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 TOPICS This page:   division    Search   Dr. Math See also the Dr. Math FAQ:   divisibility rules and   order of operations Internet Library:   division ELEMENTARY Arithmetic    addition    subtraction    multiplication    division    fractions/decimals Definitions Geometry    2-dimensional      circles      triangles/polygons    3D and higher      polyhedra Golden Ratio/ Fibonacci Sequence History/Biography Measurement    calendars/      dates/time    temperature    terms/units Number Sense/ About Numbers    infinity    large numbers    place value    prime numbers    square roots Projects Puzzles Word Problems Browse Elementary Division Stars indicate particularly interesting answers or good places to begin browsing. Selected answers to common questions:     Dividing fractions.     Flashcards/worksheets on the Web.     Long division.     Order of operations.     Number sentences. Calculating Percentage Markup Versus Profit [01/23/2004] In order to figure a profit of 10% I would normally take my cost and then multiply by 1.1 to find the selling price. My employer tells me that in order to find a 10% profit I should divide my cost by 0.9, but I don't understand how this is 10%. Can you please explain? Cancelling Fractions [06/03/2003] I am reading a book on algebra. The author states that cancelling is division too and then shows the following without any explanation of how it's done... Casting Out Nines to Check Arithmetic [08/26/1999] Can you explain how to use the 'casting out 9's' technique in a way that a 6th grader can understand? Comments on Dividing Fractions [03/15/2007] A question on how to divide fractions leads into comments on how division and subtraction can be thought of as multiplication and addition of an "inverted" number. Commutative Property and Division [02/21/2002] I am trying to prove that the commutative property following certain rules will work in all circumstances for division... Compatible Number Estimating [01/31/2002] My homework is on compatible numbers to estimate quotients - for example, 1,625 divided by 38. Compatible Number Method for Estimating [09/10/2001] We are supposed to estimate using compatible numbers. How does one estimate something like 574/8? Confusion over Interpretation of PEMDAS [03/24/2005] Students take PEMDAS letter by letter, tending to do all multiplication before any division, rather than working from left to right. Here's a suggestion on how to help avoid that confusion. Converting Bits to Megabytes [02/12/2001] The human brain will store 100 trillion bits in its lifetime. How many million megabytes can your brain store? Counting Days of the Week [02/02/1999] If today is Thursday, what day would it be 120 days from now? Deciding How to Express the Answer to a Division Problem [07/22/2006] When dividing something like 7 by 2, is it best to express the answer as 3 1/2, 3.5, or 3 remainder 1? How do I decide which form to use? Definition of Quotient [11/13/2008] If I divide 15 by 2, I always thought that the quotient was 7 and the remainder was 1. But I've seen that the quotient can also be 15/2. How can quotient have different meanings? Definition of Vinculum [10/21/2004] Is the bar placed over the set of repeated digits in a repeating decimal called a vinculum? I've heard that but I can't confirm it. Distributing Division [11/23/2003] I have a book that says division distributes over addition. Isn't it multiplication that distributes? Dividing a Large Number by a Small Number [3/25/1996] How do you divide 7557 by 8? Dividing and Rounding [08/23/2001] I have to answer a division problem and then round the quotient to the nearest hundredth... Dividing a Small Number by a Larger Number [2/6/1996] What is 7 divided by 22, and what is 2 + 2? Dividing by Powers of 10 [09/12/1998] Can you explain how to move the decimal place when you divide by powers of 10? Dividing by Zero [05/18/2001] I cannot comprehend that a human being is not able to divide a number by zero... Dividing Decimal Numbers [7/26/1996] How do I divide 4.58 into 46.63? Dividing Decimals with a Remainder [03/30/2001] What should I do when the directions say to divide and I get a remainder, or if they say round to the hundredths place and there is a remainder? Dividing Fractions [03/16/1999] Why can't we divide fractions directly? Why do we have to do it by multiplying? Dividing Fractions [3/18/1995] My class would like an explanation on why you invert and multiply when dividing fractions. Dividing Into or Dividing By? Dividends and Decimal Zeros [01/29/2013] A student struggles to understand the equivalence of 3/5 and 0.6: three clearly goes into five at least one time; and extending the five into fifty only makes matters worse. Emphasizing the importance of keeping the dividend and divisor in the right order, Doctor Peterson clarifies, first explaining fractions with a sharing scenario, then walking through an example. Dividing Two Decimals [8/30/1995] I don't understand dividing one decimal number by another decimal number. Dividing Two-Digit Numbers [03/01/2002] How do you divide two-digit numbers? Divisibility Algorithm [11/26/2001] Is there a trick for figuring out multiples of seven? Divisibility by 9 [03/22/2002] Why is an integer that is rearranged and then subtracted from itself always divisible by nine? Divisibility of Nine-Digit Numbers [03/08/1998] Find a nine-digit number such that the first digit is divisible by one, the first two digits are divisible by 2, the first three digits are divisible by 3,..., the whole nine-digit number is divisible by nine. Divisibility Rules [4/10/1996] What are some divisibility rules beyond the number 11? Divisibility Rules, 1-10 [9/11/1996] Please tell me the divisibility rules for numbers one through ten. Divisible... [8/27/1996] Which of these numbers are divisible by {5, 8, 9}... ? Division as Repeated Subtraction [03/06/1998] How can you divide one integer by another using only addition and subtraction? Division by Estimation [11/4/1996] Estimate the quotient when 716 is divided by 12. Division by Zero [8/27/1996] What is the value of a number divided by zero? Division of 28 by 13 [9/12/1996] Can you divide seven into twenty-eight thirteen times? Division Symbols [10/23/1998] What is the name of the symbol used in long division problems? What about other division symbols? Division with Roman Numerals [03/02/2004] I'm having real problems trying to divide using a non place system, like with Roman numerals. The concept of using letters rather than numbers is confusing me. Can you please give me an example of a division calculation? Does Divisibility by 4 always work? [6/17/1996] One hundred is divisible by 4 but I don't how 4/00 gets a quotient of 25. Dollarwise Division [02/20/2013] What could it mean to divide dollars into dollars? Doctor Peterson provides examples of contexts where it makes sense to see units in a divisor, then introduces dimensional analysis. Page: []

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