Division which number goes first

We check our answer to division by multiplying the quotient by the divisor to determine if it equals the dividend. These two ideas are stated in the Division Properties of One. How much would each person get? Division by zero is said to be undefined. Another way to explain why division by zero is undefined is to remember that division is really repeated subtraction.

Then check by multiplying:. This process is called long division. We would repeat the process until there are no more digits in the dividend to bring down. In this problem, there are no more digits to bring down, so the division is finished. Check by multiplying the quotient times the divisor to get the dividend. It equals the dividend, so our answer is correct. The Standard Algorithm for Division As students master their basic division facts, the need will arise for students to learn how to divide larger dividends.

Lesson 1: Introducing the Concept of Division As with addition, subtraction, and multiplication, students practice strategies and algorithms that allow them to perform operations beyond basic facts. Materials: Base-ten blocks that all students can see for example, with an overhead projector ; base-ten blocks that students can use Preparation: Be sure to provide at least one set of base-ten blocks for each pair of students.

The 54 represents the total number of items you begin with. The 9 represents how many items are in each group. The quotient is 6. It is the quotient, but more importantly, the 6 represents the number of groups you will divide the 54 items into groups to have 9 items in each group. The quotient, or number of groups, is written above the Ask: Let's try another problem now.

The 68 represents the total number of items you begin with. The 4 represents how many items are in each group. Since this is not a basic division fact, it is unlikely that students will be able to find a correct quotient. If students do think they know the quotient, have them share their thinking.

Compare strategies, and share that one common strategy for performing more complicated division with multi-digit numbers is using the standard algorithm. Say: When we are dividing numbers too large for us to immediately know the answer to, it is best to do the problem in several small parts.

Say: When completing the long division expression "68 divided by 4," remember that 68 is 6 tens and 8 ones. Show 6 tens so that the entire class can see them.

Ask: How many equal groups of 4 tens can you make? You can make 1 group that will contain 4 tens. Say: Since you can make only 1 group, you write a 1 over the tens place in Say: Since you cannot make additional groups containing four tens, you will need to regroup the remaining 2 for 20 ones.

Show 2 tens being regrouped as 20 ones so that the entire class can see. Next, combine the 20 ones with the 8 ones. Ask: If we combine the 20 ones with the 8 ones, how many ones will we have? Ask: How many groups with 4 ones in each group can we make from the 28 ones? We can make 7 groups with 4 ones in each group. Say: Since 7 groups of 4 ones can be made, we write 7 above the ones place in Say: Since there are no ones remaining, our quotient is If we make 17 groups with 4 items in each group, we should have a total of 68 items.

Have students individually or in pairs make 17 groups with 4 items in each group. Then have them count the total number of items to see if there are indeed Continue this activity using slightly larger numbers. Have the students use their base-ten blocks to determine the place value for the quotient. Remember to always have the students check their work using their base-ten blocks. Lesson 2: Developing the Concept of Division After using manipulatives to introduce the division algorithm for multi-digit numbers, it's time to develop the concept more fully.

Six divided by two gives you a quotient of three. You may also see it written in this format When you move into more advanced math, you may even write out division problems that look like fractions. As you work with decimals , you will quickly discover that 1 divided by 4 is 0.

Division is even important to percentages. The decimal 0. All of the values are identical, but you use them in different ways. That example shows you that there are many ways to say the same thing in math. That is 0 sweets shared equally among 2 children - each child gets 0 sweets. When you divide a number by 0 you are not dividing at all this is quite a problem in mathematics. You have 2 sweets but no children to divide them among. You cannot divide by 0. When you divide by 1, the answer is the same as the number you were dividing.

Two sweets divided by one child. Any number divided by the same number is 1. Twenty sweets divided by twenty children - each child gets one sweet. Numbers must be divided in the correct order. Ten sweets divided by two children is very different to 2 sweets divided by 10 children.

One sweet divided by two children. See our page Fractions for more information. Just as multiplication is a quick way of calculating multiple additions, division is a quick way of performing multiple subtractions. If John has 10 gallons of fuel in his car and uses 2 gallons a day how many days before he runs out? We can work this problem out by doing a series of subtractions, or by counting backwards in steps of 2. A quicker way of performing this calculation would be to divide 10 by 2.

That is, how many times does 2 go into 10, or how many lots of two gallons are there in ten gallons? The multiplication table see multiplication can be used to help us find the answer to simple division calculations. To do this, using the multiplication table locate the column for 2 the red shaded heading. Work down the column until you find the number you are looking for, Move across the row to the left to see the answer the red shaded heading 5.