividend.

Do these problems.

```16 ÷ 5 gives quotient    and remainder

-17 ÷ 3 gives quotient    and remainder

Here is the method to perform long division function namecheck(c,s,a)
{    var name = document.getElementById(s);
var cname = document.getElementById(c);
if ( name.value == null || name.value == "" )
name.select();
return false;
}
if ( cname.value == null || cname.value == "" )
cname.select();
return false;
}
var ans = document.getElementById(a);
if ( ans.value == null || ans.value == "" )