Division 

2021年6月28日
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Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers.The other operations are addition, subtraction, and multiplication (which can be viewed as the inverse of division). The Division, an autonomous unit of tactical agents, is activated. Leading seemingly ordinary lives among us, these agents are trained to operate independently in order to save society. When society falls, we rise. TAKE BACK NEW YORK. Civil Rights Division  : Office of the Assistant Attorney General: Washington, DC 20530      : May 29, 2009: The Honorable Thurbert E. Baker Attorney General 40 Capitol Square, S.W. Atlanta, Georgia. Dear Attorney General Baker.Division Symbol
The division is a method of distributing a group of things into equal parts. It is one of the four basic operations of arithmetic, which gives a fair result of sharing. The division is an operation inverse of multiplication. If 3 groups of 4 make 12 in multiplication; 12 divided into 3 equal groups give 4 in each group in division.
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.
Most Popular Division Worksheets this WeekDivision Facts Worksheets
Division facts worksheets including division tables, division facts and worksheets with individual division facts.
Manipulatives can help students ’get’ the concept of division. For example, students could regroup base ten blocks into units, then divide the units into piles. For example, 81 ÷ 9 would end up being 9 piles of 9 units.
Division is essentially asing the question, ’How many _____’s are in _____?’ For the question, 81 ÷ 9, the prompt would sound like, ’How many 9’s are in 81?’ This prompt will benefit students in later math studies when there are more complex concepts such as dividing decimals or fractions. ’How many thirds are in four?’ or even better, How many third cups are in four cups?’ If necessary, get out the measuring cups.Horizontal Division facts worksheets with focus numbersDivision facts worksheets with combinations of focus numbersLong Division Worksheets
Long division worksheets for practicing various long division strategies including questions with no remainders, remainders and decimal quotients.
Need an easier way to divide large numbers? Try this method using powers of ten. To successfully use this method, students need to be able to multiply by powers of ten and to subtract. Students subtract the dividend multiplied by decreasing powers of ten until they have zero or a remainder. Example: 1458 ÷ 54. Note 54 × 1 = 54, 54 × 10 = 540 (nothing greater is needed). 1458 - 540 - 540 = 378. Note that 540 was subtracted twice, so the number of times that 54 ’goes into’ 1458 so far is 20 times. Continuing, 378 - 54 - 54 - 54 - 54 - 54 - 54 - 54 = 0. Since 54 was subtracted seven times, the quotient increases by seven for a total of 27. In other words, 54 ’goes into’ 1458, 27 times.
We might also mention that this method can be even more sophisticated by using multiples of powers of ten. In the above example, using 54 × 5 = 270 would have helped to get to the quotient quicker.European Long division worksheets with no remainders
Criminal minded 2graffiti movies & documentaries. 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..).European long division worksheets with decimal quotientsLong Division with Remainders worksheets with the steps shown on the answer key
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.Long Division on a GridLong division with grid assistance and NO remainders worksheets
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.Long division with grid assistance and SOME remainders worksheetsDivisibility Rules
Worksheets for practicing divisibility rules including a variety of small and large numbers and focusing on various divisors.
Divisibility by 2, 5 and 10
A number is divisible by 2 if the final digit (the digit in the ones place) is even. Numbers ending in 0, 2, 4, 6, or 8 therefore are divisible by 2. A number is divisible by 5 if the final digit is a 0 or a 5. A number is divisible by 10 if the final digit is a 0.
Divisibility by 3, 6 and 9Long Division Calculator
A number is divisible by 3 if the sum of its digits is divisible by 3. For example, 285 is divisible by 3 because 2 + 8 + 5 = 15 is divisible by 3. A number is divisible by 6 if it is divisible by both 3 and 2 (see above rules). A number is divisible by 9 if the sum of its digits is divisible by 9. For examples, 285 is not divisible by 9 because 2 + 8 + 5 = 15 is not divisible by 9.
Divisibility by 4, 7 and 8
A number is divisible by 4 if the last two digits of the number are divisible by 4. For 7, there are a couple of strategies to use. Please see Divisibility Tricks for Learning Math for more information. A number is divisible by 8 if the last three digits are divisible by 8. This is the standard rule which can be a little sketchy for larger numbers, like who knows if 680 is divisible by 8? Because of this, we offer our Math-Drills.com solution which requires a little arithmetic, but can be accomplished quite easily with a little practice. As you know 8 is 2 to the third power, so we thought if you could divide the last three digits of a number by 2 three times, it would be divisible by 8. 680 ÷ 2 ÷ 2 ÷ 2 = 340 ÷ 2 ÷ 2 = 170 ÷ 2 = 85. We have a winner! 680 is indeed divisible by 8.Dividing in Other Base Number Systems
Dividing numbers in number systems other than decimal numbers including binary, quaternary, octal, duodecimal and hexadecimal numbers.U.S. Department of Justice
Civil Rights Division&nbspOffice of the Assistant Attorney GeneralWashington, DC 20530&nbsp&nbsp&nbspMay 29, 2009
The Honorable Thurbert E. Baker
Attorney General
40 Capitol Square, S.W.
Atlanta, Georgia 30334-1300

Dear Attorney General Baker:
This refers to the establishment of the voter verification program for voter registration application data, including citizenship status, and changes to the voter registration application for the State of Georgia, submitted to the Attorney General pursuant to Section 5 of the Voting Rights Act of 1965, 42 U.S.C. § 1973c. We received your response to our December 15, 2008 request for additional information on March 30, 2009; supplemental information was received on April 2, 2009.
We turn first to the verification program for voter registration application data contained in Submission 2008-5243. Changes to the voter registration process constitute a voting change under Section 5. Procedures for the Administration of Section 5 of the Voting Rights Act of 1965, 28 C.F.R. § 51.13(b); Morales v. Handel, Civil Action No. 1:08-CV-3172-JTC (N.D. Ga. Oct. 27, 2008). As such, the submitting authority has the burden of establishing that a proposed change does not have a retrogressive effect on the ability of minority voters to participate in the political process and to elect candidates of choice, nor a discriminatory purpose. Georgia v. United States, 411 U.S. 526 (1973); 28 C.F.R. § 51.52. The voting change at issue must be measured against the benchmark practice to determine whether the opportunities of minority voters to participate in the political process and elect candidates of their choice will be ’augmented, diminished, or not affected by the change affecting voting.’ Beer v. United States, 425 U.S. 130, 141 (1976).
We have carefully considered the information you have provided, as well as information from other interested parties. Under Section 5, the Attorney General must determine whether the submitting authority has met its burden of showing that the proposed change ’neither has the purpose nor will have the effect’ of denying or abridging the right to vote on account of race, color or membership in a language minority group. As discussed further below, I cannot conclude that the state has sustained its burden in this instance. Therefore, based on the information available to us, I must object to the voter verification program, on behalf of the Attorney General.
Under the benchmark system, all applicants swear or affirm, under penalty of law, on a voter registration application form that the information they are providing, including their citizenship status, is true. No further information is statutorily required. Under normal circumstances, registering to vote in Georgia is a single action, which can be accomplished at the applicant’s convenience. Challenges to an individual’s eligibility on any basis, including citizenship, happen infrequently under the benchmark system, by the state’s own admission. Under the benchmark system, the state has indicated that there is no program for automated verification of information contained on voter registration applications.
The proposed verification system seeks to match the information provided by the applicant with the information maintained by the state’s Department of Driver Services [DDS] and, in many cases, the federal Social Security Administration [SSA], and provides a list of those persons whose information does not match to local registrars for further inquiry. As an initial matter, we address the state’s claim that it adopted the submitted verification system as part of its program for implementation of the minimum requirements for elections for federal office contained in the Help America Vote Act of 2002, 42 U.S.C. § 15301 et seq. Specifically, the state has indicated that the verification program was adopted to implement the requirements of Section 303(a)(5) of HAVA, after the state lost a private lawsuit challenging the state’s previous full social security number requirement for voter registration.
A brief recap of the relevant HAVA requirements is in order. As part of the requirement that states create a computerized statewide voter registration database for elections for federal office, HAVA provides that, for a state that does not require a full social security number, it cannot accept or process an application for voter registration unless the applicant provides a driver license number or, where the applicant does not have such a number, the last four digits of the applicant’s social security number. In the absence of either number, HAVA requires a state to issue the applicant a unique identification number. 42 U.S.C. § 15483(a)(5)(A)(i) and (ii). Consistent with this requirement, HAVA next provides for the attempted verification of these types of numbers and accompanying identification information, such as name and date of birth, through the use of either the state driver license agency database or, as necessary, the SSA database. 42 U.S.C. § 15483(a)(5)(B). Finally, HAVA leaves it up to the state as to whether the information provided by an applicant is sufficient to meet HAVA’s requirements, in accordance with state law. 42 U.S.C. § 15483(a)(5)(A)(iii). Thus, these HAVA requirements are directed at identification, not eligibility. See Florida State Conf. of the NAACP v. Browning, 522 F.3d 1153, 1168 (11th Cir. 2008). HAVA does not speak to the question of whether a state should deem an applicant eligible or ineligible, whose information fails to match on some element contained in a state or federal database. Indeed, HAVA takes no position concerning verification of citizenship, neither requiring nor prohibiting state action to verify the citizenship of voter registration applicants. Likewise, HAVA explicitly grants the state discretion in how it implements its requirements, see, e.g., 42 U.S.C. §§ 15484-15485. Such discretion on the part of state officials is the touchstone for coverage under Section 5. Young v. Fordice, 520 U.S. 273 (1997).
We now proceed to discuss the substance of the state’s verification program. The results of the verification matching process described above are contained in two reports generated by the state for local registrars: the R1 and R2. The R1 report, which attempts to verify information other than citizenship, results from a data comparison that we agree with the state is required by HAVA; the issue is what the state in its discretion chooses to do with that information. The R2 report, which seeks to verify citizenship status, results from a data comparison that is discretionary on the state’s part. The state has informed us that it intends to utilize the information concerning non-matches set forth in these reports in the following way:
The R1 report lists non-matched registrants for the following criteria: first name, last name, date of birth, driver’s license number and last four digits of a social security number. A failure to match in any of those categories [on the R1], pursuant to the HAVA verification process, means that the applicant has not been verified as required by HAVA and they are not considered a registered voter at that point in time.
Failures to verify or match on the criteria of citizenship are listed on the R2 report. The failure to match on this criterion is treated in the same way failures to match on other criteria listed above.
In all instances, a failure to verify registration then triggers further inquiry by the county registrars to resolve any questions in order to verify the registration and move the applicant onto the registration list. Letter of March 24, 2009, at 20-21. Thus, ’non-matched registrants,’ who have submitted registration applications or changes to their existing registration, must take further steps to establish their voting eligibility. Under the state’s proposed procedures, pursuant to state law, local election officials can require these individuals also to appear at the county courthouse or office building, not at the voter’s convenience, but rather on a week day, during normal business hours and, pursuant to state law, with only three days notice. O.C.G.A. § 21-2-228.
Because the state implemented these changes in violation of Section 5, see Morales, supra, we have the actual results of the state’s verification process. As of March 13, 2009, a total of 199,606 individuals are flagged as a ’non-match based on any criteria’ on the R1 report. Since its inception, the R2 report has flagged 7,007 individuals as potential non-citizens. Under the state’s proposed procedures all of the individuals flagged would have to take further, inconvenient steps to be considered registered voters.
We have considered the accuracy of the state’s verification process. Our analysis shows that the state’s process does not produce accurate and reliable information and that thousands of citizens who are in fact eligible to vote under Georgia law have been flagged. As an example, recent deposition testimony by state employees in the Morales litigation indicates that an error as simple as transposition of one digit of a driver license number can lead to an erroneous notation of a non-match across all compared fields. In addition, the state’s response to the Department’s October 2008 inquiry concerning the state’s use of the SSA HAVV system indicates error-laden and possibly improper use of the system, thereby increasing the potential for unreliable results. The R2 report has flagged a large number of persons who have subsequently demonstrated that they are in fact citizens. Indeed, of the 7,007 individuals who have been flagged on the R2 report as potential non-citizens, more than half were in fact citizens. Perhaps the most telling statistic concerns the effect of the verification process on native-born citizens. Of those persons erroneously identified as non-citizens, 14.9 percent, more than one in seven, established eligibility with a birth certificate, showing

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