# Long Division Method Pdf Free

Long division is a skill which requires a lot of practice with pencil and paper to master. Our grade 4 long division worksheets cover long division with one digit divisors and up to 4 digit dividends.

## Long Division Method Pdf Free

Let students get comfortable with the formula and work on smaller problems. As they develop confidence and begin to understand how to do long division, start presenting them with problems that have a three-digit dividend, and then problems that have a two-digit divisor.

This method uses a grid to present the process of division as an area problem: for example, 1484 would be divided into a grid that is 4 units high, 148 square units in area, and an unknown number of units wide.

Prodigy is a fun and engaging resource for in-class or at-home long division practice. Students explore a world filled with adventure, where success depends on correctly answering math questions.

Bring math to life with a hands-on long division puzzle. Cut out squares of colorful paper with all the numbers that students need to solve a long division problem from start to finish. Use masking tape to make division lines on the floor, and give students the numbered cards.

Boost literacy and math learning at the same time with fun books covering tricky math concepts. Use them to explain division and remainders to students in a fun and engaging way, and even to cover more basic concepts before they start learning how to do long division.

Worksheets are a tried-and-true staple of math class. Lucky for you, there are lots of websites that will do the work for you and generate a custom worksheet that will give your students the change to practice how to do long division. Here are a few of our favourites:

These task cards give students the opportunity to practice the box method/area model for long division in a variety of different ways. Students will calculate quotients, solve division problems, figure out missing dividends and divisors, think about how to efficiently solve an equation using the box method, and more. See the Box Method Task Cards HERE or the Big Bundle of Long Division Task Cards HERE.

The Long Division Station is a self-paced, student-centered math station for long division. Students gradually learn a variety of strategies for long division, the box method being one of them. One of the greatest advantages to this Math Station is that is allows you to target every student and their unique abilities so that everyone is appropriately challenged. See The Long Division Station HERE.

That is wonderful! My son uses the box method for multiplication , but becomes visually frustrated and angry when he was figuring out long division today. I have never seen this method before in my life. Totally makes sense. Thank you

Long division worksheets help students in practicing problems with 3-digit and 4-digit numbers by using the basic division method that the student learned in lower grades. Students might find it difficult at the beginning but with thorough practice, they can learn the concept quickly.

The benefits of long division worksheets are that the worksheets not only provide ample questions to practice but also provide a detailed answer key that helps students to compare the solutions at every step. Through these math worksheets, students learn how to solve complex word problems, multiply the quotient by the divisor and add the remainder to find it equal to the dividend, and using subtraction in a few complex questions.

Welcome to the division worksheets page at Math-Drills.com! Please give us your undivided attention while we introduce this page. Our worksheets for division help you to teach students the very important concept of division. If students have a good recall of multiplication facts, the division facts should be a breeze to teach. If you want your students to experience success in learning division, please make sure they know their multiplication facts to 81, how to multiply by 0 and how to multiply by 10. If they don't know these things, this is going to take a lot longer.

On this page you will find many Division Worksheets including division facts and long division with and without remainders. We start off with some division facts which as you know are just the multiplication facts expressed in a different way. The main difference is that you can't divide by 0 and get a real number. If you really want your students to impress, say at their dinner table when their parents ask them what they learned today, you can teach them that division by zero is undefined.

The rest of the page is devoted to long division which for some reason is disliked among some members of the population. Long division is most difficult when students don't know their multiplication facts, so make sure they know them first. Oh, we already said that. What about a long division algorithm... maybe the one you or your parents or your grandparents learned? We adamantly say, yes! The reason that you and your ancestors used it is because it is an efficient and beautiful algorithm that will allow you to solve some of the most difficult division problems that even base ten blocks couldn't touch. It works equally well for decimals and whole numbers. Long division really isn't that hard.

Have you ever thought that you could help a student understand things better and get a more precise answer while still using remainders? It's quite easy really. Remainders are usually given out of context, including on the answer keys below. A remainder is really a numerator in a fractional quotient. For example 19 3 is 6 with a remainder of 1 which is more precisely 6 1/3. Using fractional quotients means your students will always find the exact answer to all long division questions, and in many cases the answer will actually be more precise (e.g. compare 6 1/3 with 6.3333....).

We thought it might be helpful to include some long division worksheets with the steps shown. The answer keys for these division worksheets use the standard algorithm that you might learn if you went to an English speaking school. Learning this algorithm by itself is sometimes not enough as it may not lead to a good conceptual understanding. One tool that helps students learn the standard algorithm and develop an understanding of division is a set of base ten blocks. By teaching students division with base ten blocks first then progressing to the standard algorithm, students will gain a conceptual understanding plus have the use of an efficient algorithm for long division. Students who have both of these things will naturally experience more success in their future mathematical studies.

Some students find it difficult to get everything lined up when completing a long division algorithm, so these worksheets include a grid and wider spacing of the digits to help students get things in the right place. The answer keys include the typical steps that students would record while completing each problem; however, slight variations in implementation may occur. For example, some people don't bother with the subtraction signs,some might show steps subtracting zero, etc.

This page contains extensive division word problems replete with engaging scenarios that involve two-digit and three-digit dividends and single digit divisors; three-digit dividends and two-digit divisors; and advanced division worksheets (four-digit and five-digit dividends). Thumb through some of these worksheets for free!

Synthetic Division Synthetic division is another way to divide a polynomial by the binomial x - c , where c is a constant. Step 1: Set up the synthetic division. An easy way to do this is to first set it up as if you are doing long division and then set up your synthetic division. If you need a review on setting up a long division problem, feel free to go to Tutorial 36: Long Division. The divisor (what you are dividing by) goes on the outside of the box. The dividend (what you are dividing into) goes on the inside of the box. When you write out the dividend make sure that you write it in descending powers and you insert 0's for any missing terms. For example, if you had the problem , the polynomial , starts out with degree 4, then the next highest degree is 1. It is missing degrees 3 and 2. So if we were to put it inside a division box we would write it like this: . This will allow you to line up like terms when you go through the problem. When you set this up using synthetic division write c for the divisor x - c. Then write the coefficients of the dividend to the right, across the top. Include any 0's that were inserted in for missing terms. Step 2: Bring down the leading coefficient to the bottom row. Step 3: Multiply c by the value just written on the bottom row. Place this value right beneath the next coefficient in the dividend: Step 4: Add the column created in step 3. Write the sum in the bottom row: Step 5: Repeat until done. Step 6: Write out the answer. The numbers in the last row make up your coefficients of the quotient as well as the remainder. The final value on the right is the remainder. Working right to left, the next number is your constant, the next is the coefficient for x, the next is the coefficient for x squared, etc... The degree of the quotient is one less than the degree of the dividend. For example, if the degree of the dividend is 4, then the degree of the quotient is 3. Example 1: Divide using synthetic division: . Step 1: Set up the synthetic division. Long division would look like this: Synthetic division would look like this: Step 2: Bring down the leading coefficient to the bottom row. *Bring down the 2 Step 3: Multiply c by the value just written on the bottom row. *(-1)(2) = -2 *Place -2 in next column Step 4: Add the column created in step 3. *-3 + (-2) = -5 Step 5: Repeat until done. Step 6: Write out the answer. The numbers in the last row make up your coefficients of the quotient as well as the remainder. The final value on the right is the remainder. Working right to left, the next number is your constant, the next is the coefficient for x, the next is the coefficient for x squared, etc... Example 2: Divide using synthetic division: Step 1: Set up the synthetic division. Long division would look like this: Synthetic division would look like this: Step 2: Bring down the leading coefficient to the bottom row. *Bring down the 1 Step 3: Multiply c by the value just written on the bottom row. *(1)(1) =1 *Place 1 in next column Step 4: Add the column created in step 3. *0 + 1 = 1 Step 5: Repeat until done. Step 6: Write out the answer. The numbers in the last row make up your coefficients of the quotient as well as the remainder. The final value on the right is the remainder. Working right to left, the next number is your constant, the next is the coefficient for x, the next is the coefficient for x squared, etc... Remainder Theorem If the polynomial f(x) is divided by x - c, then the reminder is f(c). This means that we can apply synthetic division and the last number on the right, which is the remainder, will tell us what the functional value of c is. Example 3: Given , use the Remainder Theorem to find f(-2). The steps to the synthetic division are the same as described above. What is different is what are final answer is going to be. This time, we are looking for the functional value, so our answer will not be a quotient, but only the reminder. Using synthetic division to find the remainder we get: Again, our answer this time is not a quotient, but the remainder. Final answer: f(-2) = -27 Factor Theorem If f(x) is a polynomial AND 1) f(c) = 0, then x - c is a factor of f(x). 2) x - c is a factor of f(x), then f(c) = 0. Keep in mind that the division algorithm is dividend = divisor(quotient)+ reminder So if the reminder is zero, you can use this to help you factor a polynomial. If x - c is a factor, you can rewrite the original polynomial as (x - c) (quotient). You can use synthetic division to help you with this type of problem. The Remainder Theorem states that f(c) = the remainder. So if the remainder comes out to be 0 when you apply synthetic division, then x - c is a factor of f(x). Example 4: Use synthetic division to divide by x - 2. Use the result to find all zeros of f. The steps to the synthetic division are the same as described above. What is different is what are final answer is going to be. This time, we are looking for all of the zeros of f. We will start by dividing using synthetic division and then rewrite f(x) as (x - 2)(quotient). Using synthetic division to find the quotient we get: Note how the remainder is 0. This means that (x - 2) is a factor of . Rewriting f(x) as (x - 2)(quotient) we get: We need to finish this problem by setting this equal to zero and solving it: *Factor the trinomial *Set 1st factor = 0 *Set 2nd factor = 0 *Set 3rd factor = 0 The zeros of this function are x = 2, -3, and -1. Example 5: Solve the equation given that 3/2 is a zero (or root) of . The steps to the synthetic division are the same as described above. What is different is what are final answer is going to be. This time, we are looking for all of the zeros of f. We will start by dividing using synthetic division and then rewrite f(x) as (x - 3/2)(quotient). Using synthetic division to find the quotient we get: Note how the remainder is 0. This means that (x - 3/2) is a factor of . Rewriting f(x) as (x - 3/2)(quotient) we get: We need to finish this problem by setting this equal to zero and solving it: *Factor the difference of squares *Note the 1st factor is 2, which is a constant, which can never = 0 *Set 2nd factor = 0 *Set 3rd factor = 0 *Set 4th factor = 0 The solution or zeros of this function are x = 3/2, -1, and 1. Practice Problems