Beginning Division: Understanding the Basics

After you've mastered basic addition, subtraction and multiplication, it's time to face division. Here are some practice problems and an explanation of how to solve long division problems without the aid of a calculator.

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Learning Division

The Basics

You may be learning both mental division and long division. Mental division consists of simple math problems that can be solved in your head after you've memorized some key math facts. Also, the multiplication tables are the reverse of these fundamental division problems, so you can master them simultaneously.

You will use long division to solve division problems with larger numbers. These will not be the math facts you practice with flashcards. These problems will likely be too complex for you to solve in your head. In fact, you can expect problems that include up to 3-digit numbers as well as remainders.

Division Math Vocabulary

Dividend The dividend is the first number in a division equation. So in the problem 12 ÷ 4, the dividend is 12. In long division, this is the number that goes inside the division bracket.
Divisor The divisor is the second number in the division problem. In the previous example, the divisor is 4. To remember this, try repeating this tongue twister five times fast, 'the dividend is divided by the divisor'. In long division, this number is placed outside of the division bracket.
Quotient The quotient is the answer to a division problem. In the example above, 3 is the quotient, because 12 ÷ 4 = 3.

Long Division Steps

The first step is learning how to format long division problems. Let's say you have the problem 650 ÷ 2. In this case, 650 is the dividend and two is the divisor. Place the dividend inside the long division bracket, and place the divisor on the outside. You will be writing your answers on top of the long division bracket, above the dividend.

Here are the steps for completing long division problems: divide, multiply, subtract and bring down. Using the problem 650 ÷ 2, being by dividing two into six. Above the six in 650, you'll write the number three because two goes into six three times. Next, you'll multiply two (the divisor) times three (the first number in your quotient), and write 'six' underneath the 650, directly below the number six.

Repeat these steps with the other digits (the five and the zero from 650). For the five, ask yourself how many times two goes into five, then write that number above the 650. Because two goes into five two times, write two above the five in 650. Then multiply two times two, and write 'four' underneath the 'five' from 650. Subtract four from five to find the remainder, which is this case is one.

Now, bring down the zero, and repeat the steps. Your final answer should be 325.

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