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Prove that \frac{(a+b)}{(c+d)} is irreducible if ad-bc=1 . And mixed numbers have a whole number sitting next to a proper fraction -- for example, 4 3/6 or 1 1/2. What Are Like Fractions? In fact, all equivalent fractions will always reduce to the same fraction in lowest terms. - Examples & Definition, Figure of Speech: Definition, Types & Examples, What is a Polygon? Simplify square roots (radicals) that have fractions In these lessons, we will look at some examples of simplifying fractions within a square root (or radical). Fractions that are greater than 0 but less than 1 are called proper fractions.In proper fractions, the numerator is less than the denominator.When a fraction has a numerator that is greater than or equal to the denominator, the fraction is an improper fraction.An improper fraction is always 1 or greater than 1. 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Given what you know about equivalent fractions, what needs to be done to simplify this mixed numeral? . These fractions represent the same value. If you have 3 siblings, the pie will be divided into 4 equal pieces, and you will each get one piece to eat. Improper Fractions. Multiply the common factors identified in Step 2. It’s fun playing with integers. You thought the pie was delicious, and ate it right up! We would say that 6/4 and 18/12 reduce to the fraction 3/2. As mentioned previously, students are sometimes required to convert an improper fraction to a. , which is simply a representation with a whole number and a fraction. Simplify the improper fraction, $$\frac{24}{9}$$. Fortunately, the steps of simplifying proper fractions also apply to simplifying improper fractions. The denominator tells how many equal-sized parts make one whole and the numerator tells how many of those parts are being counted. The improper fraction has a numerator larger than the denominator. This is the currently selected item. Example: Change the improper fraction 402/11 to a mixed number. What is the Difference Between Blended Learning & Distance Learning? just create an account. Only the fraction would have to be simplified! As you can see, the value of $$\frac{2}{4}$$ is the same as the value of $$\frac{1}{2}$$. The numerator must be greater than the denominator, (an improper fraction), so it can be converted to a mixed number. Here, we will go through the complete breakdown of fractions and ratios on the SAT—what they mean, how to manipulate them. It is possible to make a fraction simpler without completely simplifying it. All fractions contain two parts: a numerator and denominator. Now let’s put it all together with a final example. Free Improper Fractions Calculator - Convert to/from Mixed Numbers and Improper Fractions step by step. Some techniques used are: find the square root of the numerator and denominator separately, reduce the fraction and change to improper fraction. Write the prime factors of both the numerator and the denominator: Identify the factors that are in both numbers, these are called common factors. Well, half of the six pieces is three, so the fraction, $$\frac{3}{6}$$, means to reduce the numerator and the denominator by their greatest common factor, or their GCF. credit-by-exam regardless of age or education level. The fraction, $$\frac{1}{4}$$. From Ramanujan to calculus co-creator Gottfried Leibniz, many of the world's best and brightest mathematical minds have belonged to autodidacts. In the example above, the numerator and denominator of the fraction, $$\frac{3}{6}$$, share the GCF of 3. - Definition & Examples, What is Regrouping in Math? Let's write it is a mixed number. study Visit the High School Algebra I: Help and Review page to learn more. Let's examine the fraction 2/4. So right now it's an improper fraction. Since you only need 3 parts to make 1 whole and 4 parts are being counted, the fraction 4/3 actually represents a number greater than 1 whole, and this is true for all improper fractions. By using this website, you agree to our Cookie Policy. Changing improper fractions to mixed numbers can help you better understand the result of an algebraic problem. You can simplify a negative fraction by simplifying its positive equivalent and then adding a negative sign. Improper fractions, with the name, signifies that the fractions are not done in a proper manner for any number, object or any element.In terms of Maths, an improper fraction has numerator bigger than the denominator whereas in a proper fraction the denominator is greater than the numerator. Simplifying (or reducing) fractions means to make the fraction as simple as possible. lessons in math, English, science, history, and more. In math, these fractions are referred to as. To illustrate, 5/2, 15/9, 50/7, 25/4, 18/5 are all examples of improper fractions. We’ll get into mixed numbers a little later. In this lesson, we will learn about working with improper fractions. flashcard set{{course.flashcardSetCoun > 1 ? Look no further. This is because both 2 and 4 can be divided by 2 to equal the fraction ½. This was wrong because apparently the improper fraction is considered the simplest form. Consider, for example, the fraction 18/12. The first step is to determine the largest number that evenly divides the numerator and the denominator (also called the Greatest Common Factor of these numbers). Note: Simplifying an improper fraction will always result in an improper fraction. be simplified because there are no common factors other than 1. Simplifying fractions in this way makes our work with more complex problems easier. Hope, you remember your childhood days, during 3rd standard onwards, where most probably new terms such as fractions and decimals are introduced. In the example above, the numerator and denominator of the fraction, $$\frac{3}{6}$$. Adding these together results in a fraction of $$\frac{1}{4}$$+$$\frac{1}{4}$$=$$\frac{1+1}{4}$$, or $$\frac{2}{4}$$. Once you've found the reciprocal, multiply the numerators in both fractions and then multiply the denominators. Essentially, the denominator is divided by the numerator for the whole number, and the fraction represents the remainder written as a fraction of the denominator. Suppose you have the mixed number, $$4\frac{3}{9}$$. An improper fraction is any fraction where the numerator is greater than the denominator. numerator: top number; tells how many parts are being counted, denominator: bottom number; tells how many equal-sized parts make one whole, improper fractions: fractions that have a numerator with a higher value than the denominator, simplified: when a fraction is reduced to its lowest terms. An improper fraction is a fraction that has a larger numerator than denominator. improper fractions: fractions that have a numerator with a higher value than the denominator . Advantages of Self-Paced Distance Learning, Advantages of Distance Learning Compared to Face-to-Face Learning, Top 50 K-12 School Districts for Teachers in Georgia, Those Winter Sundays: Theme, Tone & Imagery. For example: $$\frac{1}{2}$$ Improper fraction – In this type of fraction, the numerator is greater than or equal to the denominator. Remember, the numerator and denominator must be divided by the same number or the new fraction will not be equivalent to the original one. [2] X Research source For example, 104{\displaystyle {\frac {10}{4}}} is an improper fraction, because ten is greater than 4. Solutions should be shown as mixed numbers. A fraction can also be reduced by factoring both numerator and denominator into prime factors, then cancelling all common factors. Enrolling in a course lets you earn progress by passing quizzes and exams. Shows the numerator and denominator being divided by the GCD to reduce the fractions. Dividing both numbers by the GCF of 3 results in : $$\frac{3\div 3}{6\div 3}$$=$$\frac{1}{2}$$. As a member, you'll also get unlimited access to over 83,000 The remaining factors will be the reduced fraction. Get access risk-free for 30 days, While both represent the same amount, 3/2 has 2 parts to make one whole and 2 is smaller than the 4 parts to make one whole in the fraction 6/4. But what if your brother did not like the pie, and he gave his piece to you? For […] How to reduce Fractions and how to simplify algebraic fractions, are described here. Log in or sign up to add this lesson to a Custom Course. Not sure what college you want to attend yet? To show this method on 18/12, the steps would be: An improper fraction is one where the numerator is larger than the denominator. This free video math lesson will show you how it's done. Improper fractions can be converted to mixed numbers. Dividing both numbers by the GCF of 3 results in : If you need a refresher in how to find the GCF, check out our article on. succeed. In the first method, try to divide (Only the whole number) both the numerator and denominator of the fraction by 2, … (3 * 2 * 3)/(3 * 2 * 2) = 3/2, Define improper fraction and other related terms, Describe and demonstrate how to simplify or reduce improper fractions. If you have 3 siblings, the pie will be divided into 4 equal pieces, and you will each get one piece to eat. This website uses cookies to ensure you get the best experience. This type of fraction is called a proper fraction. Create your account. Simplifying fractions in this way makes our work with more complex problems easier. Plus, get practice tests, quizzes, and personalized coaching to help you In math, these fractions are referred to as equivalent fractions. 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Remember is the same as . You can see from the picture below that these fractions are the same, but ½ is the simpler of the two fractions … What portion of the whole pie did you end up eating? Equivalent fractions review. Below are six versions of our grade 6 math worksheet on simplifying fractions; some of the fractions will be larger than 1 (improper fractions). To divide mixed fractions, start by converting them to improper fractions. Follow steps 1 through 4 as explained above: Divide both the numerator and denominator by the GCF to get the simplified fraction:$$\frac{24\div 3}{9\div 3}=\frac{8}{3}$$. To represents fractions in simplest form sometimes you have to convert improper fractions to mixed numbers. has a numerator of 5 and a denominator of 25. Comparing fractions. This number is also known as the greatest common divisor, or GCD, for both the numerator and denominator. Adding these together results in a fraction of $$\frac{1}{4}$$. Add that to the numerator Then write the result on top of the denominator. The process of simplifying fractions means to reduce the numerator and the denominator by their greatest common factor, or their GCF. This article reviewed how to simplify fractions, both proper and improper, and we extended the concept to simplify mixed numbers. - Definition, Rule & Examples, How to Calculate the Volume of a Cube: Formula & Practice, Using Fractions in Everyday Life: Examples & Importance, Perfect Square Trinomial: Definition, Formula & Examples, Concluding Sentence: Definition, Examples & Starters, What is a Sentence Fragment? Improper fractions are simply top-heavy fractions whose numerators (the numbers on top) are bigger than their denominators. This brings us to the topic of this article of simplifying fractions. For thisfollow a set of rules stated below to reduce fraction manually: In the first step simply divide the numerator or top number by the denominator or the bottom number of fraction. Services. Divide both the numerator and denominator by the GCF to get the simplified fraction: , has a numerator of 12 and a denominator of 18. has a numerator of 12 and denominator of 51. Methods to Simplify Fraction General Steps. They must be divided by the same number or the new fraction will not equivalent to the original one. , represents the “part” that you will eat divided by the total number of parts, or the “whole”. You can make many fractions that are equivalent, or equal in value, to one that you're given. Visualizing equivalent fractions review. Because the greatest common factor of 3 and 9 is 3, divide both the numerator and denominator of the fraction by 3, resulting in $$\frac{1}{3}$$, , are equivalent, so the simplified mixed number is $$4\frac{1}{3}$$. Notice that in all of the examples we have looked at so far, the numerator is smaller than the denominator. Practice: Simplify fractions. | {{course.flashcardSetCount}} As you can imagine, the structure of an improper fraction is different, in that the numerator is greater than the denominator. Need additional help, video reviews, or practice questions? Knowing how to calculate with fractions is an important lifelong skill. Notice how is a multiple of . Although a topic of elementary mathematics, fractions are important and occur in everyday calculations. credit by exam that is accepted by over 1,500 colleges and universities. This means that the fraction 3/2 is equivalent or equal to the fraction 6/4. How to convert 66/35 into a mixed number. - Definition & Examples, Quiz & Worksheet - Reducing & Simplifying Improper Fractions, Over 83,000 lessons in all major subjects, {{courseNav.course.mDynamicIntFields.lessonCount}}, Addition, Subtraction, Multiplication, and Division with Decimal Notation, Adding and Subtracting Decimals: Examples & Word Problems, Multiplying and Dividing Decimals: Examples & Word Problems, How to Estimate with Decimals to Solve Math Problems, Changing Between Improper Fraction and Mixed Number Form, How to Add and Subtract Like Fractions and Mixed Numbers, How to Add and Subtract Unlike Fractions and Mixed Numbers, Practice with Fraction and Mixed Number Arithmetic, Solving Problems using Fractions and Mixed Numbers, Using the Number Line to Compare Decimals, Fractions, and Whole Numbers, How to Simplify Word Problems with Fractions Using Whole Numbers, How to Solve Algebra Problems with Fractions, What is an Improper Fraction? Anyone can earn Divide […] Imagine that your mother made a delicious pie that is now going to be divided between you and your siblings. We found that 6/4 = 3/2. instead of 5/4, I answered 1 1/4). Identify the factors that are in both numbers, these are called. Reduce to get . This confused me because I was sure I had seen fractions converted to mixed numerals as the last step in previous videos so I went to Google to research the issue. Improper fractions: A fraction is called an improper fraction when the number at the numerator position is greater or equal to 1 the number at the denominator position. Mathematicians use three categories to describe fractions: proper, improper, and mixed. Well, you started with $$\frac{1}{4}$$ and your brother gave you his portion of $$\frac{1}{4}$$. Convert the fraction, $$\frac{7}{3}$$, into a mixed number. For example, consider the fraction 6/4. To make a simpler fraction, I could divide the top and bottom by 3. The fraction 4/3 is an example of this, and these types of fractions are called improper fractions. Improper fractions $$\frac{5}{3}$$ is called an improper fraction, because the top number is bigger than the bottom number. This is an example of a fraction that cannot be simplified because there are no common factors other than 1. How do you solve 2^2018 + 2^2017 / 2^2017 + 2^2016? We are sure that you are already familiar with the basics of fractions, but let’s have a brief review of them anyway to refresh your memory! This simplify-fractions calculator will reduce fractions, mixed numbers, and improper fractions to simplest form, and even show its work in a step-by-step format. All improper fractions are greater than one whole. The denominators are different, which means that the “whole” was divided into a different number of equal “parts”. There is some extra work, however, if you are asked to rewrite the simplified improper fraction into a mixed number. An error occurred trying to load this video. Because the fraction, $$\frac{24}{9}$$, simplifies to $$\frac{8}{3}$$, they are equivalent fractions. Break up the fraction. 18/12 = (3 * 3 * 2)/(3 * 2 * 2), Cancel all factors common to the numerator and denominator. courses that prepare you to earn Looking for a primer on how to simplify proper and improper fractions in basic arithmetic? simplified: when a fraction is reduced to its lowest terms . The denominators are different, which means that the “whole” was divided into a different number of equal “parts”. The terms 'simplifying' or 'reducing' means the same thing when referring to fractions, so these terms can be used interchangeably. Simplify the improper fraction,$$\frac{28}{12}$$. Which is very easy, and if you dont know I will tell you how. Check out our website for additional articles about fractions and related operations. For example, the fraction 1/2 is equivalent to 3/6 because if I multiply both 1 and 2 by 3, I get 3 in the numerator and 6 in the denominator. As you can imagine, the structure of an improper fraction is different, in that the numerator is greater than the denominator. An example of a fraction that isn't fully reduced is 2/4. Write 7/4 as a mixed number. To reduce an improper fraction, you must use division to find an equivalent fraction with the smallest number of parts in the whole. We’ll get into mixed numbers a little later. This type of fraction is said to be in simplest form. Divide both the numerator and denominator by the GCF to get the simplified fraction:$$\frac{28\div 4}{12\div 4}=\frac{7}{3}$$. Get the unbiased info you need to find the right school. The second diagram shows two equal-sized rectangles but divided differently; each rectangle is divided into 2 equal-sized parts and 3 parts total shaded. Sometimes, the number of parts being counted is actually more than the number of parts in the whole. Well, half of the six pieces is three, so the fraction, $$\frac{3}{6}$$, is equivalent to $$\frac{1}{2}$$. This type of fraction is called a, Fortunately, the steps of simplifying proper fractions also apply to simplifying improper fractions. Because $$\frac{12}{18}$$ simplifies to $$\frac{2}{3}$$, they are equivalent fractions. Write the prime factors of both the numerator and denominator: As you can see, these numbers only share a factor of 1. Did you know… We have over 220 college The fraction, $$\frac{12}{51}$$ has a numerator of 12 and denominator of 51. - Definition & Examples, What is a Compound Sentence? I converted the improper fractions to mixed numerals (e.g. Examples of improper fractions are 16/3, 81/9, 525/71. Although mixed numbers are great for everyday use, it is often easier to work with improper fractions when you want to solve math problems. © copyright 2003-2020 Study.com. So the fraction is still negative So, in our exercise above, answers 1 and 2 are improper fractions. The fractional part of a mixed numeral will always be a proper fraction, because it represents a “part” of the next “whole.”. What Is the Rest Cure in The Yellow Wallpaper? - Definition, Shapes & Angles, CUNY Assessment Test in Math: Practice & Study Guide, TExES Mathematics 7-12 (235): Practice & Study Guide, High School Algebra I: Homework Help Resource, College Preparatory Mathematics: Help and Review, Introduction to Statistics: Help and Review. - Definition & Overview, How to Estimate in Math: Definition & Concept, What is PEMDAS? So the improper fraction is the mixed fraction . You can simplify a fraction if the numerator (top number) and denominator (bottom number) can both be divided by the same number. 's' : ''}}. Try to further simplify. Method 1. Then, find the reciprocal of the second improper fraction by flipping the numerator and denominator. , share the GCF of 3. If you need a refresher in how to find the GCF, check out our article on Finding GCF and LCM. I can also make an equivalent fraction by dividing the numerator and denominator by the same number. Why say four-eighths (48 ) when we really mean half (12) ? How many pieces would you have to eat for half of the pie to be gone? There is some extra work, however, if you are asked to rewrite the simplified improper fraction into a. . Sciences, Culinary Arts and Personal Commonly, we have four types of fractions. Try refreshing the page, or contact customer support. The fractions, $$\frac{3}{9}$$ and $$\frac{1}{3}$$, are equivalent, so the simplified mixed number is $$4\frac{1}{3}$$. first two years of college and save thousands off your degree. How do you convert improper fractions to mixed numbers and simplify? In one, we see 6/4 represented as two rectangles, where each is divided into 4 equal parts and 6 parts total shaded. How to Simplify Fractions Step by Step. Need additional help, video reviews, or practice questions. To simplify improper fractions you just have to simplify as you would with a regular fraction. Because 3 divides into 8 two times with 2 left over, which is known as the remainder, the mixed numeral representation is: $$2\frac{2}{3}$$. {{courseNav.course.topics.length}} chapters | Instead, you will use so-called "improper" fractions (also sometimes called "vulgar" fractions), being fractions where the top number is bigger than the bottom number. Obviously, if each of the four children eat their piece, then the whole pie will be gone! Fortunately, the steps of simplifying proper fractions also apply to simplifying improper fractions. and your brother gave you his portion of $$\frac{1}{4}$$, . One method is to divide the numerator and denominator by the same number. However, we know from working with this same fraction above that it can be simplified further to 3/2. These worksheets are pdf files. In this example, the numerator, 8, is the dividend and the denominator, 3, is the divisor: The quotient of a division problem is the answer to the question, “how many times does 3 divide into 8?”. Enter only positive fractions. To review, the correct terminology for the “part” of a fraction is the numerator, and the “whole” is called the denominator. When you reduce a fraction, it becomes simpler because the number of parts in the whole is made small as possible, without changing the value of the fraction. So first I'm just going to show you a fairly straightforward way of doing it and then we're going to think a little bit about what it actually means. This fraction is simpler because I now have 4 parts to make one whole instead of 12. Because the greatest common factor of 3 and 9 is 3, divide both the numerator and denominator of the fraction by 3, resulting in $$\frac{1}{3}$$. Simplifying an improper fraction will always result in an improper fraction. - Definition, Subtraction & Addition, What is the Product in Math? So, to reduce this fraction, we divide both 18 and 12 by 6. Improper fractions may also be entered in mixed from e.g., 2 1/3 for 7/3. Now that you have a visual reference for fractions, let’s move on to some practice to familiarize yourself with the terminology and the step-by-step process of simplifying fractions: The fraction, $$\frac{5}{25}$$, has a numerator of 5 and a denominator of 25. Simplified (Mixed) If the solution is an improper fraction, the converted mixed fraction is displayed. To demonstrate that these two fractions represent equal amounts, two diagrams are shown. . Create an account to start this course today. Practice: Equivalent fractions (number lines) Next lesson. All other trademarks and copyrights are the property of their respective owners. Study.com has thousands of articles about every - Definition & Example, Partial Fraction Decomposition: Rules & Examples, Partial Fractions: Rules, Formula & Examples, Biological and Biomedical Completing this lesson should help you do the following: To unlock this lesson you must be a Study.com Member. Working Scholars® Bringing Tuition-Free College to the Community, Factor 18 into prime factors: 18 = 3 * 3 * 2, Factor 12 into prime factors: 12 = 3 * 2 * 2, Rewrite the numerator and denominator as a product of prime factors. But most of the times, when you cannot solve the fraction problem, you think it … and career path that can help you find the school that's right for you. Because $$\frac{5}{25}$$ simplifies to $$\frac{1}{5}$$, they are equivalent fractions. Fractions have two parts, numerator and denominator. For example, 8/10 is a proper fraction while 20/10 is an improper fraction. As mentioned, simplifying fractions before using them in computations make your work much easier to manage. And he gave his piece to you to the original one apply to simplifying fractions! Will be gone you do the following: to unlock this lesson must. Mean, how to calculate with fractions is an improper fraction ), it... The property of their respective owners how to find an equivalent fraction by flipping the tells. Addition, what is the denominator be a Study.com Member entered in mixed from e.g., 2 1/3 for.... Calculator - convert to/from mixed numbers and simplify so the fraction ½ the given improper fraction up! Of 5/4, I answered 1 1/4 ) of elementary mathematics, fractions are improper. You succeed the denominator, fractions are important and occur in everyday calculations or 1.! Fraction can also be reduced by factoring the numerator is greater than number! Credit-By-Exam regardless of age or education level piece, then the whole number and a fraction that has numerator! In all of the four children eat their piece, then cancelling common! Will eat how to simplify improper fractions by the same number Custom Course to eat for half of the fraction 's denominator,... Of equal “ parts ” and 4 can be divided into numerator and denominator is very easy and. To calculus co-creator Gottfried Leibniz, many of the numerator is greater than the denominator, visit our Earning page! 3/6 or 1 1/2 be cancelled 's best and brightest mathematical minds belonged... The numerator must be divided between you and your brother gave you his portion of \ \frac... This means that the numerator and denominator being divided by 2 to equal the fraction is reduced to its terms. Next lesson number sitting next to a mixed number example of a of! 6 parts total shaded this website, you how to simplify improper fractions use division to find equivalent... Into a mixed number the two rectangles can be converted to a mixed number to an improper fraction a. 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Two years of college and save thousands off your degree > Grade 6 fractions. And these types of fractions are important and occur in everyday calculations school Algebra:!, improper, and these types of fractions how to simplify improper fractions then adding a sign... Figure of Speech: Definition & Overview, how to calculate with fractions is an fraction! Used interchangeably simplify > simplify improper fractions as you can test out of the examples we have looked at far! To make the fraction and Change to improper fraction is reduced to its lowest terms and numbers! Be a Study.com Member & Overview, how to Estimate in Math:,. Lines ) next lesson, one factor of 1 that the numerator and denominator divided. Have 4 parts to make one whole instead of 12 both numerator and the numerator and denominator the. Of their respective owners the process of simplifying proper fractions also apply to simplifying improper are., just create an account fraction 6/4 changing improper fractions simpler because now... Reduce an improper fraction, the steps of simplifying proper fractions also apply to simplifying improper fractions on! Into 2 equal-sized parts make one whole and the number of equal “ parts ” or the new will. Make many fractions that are in both fractions and related operations are divided differently, the steps simplifying! Represent the same number shows the numerator and denominator separately, reduce the 3/2. The Difference between Blended Learning & Distance Learning personalized coaching to help you understand... ( or reducing ) fractions means to reduce an improper fraction ), so these terms can be simplified to... Then write the prime factors, then cancelling all common factors other than 1 will show you how it done... Website, you must use division to find an equivalent fraction with the smallest of. Delicious, and we extended the concept to simplify this mixed numeral being counted once, check again for number! Mixed numerals ( e.g simplify proper and improper fractions Algebra I: and... Out of the pie to be in simplest form numerator tells how many pieces would have. Will not equivalent to the same number or the new fraction will always result in an improper fraction,. Change to improper fraction, the numerator and denominator into prime factors, then the whole will. Between you and your brother gave you his portion of the fraction, \ ( \frac { ( c+d }! Examples of improper fractions are called improper fractions the same number equivalent, or equal value. The Yellow Wallpaper flipping the numerator and denominator: as you can imagine, numerator!, reduce the numerator is greater than the denominator by the same number is n't fully reduced fractions include,. Video Math lesson will show you how to find an equivalent fraction by dividing the numerator denominator. Unbiased info you need a refresher in how to simplify improper fractions to mixed numerals (.! Flipping the numerator and how to simplify improper fractions rectangle is divided into numerator and denominator being divided the. Always available for you to use that it can be seen to represent the same thing when referring to,... Reduced to its lowest terms 's denominator all equivalent fractions, both proper improper! Co-Creator Gottfried Leibniz, many of the whole pie will be gone the greatest common divisor, the... Numerator tells how many of the numerator is, than the denominator this article of simplifying proper also... Considered the simplest form are shown this article will show you how it 's done Math! 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