Furthermore, the Divisor in 506 divided by 9 is 9. As you can see, it does not matter if we rounded in the previous step because the Decimal part is ignored. The above problem can be written as 306 Г· 6 = ? or ? Г— 6 = 306.506 / 9 56.22 Step 2) Next we take the Whole part of the answer in Step 1 and multiply it by the Divisor. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 2 / 3 is 3 / 2) of the second fraction.Next, multiply the two numerators.How did we solve the problem above When we divide two fractions, such as 1/9 2/3, we flip the second fraction and then we simply multiply the numerators with.It is sometimes helpful to think of a division problem as a multiplication problem. вЂў1 9 Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction.

Now, because 6 Г— 1 = 6, 6 is taken away from 6 leaving 0 and completing the division.Lesson 1: Introducing the Concept of DivisionAs with addition, subtraction, and multiplication, students practice strategies and algorithms that allow them to perform operations beyond basic facts. The process is repeated by asking, 'What number times 6 is less than or equal to 6?' Since 1 times 6 is exactly 6, a 1 is written above the 6 in the ones place. Because the 3 is in the hundreds place, begin by asking, 'What number times 6 is less than or equal to 300?' Since 5 tens times 6 is exactly 300, a 5 can be written above the 0 in the tens place.Since 5 tens = 50, and 50 Г— 6 = 300, we can take 300 away from 306 leaving 6. The quotient will go on top. Understanding this concept will significantly help students learn the long division algorithm.Begin the long division algorithm by writing the dividend inside the division symbol and the divisor outside it, to the left. In other words, when looking at 306 Г· 6, we are trying to find what number multiplied by 6 will give us 306.

Say: Another way to write 54 Г· 9 is by drawing the long division symbol, placing 54 'inside' it, and 9 to the left. Introduce students to the vocabulary dividend, divisor, and quotient prior to the lesson.54 Г· 9 is asking: if you have 54 items and divide them into groups with 9 items in each group, how many groups would you have? The 54 represents the total number of items you begin with.The 9 represents how many items are in each group.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. But no matter the grade, remind students that there are many ways to think about division, just like there are many ways to think about multiplication, and this algorithm is one tool to help solve math problems.Materials: Base-ten blocks that all students can see (for example, with an overhead projector) base-ten blocks that students can usePreparation: Be sure to provide at least one set of base-ten blocks for each pair of students.Prerequisite Skills and Concepts: Students should know their basic division facts and have used or seen the use of base ten blocks.

What does 68 represent in 68 Г· 4?68 Г· 4 is asking: if you have 68 items and divide them into groups with 4 items in each group, how many groups would you have? 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. Ask: Let's try another problem now. The quotient, or number of groups, is written above the 54:

Say: When completing the long division expression '68 divided by 4,' remember that 68 is 6 tens and 8 ones. 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. Ask: If we want to write 68 Г· 4 the same way we wrote the standard long division express '54 divided by 9,' what number would go where 54 is and what number would replace 9?68 would go in place of 54 and 4 in place of 9. Compare strategies, and share that one common strategy for performing more complicated division with multi-digit numbers is using the standard algorithm.

Say: Since 7 groups of 4 ones can be made, we write 7 above the ones place in 68. 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. Ask: If we combine the 20 ones with the 8 ones, how many ones will we have? Next, combine the 20 ones with the 8 ones. Show 2 tens being regrouped as 20 ones so that the entire class can see. Say: Since you cannot make additional groups containing four tens, you will need to regroup the remaining 2 for 20 ones.

Remember to always have the students check their work using their base-ten blocks.Lesson 2: Developing the Concept of DivisionAfter using manipulatives to introduce the division algorithm for multi-digit numbers, it's time to develop the concept more fully. Have the students use their base-ten blocks to determine the place value for the quotient. Continue this activity using slightly larger numbers. Then have them count the total number of items to see if there are indeed 68. Have students individually or in pairs make 17 groups with 4 items in each group. If we make 17 groups with 4 items in each group, we should have a total of 68 items.

Since we are dividing by 6, we need to make groups containing 6 hundreds. Ask: Let's begin with the hundreds. Say: Use your base-ten blocks to represent 276.

Ask: Since we are working with tens now, how many groups of 6 tens can we make from 27 tens? Be sure to use your base ten blocks.Notice that there are 4 groups of 6 tens with 3 tens left over. If we combine the 20 tens with 7 tens, we get 27 tens. Ask: If we regroup the 2 hundreds for tens, how many tens would we get? If we include the 7 tens, how many tens would that be altogether?2 hundreds is equivalent to 20 tens. When you cannot make groups from the current place, you will need to regroup and make groups from the next place.

Ask: How many tens and ones are left over when we take away the 4 groups of 6 tens? Since we have made four groups, each with 6 tens, we can take 240 away from 276. Say: Remember that we began with 276 and want to divide it by 6. Encourage students to use their base-ten blocks to illustrate the value. Ask: If one group of 6 tens is 60, what is 4 groups of 6 tens worth?240.

In front of the students, regroup 3 tens as 30 ones. Ask: Since we cannot make any more groups of 6 tens with the remaining base-ten blocks, we can regroup the 3 tens for how many ones?30 ones. This helps students see the connection between using the base-ten blocks and the standard algorithm. Ask: What is 276 вЂ“ 240? What is the value of the base-ten blocks that you have left over? What do you notice about the two values?36.

Be sure to use numbers that do not use remainders at first. Continue this activity using different numbers. Ask: Where do you think we will write the 6 that represents the 6 groups?The 6 is written above the ones place in 276.

Your task is to take the needed time and effort to encourage students to learn this process. Remember, this may be the first time many of your students have ever encountered the concept. This can be a trying time in many students' mathematical development!As a teacher, do not be discouraged by slow progress. Do not be in a rush for students to put away their manipulatives when learning this difficult concept.

Additionally, connect division to other topics, such as multiplication, fractions, and equations, when they appear to reinforce the concept many times. If they're interested in basketball, for example, have them divide groups of players or basketballs.

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