# Fractions

 Categories : Fractions Which has the largest value?a) 1/5 +1/5+ 1/5b) 3/5*2/5 – 4/5*1/5c) (½)^3 + (1/2)^2 + (1/2)^1d) ½ +1/3 +1/6+1/8e) 1/9 * (1/3+9/27+9/12)AnswerTo find the answer to the above question in the shortest time require remembering just two rules:a)    For Fraction a/b where a>b, then a/b is greater than b/ab)    Finding LCM is the easiest ways to simplify operation on fractionsNow let us try each answer choicesa)    1/5 +1/5+ 1/5       3/5b)    3/5*2/5 – 4/5*1/5(6/25-4/25) = 2/25  Answer Choice B less than answer choice a, ELIMINATEc) (½)^3 + (1/2)^2 + (1/2)^11/8 + ¼ + ½= 7/8d)    ½ +1/3 +1/6+1/8LCM = 24= (12+8+4+3)/24 = 27/24 Answer Choice D greater than 1 and greater than A and CEliminate A & Ce)  1/9 * (1/3+9/27+9/12)1/9 * (9/27 + 13/12)Instead of adding the numbers in the bracket, group 1/3 and 9/12 and add it to get 13/12... Categories : Exponents, Fractions To answer questions that involve negative fractions and exponents, you have to know the following rules:1) Fraction with one in the numerator always obeys the following rule1/High Number < 1/Low NumberWhat confuses test takers is the definition of High Number and Low Number when it comes to negative denominator2) For negative numbers, remember this one rule-5 < -3- (Higher Positive Number) < - (Lower Positive Number)3) When it comes to negative fraction, the rule reverses-(1/High Number) > - (1/Low Number)4) Even power of negative fraction is positive and odd power of negative fraction is negative (-(a/b)) ^n is positive if n is even and negative is n is oddQ) If a = -1/4 & b = -1/3, which of the following is true?a) a^2 < b^3b) a^3 > b^2c) a^4 > b^6d) a^3 < b^3e) a^2 < b^4SolutionOnce you know the four rules, it becomes easier to eliminate answer choices. The question asks us to find the cube and square of two negative fractions a and b... Categories : Data Sufficiency, Fractions, Problem Solving Have you wondered how writers can make a seemingly simple GMAT topic like fractions into time-consuming calculations. One strategy that GMAT test takers must adopt to simplify the calculations. For exampleDividing by 5 is the same as multiplying by 2/10. For example:• 840/5 = ?• 840/5 = 840*(2/10) = 84*2 = 168Multiplying or dividing by 10’s and 2’s is generally easier than using 5’s. 90% of the time, fractions will be easier to perform arithmetic. Decimals are sometimes more useful when comparing numbers relative to one another, such as in a number line, but these questions are the exception. Even if given a decimal (or percent) looks easy, quickly convert to a fraction. Some common ones to memorize:• 1/9 = 0.111 repeating• 1/8 = 0.125• 1/7 = ~0.14• 1/6 = 0.166 repeating• 1/5 = 0.20• 1/4 = 0.25• 1/3 = 0.333 repeating• 1/2 = 0.5 repeatingNote: Multiples of these, such as 3/8 (0.375) are also important to remember, but can easily be derived by multiplying the original fraction (1/8 * 3 = 3/8 = 0.125 * 3 = 0.375)Denominators are super important. A denominator of a reduced fraction with a multiple of 7 will not have a finite... Categories : Number Properties, Equations, Fractions If Y < 0 and -1 < -1 + X/Y < 0, which must be true? 1. X < 0 2. Y/X>1 3. Y^2-X^2 > 0 A. I only B. II only C. I and II only D. II and III only E. I, II, and III Answer If X is negative, and we already know that Y is negative, than X/Y would have to be positive (a negative divided by a negative is always positive). This means that for all values in which Y is smaller than X, X/Y would be between 0 and 1. More importantly, X must be negative, because if it were positive, the fraction X/Y would be negative. Statement I must be true. Statement II claims that Y/X>1. We already know that both X and Y are negative. We also know that Y has a larger absolute value. Statement II must also be true. On statement III, since we're talking about numbers squared, we can forget about the signs. We only need to figure out which of the two variables is greater. Statement III is true as well. Correct Answer - Choice E Categories : Fractions Exactly 5/6 of the cows on a certain farm have cow bells. If exactly half of the cows with bells arebrown, what is the minimum possible number of cows on the ranch?A. 6B. 8C. 12D. 18E. 24Answer: The trick to this question is that the number of cows cannot be fractional; it must be an integer. The number of brown cows is: (1/2) × (5/6) × the number of cows. 12 is the smallest positive integer that yields another integer when multiplied by 5/12, so it is the minimum possible number of cows.Correct Answer: Choice C

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