- Topics At a Glance
- Different Types of Numbers
- Natural Numbers
- Whole Numbers
- Integers and Negative Numbers
- Integers and Absolute Value
- Rational Numbers
- Irrational Numbers
- Real Numbers and Imaginary Numbers
- Different Ways to Represent Numbers
- Fractions
- Equivalent Fractions
- Mixed Numbers
- Reducing Fractions
- Comparing Fractions
- Least Common Denominator
- Addition and Subtraction of Fractions
- Multiplication of Fractions
- Equivalent Fractions and Multiplication by 1
- Multiplication by Clever Form of 1
- Multiplicative Inverses
- Division of Fractions
- Multiplication and Division with Mixed Numbers
- Decimals
- Converting Fractions into Decimals
- Converting Decimals into Fractions
- Comparing Decimals
- Adding and Subtracting Decimals
- Multiplication and Division by Powers of 10
- Multiplying Decimals
- Dividing Decimals
- Infinite Decimals
- Percents
- Portion of the Whole
**Things to Do with Real Numbers**- Addition and Subtraction of Real Numbers
- Properties of Addition
- Subtraction
- Multiplication
- Division
**Long Division Remainder**- Exponents and Powers - Whole Numbers
- Properties of Exponents
- Prime Factorization
- Order of Operations
- Even and Odd Numbers
- Infinity
- Sequences
- is Irrational
- Counting Rational Numbers
- Counting Real Numbers?
- Counting Irrational Numbers
- In the Real World
- Decimals in Use
- How to Solve a Math Problem
- I Like Abstract Things: Summary

Here's a refresher on long division, by way of example. We're hoping monkey see, monkey do. Not that you in any way resemble a monkey. Well, maybe a little around the eyes.

Sample: What is 250 divided by 4?

We need some words to help us refer to different parts of the division problem. If you've read the sections leading up to this one, they're pretty well drilled into your brain by now, but if not, here you go:

• The **dividend,** *p*, is the thing being divided up. Think of it this way - the word "dividend" ends with "end," and your end is divided up into two parts.

• The **divisor,** *q*, is the thing that performs the dividing. Definitely the alpha male in this relationship.

• The **quotient** is the answer. All hail the quotient.

Another useful word is **multiple. **A "multiple of 4" is any number that is evenly divisible by 4. 4, 8, 12, 16, are multiples of 4. We have to mention here that 396 is also a multiple of 4. He asked us to, and we owed him a favor.

To do the division problem, we're going to work our way across the dividend from left to right, and see how many times the divisor "fits" into each part of it.

First, consider just the first digit of the dividend. Above that digit, we'll write the number of times the divisor fits into that digit:

4 doesn't fit into 2 at all (not without a healthy dose of elbow grease), since 4 is bigger than 2. So we write a 0 in that space:

We then subtract the multiple of 4 that fits into 2 - in this case, 0:

We address the next digit of the dividend by "carrying it down." Lift with your legs, not with your back.

Now, we write how many times 4 fits into 25 in the space above the 5 in the dividend. Since 24 (4 x 6) is the largest multiple of 4 that fits into 25, we write 6 in that space:

Then we subtract the multiple of 4 that fits into 25:

Now we deal with the next digit of the dividend by "carrying it down":

Since 4 fits into 10 twice, we write 2 in the next space of the quotient and then subtract 8 (4 x 2):

While it appears we're out of digits in the dividend, we're not. Looks like we had an extra emergency supply in the basement. We can stick a decimal point onto the end and as many zeros as we need to the right of that. Remember to write the decimal point in the quotient, also. Then we can "carry down" any extra zeros:

We see 4 fits into 20 an even 5 times, so we can write the appropriate number in the appropriate place:

We stop when the subtraction results in a zero. The quotient is our "final answer," Meredith.

250 ÷ 4 = 62.5

We can check our answer by making sure that the quotient multiplied by the divisor equals the dividend: 62.5 x 4 = 250. Since this equation is correct, we know we got the right answer! *And* we're having a good hair day! Will wonders never cease?