the absolute value of -4.5 is 4.5. Step-by-step explanation: The absolute value of a number means the distance from 0. SO if you have -4.5, positive 4.5 is the distance from 0.-4.5+4.5= 0. Hence that is the reason the absolute value of -4.5 is 4.5. Hope this helps!2.14 Absolute Value Equations; 2.15 Absolute Value Inequalities; 3. Graphing and Functions. 3.1 Graphing; 3.2 Lines; 3.3 Circles; ... Section 4.4 : Finding Absolute Extrema. For each of the following problems determine the absolute extrema of the given function on the specified interval. \(f\left( x \right) = 8{x^3} ...Math is represented in the book by Mike's father, and he is a man with lots of problems: He is forgetful, overweight, anti-social, and not able to manage his daily life without the help of his teenage son. Mike's father is also seemingly biased against everything other than math and engineering. Finally, the father is an extremely serious work ...So if we want to sort it from least to greatest, well, we just have to start at the left end of the number line. The smallest of them, or the least of them, is -28. Then we go to -17. -17. Then we go to 22.4. Then we go to 22.4. And then we go to the absolute value of -27, and we are done. Learn for free about math, art, computer programming ...5.4. Absolute values and the triangle inequality. The triangle inequality is a very simple inequality that turns out to be extremely useful. It relates the absolute value of the sum of numbers to the absolute values of those numbers. So before we state it, we should formalise the absolute value function.Compare the f (x) f ( x) values found for each value of x x in order to determine the absolute maximum and minimum over the given interval. The maximum will occur at the highest f (x) f ( x) value and the minimum will occur at the lowest f (x) f ( x) value. Absolute Maximum: (4,15) ( 4, 15)its distance from zero on the number line. * For the notation, we use two big vertical lines. Check it out: Find the absolute value of 4: Find the absolute value of -5: continue. 1. of 2. This prealgebra lesson defines and explains how to find the absolute value of a number.the absolute value is never negative; the absolute value of 0 is 0 because the distance between a number and itself is zero. The absolute value of a number a is written as ∣ a ∣ . For example, the absolute value of - 7 is written as | - 7|. Example 1: Find the absolute value of 2. Solution: Graph 2 on a number line. Answer: ∣ 2 ∣ ...The absolute value of a number is simply the distance that number lies away from 0 on the number line. Absolute value eliminates the "direction" traveled to get there. It's like saying that you walked 3 meters frontward versus 3 meters backward. You walked 3 meters in different directions from where you started! With a number line in front of ...Absolute value equations calculator. Added Aug 29, 2011 by kyllemkl in Mathematics. Equation solver. Send feedback | Visit Wolfram|Alpha. Get the free "Absolute value equations calculator" widget for your website, blog, Wordpress, Blogger, or iGoogle. Find more Mathematics widgets in Wolfram|Alpha.The extreme value theorem states that a continuous function over a closed, bounded interval has an absolute maximum and an absolute minimum. As shown in Figure 4.13, one or both of these absolute extrema could occur at an endpoint. If an absolute extremum does not occur at an endpoint, however, it must occur at an interior point, in which case ...Attempting to isolate the absolute value term is complicated by the fact that there are \textbf{two} terms with absolute values. In this case, it easier to proceed using cases by re-writing the function \(g\) with two separate applications of Definition 2.4 to remove each instance of the absolute values, one at a time. In the first round we get2.14 Absolute Value Equations; 2.15 Absolute Value Inequalities; 3. Graphing and Functions. 3.1 Graphing; 3.2 Lines; 3.3 Circles; ... Section 4.4 : Finding Absolute Extrema. For each of the following problems determine the absolute extrema of the given function on the specified interval. \(f\left( x \right) = 8{x^3} ...This calculus video tutorial explains how to evaluate limits involving absolute value functions. It explains how to do so by evaluating the one sided limits...We can see two scale factors applied to n(x): 3 on the output value and 1/4 for the input value. Applying what we know on vertical and horizontal stretches, we have n(x) = 3·m(1/4 · x). Meaning, n(x) is the result of m(x) being vertically stretched by a scale factor of 3 and horizontally stretched by a scale factor of 1/4.This article reviews how to draw the graphs of absolute value functions. General form of an absolute value equation: f ( x) = a | x − h | + k. The variable a tells us how far the graph stretches vertically, and whether the graph opens up or down. The variables h and k tell us how far the graph shifts horizontally and vertically.Click here 👆 to get an answer to your question ️ Select all numbers that have an absolute value of 4. See what teachers have to say about Brainly's new learning tools! WATCH. close. Skip to main content. search ... 4 & -4. Absolute (denoted by the vertical bars) means that everything between them is converted to non-negative ...The absolute value of a number is the number without its sign. Syntax. ABS(number) Number is the real number of which you want the absolute value. Example. Col1. Formula. Description (Result)-4 =ABS([Col1]) Absolute value of -4 (4) Need more help? Want more options? Discover Community.The extreme value theorem states that a continuous function over a closed, bounded interval has an absolute maximum and an absolute minimum. As shown in Figure 4.13, one or both of these absolute extrema could occur at an endpoint. If an absolute extremum does not occur at an endpoint, however, it must occur at an interior point, in which case ...Remember that the absolute value sign is a negative sign eraser, so we have: #{(|-10|=10),(|10|=10):}# I hope that this was helpful. Answer link. Firelight Nov 11, 2014 The absolute value is how far away a number is form zero |10| and |-10| so 10 is 10 values away from zero and -10 is 10 values away from zero ...Definition: Absolute Value Function. The absolute value function can be defined as. f(x) = |x| = { x if x ≥ 0 − x if x < 0. The absolute value function is commonly used to determine the distance between two numbers on the number line. Given two values a and b, then |a − b| will give the distance, a positive quantity, between these values ...Transcript. Absolute value is a fundamental math concept that measures the distance of a number from zero, regardless of its sign. It's always a positive value, as it represents the magnitude of a number without considering its direction. This concept is useful in real-world applications, such as calculating distances and comparing heights.The absolute value of a real number is the distance of the number from 0 0 on a number line. The absolute value of x x is written as \left|x\right|. ∣x∣. For example, \left|5\right| …Oct 25, 2023 · To find the absolute value of a complex number, we need to take the square root of the sum of the squares of its real and imaginary parts. In this case, the complex number is 4 - 7i. We have 4 as the real part and -7 as the imaginary part. So, the absolute value is given by √(4^2 + (-7)^2). Shift absolute value graphs Get 3 of 4 questions to level up! Scale & reflect absolute value graphs Get 3 of 4 questions to level up! Graph absolute value functions Get 3 of 4 questions to level up! Quiz 1. Level up on the above skills and collect up to 240 Mastery points Start quiz. Piecewise functions.This page titled 1.2: Solving Absolute Value Equations is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request. Now that we can graph an absolute value function, we will learn how to solve an absolute value equation. To solve an equation such as 8 = | 2 x − 6 |, 8 = | 2 x − 6 |, we notice that the absolute value will be equal to 8 if the quantity inside the absolute value is 8 or -8. This leads to two different equations we can solve independently. In this video I explained how to integrate a function with argument containing absolute values.The extreme value theorem states that a continuous function over a closed, bounded interval has an absolute maximum and an absolute minimum. As shown in Figure 4.13, one or both of these absolute extrema could occur at an endpoint. If an absolute extremum does not occur at an endpoint, however, it must occur at an interior point, in which case ...As you’ll recall, according to the law of demand, price and quantity demanded are inversely related. By convention, we always talk about elasticities as positive numbers, however. So, mathematically, we take the absolute value of the result. For example, -0.45 would interpreted as 0.45.The absolute value is defined as the distance from a number to 0, and so it is always positive. So, the absolute value of −6 will be the distance from −6 to 0 on the number line, and it is 6. Remember that, | ± x| = x,x ∈ R. Answer link. 6 The absolute value is defined as the distance from a number to 0, and so it is always positive.Define absolute value. absolute value synonyms, absolute value pronunciation, absolute value translation, English dictionary definition of absolute value. n. 1. The numerical value of a real number without regard to its sign. For example, the absolute value of -4 is 4. Also called numerical value .Yes, because the spaces (Draw a number line if your confused about "spaces"!) |-6| or -6 from 0 is exactly 6. So to make the equation simpler, you rewrite it. So 6 x 6 = 36. (: Hope this helps! Absolute Value. <----- (-6)----- (-5)----- (-4)----- (-3)----- (-2)----- (-1)----- (0)----->.Sometimes called a numerical value, the absolute value is the non-negative value of a real number without regard for its sign. For example, the absolute value of both "12" and "-12" is 12. When writing absolute value, you can use two vertical lines around a number to represent absolute value. For example: Is short for "the …A low absolute neutrophil count is referred to as neutropenia . This occurs when the ANC is less than 2,500 cells/mcL. At levels below 1,000, you are at an increased risk of infection. A high absolute neutrophil count is called neutrophilia . This occurs when the ANC is over 6,000 cells/mcL.The absolute value of a number is the distance of the number from zero on the number line. The absolute value of a number is never negative. Learn what an absolute value is, and how to evaluate it. Explains absolute value in a way that actually makes sense. Using a number line, the concept of absolute value is illustrated through several example. The absolute value of a number a, denoted | a |, is the distance fromn a to 0 on the number line. Absolute value speaks to the question of "how far," and not "which way." The phrase how far implies length, and length is always a nonnegative (zero or positive) quantity. Thus, the absolute value of a number is a nonnegative number. 4. Write in symbols: The absolute value of a number, n, is 15. This is a page from the dictionary MATH SPOKEN HERE! , published in 1995 by MATHEMATICAL CONCEPTS, inc., ISBN: 0-9623593-5-1.Two Numbers Absolute Value Calculator. Welcome to the Two Numbers Absolute Value Calculator. This calculator calculates the two numbers that have the absolute value of any number. Please enter your number below to find the two numbers that have it as their absolute value. Here are some examples of what our calculator can explain and answer.What is the modulus (absolute value) of − 6 + 4 i ? Don't round. If necessary, express your answer as a radical. | − 6 + 4 i | =. Report a problem. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a ...We can see the following: The output values of the absolute value are equal to 4 at x = 1 and x = 9. The graph of f is below the graph of g on 1 < x < 9. This means the output values of f(x) are less than the output values of g(x). The absolute value is less than or equal to 4 between these two points, when 1 < x < 9.Absolute Value. The absolute value of a real number is denoted and defined as the "unsigned" portion of , where is the sign function. The absolute value is therefore always greater than or equal to 0. The absolute value of for real is plotted above. The absolute value of a complex number , also called the complex modulus, is defined as.You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Question: The absolute value of the sum of 4 times a number and 7 is the sum of 2 times a number and 3. Write and solve an absolute value equation to represent the situation. The absolute value of the sum of 4 times a number and 7 is the sum of 2 ...It's pretty simple: An absolute value function is a function in which the variable is inside the absolute value bars. As always, to find the integral, properties of integrals need to be used, so be sure to keep our favorite table handy! Constant multiple property of integrals. $$\int { (c\times f (x))}dx=c\times \int {f (x)}dx$$. Sum rule for ...Facts about Absolute Value 4: absolute value in mathematics. Absolute value is one of the important topics in mathematics. You can also find it in other mathematical settings. The ordered rings, quaternions, complex numbers, and vector spaces are defined using absolute value. Absolute Value Learning.Example. What is the absolute value of the following numbers? -4, -18.2, and 17 1/3. -4 – the absolute value is 4, as -4 is four numbers from 0. -18.2 – the …Attempting to isolate the absolute value term is complicated by the fact that there are two terms with absolute values. In this case, it easier to proceed using cases by rewriting the function \(g\) with two separate applications of \( \ref{AbsValDefn} \) and to remove each instance of the absolute values, one at a time.When the entropy value is calculated for one mole of the substance in its standard state, the resulting absolute entropy is called the standard entropy. The standard entropy is usually given the symbol So S o. It is usually included in compilations of thermodynamic data for chemical substances. We write So A (T) S A o ( T) to indicate the ...Purplemath. When we take the absolute value of a number, we always end up with a positive number (or zero). Whether the input was positive or negative (or zero), the output is always positive (or zero). For instance, | 3 | = 3, and | −3 | = 3 also. This property — that both the positive and the negative become positive — makes solving absolute-value equations a little tricky.Question: f a Complex Number Calculate |4+7i| The absolute value of 4+7i is equal to the squa root of. f a Complex Number Calculate |4+7i| The absolute value of 4+7i is equal to the squa root of. There are 2 steps to solve this one. Who are the experts? Experts have been vetted by Chegg as specialists in this subject.1-4) Computes the absolute value of the floating-point value num. The library provides overloads of std::abs and std::fabs for all cv-unqualified floating-point types as the type of the parameter num. (since C++23) A) Additional overloads are provided for all integer types, which are treated as double.An absolute number takes the positive value of a number, without regards to its sign. Mean is an average of a set of numbers. So, what is the mean absolute deviation? It's the average of every value's distance from a certain central point. This point can be a mean, median, mode, or any other statistically significant number.2.14 Absolute Value Equations; 2.15 Absolute Value Inequalities; 3. Graphing and Functions. 3.1 Graphing; 3.2 Lines; 3.3 Circles; 3.4 The Definition of a Function; 3.5 Graphing Functions; 3.6 Combining Functions; 3.7 Inverse Functions; 4. Common Graphs. 4.1 Lines, Circles and Piecewise Functions; 4.2 Parabolas; 4.3 Ellipses; 4.4 Hyperbolas; 4.5 ...In this case, a = 4 and b = -3, so: |4 - 3i| = √ ( (4)^2 + (-3)^2) = √ (16 + 9) = √25 = 5. So, the absolute value of 4 - 3i is 5. The absolute value of the complex number 4 - 3i, represented as |4-3i|, is equal to 5. This conclusion is reached by applying the formula for absolute value. Option D is answer. Learn more about complex number ...The absolute value of complex number is also a measure of its distance from zero. However, instead of measuring this distance on the number line, a complex number's absolute value is measured on the complex number plane. $ \text{ The General Formula} $ $|a + bi| = \sqrt{a^2 + b^2 } $ ...You can use the built-in math function abs() to get the absolute value (magnitude without the sign) of a number in R. Pass the number for which you want to get the absolute value as an argument to the abs() function. The following is the syntax –. It returns the number without any sign.4.1: Piecewise-Defined Functions In preparation for the definition of the absolute value function, it is extremely important to have a good grasp of the concept of a piecewise-defined function. 4.2: Absolute Value The absolute value of a number is a measure of its magnitude, sans (without) its sign. 4.3: Absolute Value EquationsCompare |-4| and |-4|. Solution : Step 1 : The absolute value of a number is the number’s distance from 0 on a number line. To understand this, let us mark -4 and 4 on a number line. Step 2 : On the above number line, -4 is 4 units from 0 to the left. Since -4 is 4 units from 0, we say that the absolute value of -4 is 7.Learn how to graph absolute value functions in vertex form with this interactive calculator. Adjust the sliders and see the changes in real time.Absolute value is the distance between 0 to the number on the number line. In other words, it is a number's magnitude or size which is calculated using a number line. The absolute value (or modulus) a of a real number 'a' is its non-negative value, regardless of its sign. For example: \ ( \left | ~-~5~ \right |~=~5 \)The absolute value of a number is the number without its sign. Syntax. ABS(number) Number is the real number of which you want the absolute value. Example. Col1. Formula. Description (Result)-4 =ABS([Col1]) Absolute value of -4 (4) Need more help? Want more options? Discover Community.Answer:-4 and 4. Step-by-step explanation: absolute value is decide how far a number is from 0 on the number line.Test prep. Improve your math knowledge with free questions in "Absolute value of rational numbers" and thousands of other math skills.Absolute monocytes per microliter of blood (mcL) Adults. 0.2 to 0.95 x 10 3. Infants from 6 months to 1 year. 0.6 x 10 3. Children from 4 to 10 years. 0.0 to 0.8 x 10 3. These ranges can vary ...To use the absolute value calculator, enter the number you'd like to find the absolute value for in the Input box. Then, click the Compute Absolute Value button. We'll return the number's absolute value in the Absolute Value box. Next, try our other calculators and tools. PK started DQYDJ in 2009 to research and discuss finance and investing ...Compare |-4| and |-4|. Solution : Step 1 : The absolute value of a number is the number's distance from 0 on a number line. To understand this, let us mark -4 and 4 on a number line. Step 2 : On the above number line, -4 is 4 units from 0 to the left. Since -4 is 4 units from 0, we say that the absolute value of -4 is 7.The absolute value of a complex number is just the distance from the origin to that number in the complex plane! This tutorial shows you how to use a formula to find the absolute value of a complex number. Keywords: problem; absolute value; complex numbers; pythagorean theorem; complex plane;Includes lessons Absolute Value Solution Sets, Absolute Value Inequalities with One Variable, and Absolute Value Inequalitiea with Two Variables.Free Complex Numbers Calculator - Simplify complex expressions using algebraic rules step-by-stepInput: N = 12. Output: 12. Naive Approach: To solve the problem follow the below idea: The absolute value of any number is always positive. For any positive number, the absolute value is the number itself and for any negative number, the absolute value is (-1) multiplied by the negative number. Learn More, Positive and Negative Numbers.Equations : Tiger Algebra gives you not only the answers, but also the complete step by step method for solving your equations |2x-4|=8 so that you understand betterStep 1. We have. % change in price = 6% increase. View the full answer Answer. Unlock. Previous question Next question. Transcribed image text: A6% increase in price results in a 4% decrease in quantity demanded. The absolute value of price elasticity of demand is (Enter your response rounded to one decimal place.)Derivative of Absolute Value Function - Concept - Examples. Now, based on the table given above, we can get the graph of derivative of |x|.Review by Joe Opaleski. Apr 24, 2024, 8:14 AM PDT. Kalahari Resort is one of the many water parks in Wisconsin Dells, Wisconsin. Joe Opaleski. I spent a day in …The absolute value of -4 is 4, because -4 is 4 units to the left of 0. The absolute value of 4 is also 4, because 4 is 4 units to the right of 0. Opposites always have the same absolute value because they both have the same distance from 0.Simplify absolute value expressions using algebraic rules step-by-step. absolute-value-calculator. en. Related Symbolab blog posts. Middle School Math Solutions – …The absolute value of -4 is 4, because it is four units to the right of zero on the number line. Learn how to simplify, compare and use absolute values with examples and exercises.5.4. Absolute values and the triangle inequality. The triangle inequality is a very simple inequality that turns out to be extremely useful. It relates the absolute value of the sum of numbers to the absolute values of those numbers. So before we state it, we should formalise the absolute value function.Shift absolute value graphs Get 3 of 4 questions to level up! Scale & reflect absolute value graphs Get 3 of 4 questions to level up! Graph absolute value functions Get 3 of 4 questions to level up! Quiz 1. Level up on the above skills and collect up to 240 Mastery points Start quiz. Piecewise functions.The absolute value of a complex number can be found using the Pythagorean theorem. For 4-7i, the absolute value is √65. Explanation: The absolute value of a complex number can be found using the Pythagorean theorem. To find the absolute value of 4-7i, we can treat 4 and -7 as the lengths of the legs of a right triangle.7. −47. −7. 171. Correct answer: 7. Explanation: The lines on either side of the negative integer represent that we need to find its absolute value. The absolute value of a number is its real distance from zero on a number line; therefore, we need to calculate how many spaces the number is tot he left of zero on a number line.Answer: Step-by-step explanation: Absolute Value of the number is the distance of the number from zero on the number line. Thus, the absolute value of -8 and 8 is the same i.e. 8. That means, the absolute value of negative or positive of that number is always a positive number of that number. Transcript. Absolute value is a fundamental math concept that measures the distance of a number from zero, regardless of its sign. It's always a positive value, as it represents the magnitude of a number without considering its direction. This concept is useful in real-world applications, such as calculating distances and comparing heights. The absolute value is used to avoid deviations with opposite signs cancelling each other out. Mean absolute deviation formula. This calculator uses the following formula for calculating the mean absolute deviation: where n is the number of observed values, x-bar is the mean of the observed values and x i are the individual values.An absolute value function is a function that contains an algebraic expression within absolute value symbols. Recall that the absolute value of a number is its distance from 0 on the number line. The absolute value parent function, written as f ( x ) = | x | , is defined as. f ( x ) = { x if x > 0 0 if x = 0 − x if x < 0.The absolute value of a number a a, denoted |a| | a |, is the distance from a to 0 on the number line. Absolute value answers the question of "how far," and not "which way." The phrase "how far" implies "length" and length is always a nonnegative quantity. Thus, the absolute value of a number is a nonnegative number. Sample Set A.Question 448581: what is the absolute value of 4+7i. Answer by jim_thompson5910 (35256) ( Show Source ): You can put this solution on YOUR website! Start with the absolute value of a complex number formula. This is also known as the magnitude of a complex number formula. Plug in and . Square to get.Therefore, the answer to "What two numbers have an absolute value of 4?" is: 4 and -4. The absolute value of 4 is 4 and the absolute value of -4 is also 4. Here it is expressed mathematically with vertical lines that we call bars: For future reference, remember that the two numbers that have an absolute value of x are x and -x.Integrating an Absolute Value Z 4 0 jx3 5x2 + 6xjdx There is no anti-derivative for an absolute value; however, we know it's de nition. jxj= ˆ x if x 0 x elsewise Thus we can split up our integral depending on where x3 5x2 + 6x is non-negative. x3 5x2 + 6x 0: x(x2 5x+ 6) 0: x(x 2)(x 3) 0:
Hence the absolute value of complex number. z = 46 - 4i is √2132. Question 4: Find the absolute value of the following complex number. z = 3 - 5i. Solution: The absolute value of a real number is the number itself and represented by modulus, To find the absolute value of complex number, Given : z = 3 - 5i. We have : |z| = √(a 2 +b 2). Design spec
One of the most common applications of absolute value, aside from simply calculating absolute value of numbers is its use on equations. For example. |x - 1 | = 3 ∣x−1∣ =3. corresponds to a absolute value equation, because there is an equation that needs to be solved for x x, and there is an absolute value involved in there.Comparing absolute values. Comparing absolute values helps us understand the distance between numbers and zero on the number line. The absolute value is always positive or zero, and it represents the magnitude of a number. By comparing absolute values, we can determine which number is further from zero, regardless of its positive or negative ...Join with Mr. B as we understand opposite numbers and absolute values. In this mathematics tutorial you'll find a visual mini-lesson along with practice and ...The absolute value of a number a, denoted |a|, is the positive distance between the number and zero on the number line. It is the value of the corresponding "unsigned" number -- that is, the number with the sign removed. Boundary Point A value of the variable that makes the equation true when an equal sign is substituted for an inequality sign ...Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.Therefore its absolute value is 9. The number -9 is the same distance from zero, so its absolute value is also just 9. In both cases the magnitude, or absolute value, of your number is just plain old "9" because you've removed any negative sign that might have existed. Taking absolute value of a number leaves a positive unchanged, and makes a ...The complex number is, We know that, The absolute value of a complex number x + iy, is defined as the distance between the origin (0, 0) and the point (x, y) in the complex plane. Its value is calculated by, Now, by using the above formula the absolute value of the complex number is, ⇒ =. To learn more about absolute value visit:And just as a reminder, absolute value literally means-- whether we're talking about a complex number or a real number, it literally just means distance away from 0. So the absolute value of 3 minus 4i is going to be the distance between 0, between the origin on the complex plane, and that point, and the point 3 minus 4i.Absolute values often show up in problems involving square roots. That's because you can't take the square root of a negative number without introducing imaginary numbers (those involving ). Example 1: Simplify This problem looks deceptively simple. Many students would say the answer is and move on. However, that is only true for positive values […]For example, the absolute value of 4, written as |4|, is 4 because it is 4 units away from 0 on a number line. The absolute value of -3, written as |-3| is 3 because it is 3 units away from 0 on a number line. Remember, distance is never negative. Would you ever tell someone you live -2 miles away? Of course not!All of the above grouping symbols, as well as absolute value, have the same order of precedence. Perform operations inside the innermost grouping symbol or absolute value first. Example \(\PageIndex{1}\) Simplify: \(5-(4-12)\). Solution: Perform the operations within the parentheses first. In this case, first subtract \(12\) from \(4\).Absolute value - The non-negative value of a number without regard to its sign. For example, the absolute value of 5 is 5, and the absolute value of −5 is also 5. The absolute value of a number may be thought of as its distance from zero along real number line. Therefore the absolute value of -1/4 is just 1/4..