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 TOPICS This page:   fractions/percentages    Search   Dr. Math See also the Dr. Math FAQ:   fractions/decimals   percentages Internet Library:   fractions/decimals   percents T2T FAQ:   fraction help MIDDLE SCHOOL About Math Algebra    equations    factoring expressions    graphing equations Arithmetic    division    exponents    factorials    factoring numbers    fractions/percents    logarithms Definitions Geometry    2-dimensional      conic sections/        circles      triangles/polygons    3D and higher      polyhedra History/Biography Logic Measurement    calendars/      dates/time    temperature    terms/units Number Sense    factoring numbers    negative numbers    pi    prime numbers    square roots Probability Puzzles Ratio/Proportion Statistics Word Problems Browse Middle School Fractions & Percentages Stars indicate particularly interesting answers or good places to begin browsing. Newton's Method and Continued Fractions [10/06/1999] Can you clarify some points on Newton's method of finding square roots without a calculator, and on the continued fraction algorithm (CFA)? Non-terminating Decimal Representations of Fractions [11/10/1997] Why when you take a finite, limited quantity like one-third and turn it into a decimal do you get .333... on into infinity? Number of Places in Products of Decimals [09/19/2002] When you multiply decimals, why is there always the same number of decimal places in the answer as in the problem? Numbers Containing Whole Number, Decimal, and Fraction at Once [10/19/2004] If I have a number that contains a whole number, decimal, and fraction all in one, such as 3.366 2/3, how would I convert all of that to one fraction in lowest terms? Numbers in a Fraction [05/20/2001] Is a fraction one number or is it two numbers? Numerator, Denominator: Etymologies [03/25/2002] Why are the parts of a fraction called the numerator and the denominator? The Oneths Place [09/29/1998] In decimal numbers, why is there no oneths place? Ordering Fractions [01/17/2003] How do I order the fractions 2/3, 3/5, and 2/7? Ordering Improper Fractions [10/12/2002] How can I explain ordering improper fractions? Order of Discounts and Taxes [04/22/2002] Why doesn't it matter in determining the cost of an item whether you take the tax off before or after you take off the discount? Order of Operations and Fractions [02/22/2002] Given a+3 and b+5, is 105 / ab 7 or 175? Origin of the Term "Improper" Fraction [07/28/2006] Why are fractions with larger numerators than denominators called "improper"? Where did the terms "proper" and "improper" originate in relation to fractions? Percentage Error [10/24/2002] Please help me find the percentage error for the following numbers: 5.7 estimated findings, 5.8 actual findings. Percentage of Decrease [11/20/1997] If last year I collected 500 cans and this year I only collected 350 cans, what would be my percentage of decrease for this year? Percentage of Increase [07/23/1997] I need to figure out a percent increase: the figure in 1995 was 50,000 and the estimated figure for 2000 is 325,000. Percentage of Votes Cast [06/03/2003] If you have two percentages, say 25% and 50%, can you do a percent change between the two? Percentages as Comparisons [11/18/1998] If A is a certain percentage of B, how do A and B relate to each other? How does this describe percentages? Percentages as Fractions [8/25/1996] What is 57 percent of 93? Percentages from Data [4/12/1996] I have totaled the use of swear words in some newsgroups, by board and by sex. I want to figure out who's swearing more, men or women, percentage- wise. Percentages in Algebra [12/29/1995] What number increased by 30% = 260 ? I know the answer, but how did I get it? Percent Greater Than vs. Increased [11/22/2002] Is there a difference between the following statements? My profits are 200% greater than they were last year; My profits from last year have increased 200%. Percent Increase and "Increase by a Factor of ..." [08/01/2006] If we start with 1 apple today and tomorrow have 2 apples, then we have a 100 percent increase. But can't I also say there was an increase by a factor of 2? The Period of 61/97 [01/12/2001] How can I find the period of 61/97? Placement of the Negative Sign in a Negative Mixed Number [10/25/2004] When you have a negative improper fraction, can the negative sign be put anywhere in the fraction? For instance, is -1 3/5 the same as 1 -3/5 and 1 3/-5? Place Value and Similar Numbers [08/15/2003] How do you read these numbers? Is there a difference? 10.200, 10.00002 Price before Discount [6/3/1996] A calculator's price is discounted 20 percent. After adding 7 percent tax... Prime Factors in Unit Fractions [2/29/1996] Why does the denominator of a unit fraction have to have prime factors of 2 and/or 5 in order to terminate? Product of Terms of a Sequence [04/18/2003] Find the product of the first 99 terms of the sequence 1/2, 2/3, 3/4, 4/5, ... Profit and Percent Waste [6/13/1996] A fruit-seller buys 240 apples for \$60, but some are bad. Calculate the percent thrown away. Profit on Investment [4/16/1996] Ann, Bill, Cynthia, and Don invest \$2000, \$3000, \$8000, and \$7000 in a joint business venture... Pronunciation of Fractions [03/28/1997] How do you pronounce fractions with 32, 42... in the denominator...? Proof for Dividing Fractions [01/18/2002] Could you please send me a proof for dividing fractions? Proper and Improper Fractions, Mixed Numbers [8/19/1996] How do you turn a proper fraction into an improper fraction? Putting Fractions in Order [01/24/2001] I am trying to order fractions from least to greatest, but am having no luck. Putting Rational Numbers in Order [09/22/2002] I have to order 4/15, 6/17, and 3/16 from least to greatest, and I can't use a calculator. Rates and Fractions [1/23/1996] Find each rate as a fraction in simplest form: 1) 24 laps in 12 minutes, 2) 180 miles with 15 gallons... Rationalizing the Denominator [04/09/1997] Must all fractions have denominators that are rational numbers? Rationalizing the Denominator [05/03/1999] Why can't you have a square root in the denominator of a fraction? Rationalizing the Denominator [07/10/2003] 1 / ((sqrt)3 + (sqrt)5 + (sqrt)7) Ratios and Fractions: A Reconciliation [04/02/2013] Teachers disagree about whether a fraction can compare part to part. Doctor Peterson first distinguishes between ratios and fractions before reconciling them and warning against inflexible thinking. Page: []

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