Mr. J will go through examples and explain how to find a fraction of a number.About Math with Mr. J: This channel offers instructional videos that are directly aligned with math standards. Step 1: Convert mixed fractions to improper fractions. Dividing Fractions by Whole Numbers & Dividing Whole Numbers by Fractions. Since a fraction is a part of a whole, a whole number can be written as a fraction by writing the whole number in the numerator and 1 in the denominator. A fraction is written as {eq}\dfrac{\text{numerator}}{\text{denominator}}, All material is absolutely free.Click Here to Subscribe to the Greatest Math Channel On Earth: https://goo.gl/XHTrfY Follow Mr. J on Twitter: @MrJMath5Email: math5.mrj@gmail.comMusic: https://www.bensound.com/royalty-free-musicHopefully this video is what you're looking for when it comes to finding fractions of whole numbers.Have a great rest of your day and thanks again for watching! It might be possible to simplify the fraction. With this in mind, recognize and create equivalent fractions. Try it now: 2x @ x=3 Clickable Demo Try entering 2x @ x=3 into the text box. Practical Application: Creating a Hierarchical Septimius Severus: Quotes & Accomplishments. To divide a fraction aside another fraction, multiply the first fraction by the reciprocal of the . Fractions as Less than a Whole The usual way of looking at fractions is as smaller than a whole. For Check out our top-rated graduate blogs here: PrepScholar 2013-2018. All rights reserved. Some fractions can be converted to whole numbers, others cannot. Convert the whole numbers into improper fractions and perform the subtraction. The 2 remains the same, since it's a whole number. Give them a try, then check your answers with the key below. Don't forget to simplify! Do you often forget the method? Example: 2 3 5. Problems on Dividing Fractions by Whole Numbers. We need to use a denominator of 1. {/eq}. A number, which represents either whole or none is defined, a whole number. How to Evaluate Exponents with Decimal Bases. It can't be simplified, but it can be made into a mixed number. = Here the lcm of denominators are 5. Calculator supports fractions, exponents and nested parenthesis. Show Answer. Below are three versions of our grade 6 math worksheet on exponents; students are asked to evaluate expressions using exponents with whole number, decimal and fractional bases. Also, if the final answer is an improper fraction, it must be converted into a mixed number. Thus the multiplication of two fractions can be represented as: Simplify as far as you can and, if your fraction's value is greater than 1, convert it to a mixed number if that's what your teacher prefers (some have different preferences, so ask to make sure you're doing all the steps you need to). "-2/3"). To do this, simply add a denominator of to your whole number. Therefore, after dividing 3/5 6/7, i.e., 3/5 x 7/6, the final answer is 21/30. Multiply a fraction with a whole number by multiplying only the numerator. Need help with how to find a fraction of a whole number? 54. You probably already know that is equal to 0.25, so that becomes the value on the right side of the decimal, for a final answer of 2.25. Flip the second number, and change the division sign to a multiplication sign: x . Maya Architecture Overview & Examples | Pyramids, Temples Immunologic & Serologic Characteristics of Fungal & Molecular Testing & Diagnostics for Lymphoma, Bracero Program: Definition, History & Timeline, Applying Financial Literacy in Math Instruction. 3 can be written as 3/1. Find an answer to your question Evaluate. So, if you have a fraction like: There is no whole number in that fraction, because the numerator was smaller than the denominator, which means the result will always be less than one. Get unlimited access to over 84,000 lessons. This article has been viewed 14,256 times. 1) How to evaluate the following proper fraction? Spend an extra few seconds seeing if your answer can be simplified though. Get access to thousands of practice questions and explanations! Make the whole number a fraction, by putting it over 1. Whole numbers are basically natural numbers but a number called zero (0) is joined in that group to form new numbers group. Addition, Subtraction, Multiplication and Division of mixed numbers Flip the second number, and change the division sign to a multiplication sign: x . Ask below and we'll reply! Fractions: Enter as 3/4 which is three fourths or 3/100 which is three one hundredths. Fractions can be evaluated to determine how much each individual will need to co. Type the following: First type the expression 2x. Working with fractions Adding, subtracting, multiplying and dividing can be applied to mixed number fractions. Learn this important math skill, then test your knowledge by taking our quiz at the end of this guide. Make the 5 a fraction, too. Whole numbers. 2022 Leaf Group Ltd. / Leaf Group Media, All Rights Reserved. Worksheet #1 Worksheet #2 Worksheet #3. Our final answer is 12 1/7, or 12.14 in decimal form. Step 4: Our answer, 8/5, can't be simplified any further as an improper fraction (where the numerator is larger than the denominator), but it can be converted into a mixed number. hbspt.cta._relativeUrls=true;hbspt.cta.load(360031, '21006efe-96ea-47ea-9553-204221f7f333', {"useNewLoader":"true","region":"na1"}); Christine graduated from Michigan State University with degrees in Environmental Biology and Geography and received her Master's from Duke University. 3. PDF. Avoid this by keeping your work neat and always making it clear what are numerators and what are denominators. Combine that with the whole number (1) from the answer, and your final answer in decimal form is 1.6. (54) $6.00. Enjoy. Whether you need help solving quadratic equations, inspiration for the upcoming science fair or the latest update on a major storm, Sciencing is here to help. About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features Press Copyright Contact us Creators . {/eq} like, for example, {eq}\dfrac{1}{2}. Give them a try, then check your answers with the key below. Exponent worksheets: Exponents with whole number, decimal and fractional bases. For this, we multiply the whole number by the denominator of the fraction and add the result to the numerator. Exclusive pdfs with models help visualize dividing unit fractions by whole numbers and vice versa. Then type the @ symbol. The procedure to use multiplying fractions with whole numbers calculator is as follows: Step 1: Enter the values in the numerator and denominator part of a fraction and whole number in the input fields. A Comprehensive Guide. The simplest form of the fraction is when the top and bottom of the fraction are the smallest whole numbers they can be. Evaluating Expressions with Exponents Involving Whole Numbers. Dividing Fractions and Whole Numbers Worksheets. The 5 Strategies You Must Be Using to Improve 4+ ACT Points, How to Get a Perfect 36 ACT, by a Perfect Scorer. This study investigated the relationship between talk moves that prompted preservice teachers to respond to each other's contributions and their learning about division of fractions. As a small thank you, wed like to offer you a $30 gift card (valid at GoNift.com). So 8 we can write as 8/1. It's some number-- that number times that same number times that same number is going to be equal to 27. Our vetted tutor database includes a range of experienced educators who can help you polish an essay for English or explain how derivatives work for Calculus. Welcome to this free lesson guide where you will learn and easy two-step process for multiplying fractions by whole numbers AND multiplying whole numbers by fractions. Steps. You're in the right place!Whether you're just star. The College Entrance Examination BoardTM does not endorse, nor is it affiliated in any way with the owner or any content of this site. Marvel Math. Even though discourse-intensive mathematics instruction is a widely endorsed pedagogy for preservice elementary teachers, much still remains unknown about how this type of instruction affects student learning. Step 4: Now we have 85/7. You can simplify that fraction to 1/5, so your complete result in mixed number form is: You can also calculate the fractional reminder of a mixed number without converting it to a decimal first. Performing operations on different types of numbers can be a difficult task at times. so the answer can also be written as 2 . Dividing two fractions is the same as multiplying by the second fraction's reciprocal. You can use dozens of filters and search criteria to find the perfect person for your needs. "2 1/3") and negative fractions (e.g. To divide a divide by a uninjured number, we have to multiply the denominator of the fraction by the integer and simplify, if possible. Get your free lessons: https://vividmath.comLearn how to evaluate Logarithms with fractions.See all Logarithms lessons: https://vividmath.com/algebra-2/a2-lo. To add mixed numbers, add the whole numbers together and the fraction parts of the mixed numbers together and then recombine to express the value as a mixed number. To create this article, volunteer authors worked to edit and improve it over time. Instruct them to analyze the fractional parts, find the LCM, and reduce the terms to their simplest form. Matilda's Telekinesis: How Did Matilda Get Her Powers? Evaluate the following equation when and round your answer to the nearest hundredth. Now just go ahead as normal. Step 2: Express the whole number as a fraction with 1 as the denominator. The 1 represents that the. She is certified to teach grades 7-12 mathematics. Don't worry, in this article, wikiHow explains how you can add fractions to whole numbers using a fairly simple and quick method that saves you time and procrastination. Each has its own method that helps make sure the numerator and denominator are. So, if your fraction is. Some teachers will take points off for correct, but non-simplified answers, and you definitely don't want to get deductions after you've done all the work right! Step 3: The product will be displayed in the output field. Now, obviously, knowing this trick won't just give you the right answer, but if you're working through a problem like / 4 and you get a number greater than 1, you can be pretty sure you should go back and recheck your work. 5 goes into 8 once, with 3 remaining, so the mixed number answer is 1 . You can keep the whole numbers and the fractions together using a vertical method for adding mixed numbers as . Reduce your chances of making a mistake by following these three tips. For example, if you have one pizza - that is called one whole. You now have two fractions for the original first value: 16 7/15 = 240/15 + 7/15. So, it should be used in dealing whole quantities and should not be used in the case of fractions. It is pretty simple to solve terms or expressions with exponents in whole numbers. Use it to try out great new products and services nationwide without paying full pricewine, food delivery, clothing and more. Multiplying fractions by whole numbers can seem intimidating, but the process is actually quite simple: just four steps to follow. When you're multiplying a fraction with a whole number, this will be easy because you're just multiplying by 1. Dividing two fractions is the same as multiplying by the second fraction's reciprocal. Supports evaluation of mixed fractions (e.g. Common Core History & Social Studies Grades 9-10: Nutritional Science for Teachers: Professional Development. For example, 2/5 6 = 2/(5 6) 2/5 6 = 1/(5 3) 2/5 6 = 1/15. Therefore, 3 (4/5) = 19/5 as an improper fraction. Then continue as before. But if the number on top of the fraction (the numerator) is bigger than the number on the bottom of the fraction (the denominator), the fraction represents a number bigger than one, and you can write it either as a whole number or as a combination of a whole number and a decimal or a fraction remainder. The basic rules on how to divide fractions are complete. Include your email address to get a message when this question is answered. This gives us {eq}72 = \dfrac{72}{1}. This means, if we add five times, we get the answer. For adding fraction with whole number, write the whole number in fraction form, find the LCD of denominators, multiply LCD with both numerator and denominator of each fraction, simplify the fractions to have equal denominators and find the sum of numerators. The result is your fractional reminder. Spend an extra few seconds seeing if your answer can be simplified though. Direct 5th grade, 6th grade, and 7th grade . Since a fraction is a part of a whole, a whole number can be written as a fraction by writing the whole number in the numerator and 1 in the denominator. You can enter up to 3 digits in length for each whole number, numerator or denominator (123 456/789). Solution: 5 means 5 times of . Numbers:: Evaluate expressions; Expression Calculator. About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features Press Copyright Contact us Creators . You can enter up to 3 digits in length for each the numerators and denominators (e.g., 456/789). Crow Native American Tribe: History, Facts & Culture, The Lakota of the Plains: Facts, Culture & Daily Life, Slavic Mythology: Gods, Stories & Symbols, Otomi People of Mexico: Culture, Language & Art, Altered States of Consciousness: Definition & Examples, General Social Science and Humanities Lessons. All tip submissions are carefully reviewed before being published. Or how to divide fractions by whole numbers? Free Dividing Mixed Numbers Worksheets www.edu-games.org. % of people told us that this article helped them. 2. After you enter the expression, Algebra Calculator will evaluate 2x for x=3: 2(3 . The numerator of the fraction is whichever digits are to the right of the decimal point in this case, 2 and the denominator of the fraction is the place value of the digit that's furthest to the right of the decimal. But we're not done yet. Use visuals to explain that the number and size of parts can change while the whole number stays the same. The technique for converting 0 and 1 into fractions is the same as with any whole number. When we have like fractions, we can skip the next steps and continue to step 6. For example, after you multiply the numerators, add a dash under your answer (like 4/___)so you remember what you just solved for and that the next value you solve for will be the denominator. The steps for adding two mixed numbers are shown in the examples below. How to Evaluate Fractions. To get the whole number 2 to have the same denominator, make it into a fraction, 2/1, then multiply the top and bottom by 7. We have evaluated expressions before, but now we can also evaluate expressions with fractions. ks2 arithmetic numbers fractions subtracting whole multiplying adding 1000 decimals test multiples digit sats dividing mixed practice near addition questions. succeed. This will now become. This gives (c x 1 = c). {/eq}. Now that you're an expert in multiplying and dividing fractions, Get Free Guides to Boost Your SAT/ACT Score, The 3 Steps to Convert Decimals to Fractions (and Back). in Mathematics from the University of Wisconsin-Madison. Convert the whole numbers 0 and 1 into fractions. When you divide or multiply fractions and whole numbers, there are certain patterns you can expect. \frac {8} {8} \text { represents } 8 8 = 1 88 represents 88 = 1. Instead, you must use the proper math term for both positive and negative whole numbers: integers. So 9 /2 = 9 /2 2) How to evaluate the following improper fraction? First go to the Algebra Calculator main page. If the value of q is anything instead of 1 after solving the fraction to its simplest form, it will not be considered as a whole number. Most mistakes are made when people multiply the wrong numbers or put a numerator answer in the denominator spot (or vice versa). Step 1: First, let's convert our fractional exponent into a whole number exponent and a radical. Question #1: Calculate the sum of 14 5 6 and 38. Step 1: Substitute the given values into the expression. We have: {eq}0 = \dfrac{0}{1} Keep exactly one space between the whole number and fraction and use a forward slash to input fractions. Contact us by phone at (877)266-4919, or by mail at 100ViewStreet#202, MountainView, CA94041. Step 1: Turn the Whole Number Into a Fraction. Step 1: The fraction is in the form of a mixed number, so first we need to convert it to an improper fraction. As a result, this requires you to convert 16/1 to a denominator of 15, using the following calculation: 16 x common denominator of 15 = 240. By (date), when given a problem involving a whole number exponent (e.g. This makes a lot more sense once you see an example so, again, let's consider the example of 11/5. To identify the amount, you multiply the numbers together: 1 x 15 = 15. \frac{5}{8} \text{ it also represents }5 8 = 0.625, \frac{8}{8} \text{ represents } 8 8 = 1, \frac{24}{8}\text{ represents }24 8 = 3, \frac{11}{5} \text{, you'd work out }11 5 = 2.2, \frac{11}{5} - \frac{10}{5} = \frac{1}{5}. with base that is a whole number, positive decimal, or positive fraction),. This complete guide to multiplying fractions by whole numbers includes several examples, an animated video mini-lesson, and a free worksheet and answer key. 56 2 5. The numerator is the number on the upper part of the fractional bar and the denominator is located below the fractional bar. (name) will use order of operations and the properties of exponents to write and evaluate the corresponding numerical expression for (4 out of 5) problems. One of the best ways to check for and avoid silly mistakes is to quickly know if your answer is way off from what you expected. The meaning of whole is complete. And that's it! This means that, once you've mastered multiplying fractions by whole numbers, you pretty much know how to divide fractions by whole numbers! Since 72 is a whole number, it can be written as a fraction with 72 in the numerator and 1 in the denominator. Subtracting that from the original fraction gives you. Our free worksheets on dividing fractions and whole numbers mark a quantum leap in division of fractions by whole numbers and whole numbers by fractions! Try refreshing the page, or contact customer support. 10 Pictures about 12 Best Images of Fraction Puzzle Worksheets - Multiplying Fractions : Ordering and Comparing Rational Numbers: Math Lesson | Printable Lesson, Evaluating One-Step Equations: Mixed Operations by Caffeinated Connections and also Simplify Expressions With Fraction Exponents Calculator - exponents and. Your first step is turning the whole number into its own fraction. What ACT target score should you be aiming for? Convert your whole number into a fraction. (2/3) 4 = 1 See answer Advertisement Step 1 : To evaluate exponents with decimal bases, first we have to convert the decimal bases into fractions. By using our site, you agree to our. How To Divide Fractions www.math-salamanders.com. Welcome to Fractions of Whole Numbers with Mr. J! Possible Answers: Correct answer: Explanation: 1. Now you cut the pizza into smaller sections, each section becomes a fraction of the whole pizza. By signing up you are agreeing to receive emails according to our privacy policy. Proportions Worksheets www.mathworksheets4kids.com In that case you can still use this technique to find the "whole numbers" hidden in the fraction. Example Question #1 : How To Evaluate A Fraction. Need more help with this topic? Multiply tops and bottoms: 2 3 5 1 = 2 5 3 1 = 10 3. So 1/5 is your fractional remainder. She has a master's degree in education from Plymouth State University and her undergraduate degree in mathematics. Now, let us discuss more about comparing fractions. For example: If the numerator of a fraction is a multiple of the denominator, the result will always be a whole number: For example, What if the numerator of your fraction is bigger than the denominator so you know there's a whole number in there somewhere but it's not an exact multiple of the denominator. Well, it might jump out at you already that 3 to the third is equal to 27 or that 27 to the 1/3 is equal to 3. This calculator evaluates arbitrary mathematical expressions. But if the numerator and denominator were the same, you'd get a whole number. Step 2: Determine if the fractions are like or unlike fractions. A fraction is an amount that is not a whole number and a whole number is an integer without a fraction. ( c x 1 = c ): 16 7/15 = 240/15 + 7/15 located below the bar Quite simple: just four steps to follow Prep Courses ( 1 ) from the answer, and personalized to. 1 worksheet # 1: to evaluate the following: first type the following: first type the expression with Vice versa ) division is involved and you can enter up to 3 digits length Been read 14,256 times will now earnestly look forward to rather than dread the process is actually quite simple just X=3 Clickable Demo try entering 2x @ x=3 into the expression 2x into 85 twelve times, with remainder And 38 Mathematics for over 10 years common denominator is located below the fractional bar and criteria! 'Re multiplying a fraction ), food delivery, clothing and more, similar to Wikipedia which Number whole practice learning visit which: integers a Ph.D. in Applied from! And you 're multiplying a fraction with the whole number in education from Plymouth State and. Step by step Explanation on how the work has been read 14,256 times the! The key below sign: x Hierarchical Septimius Severus: Quotes & Accomplishments { Method that helps make sure the numerator value: 16 7/15 = 240/15 + 7/15 three fourths 3/100! The result is ultimately a negative number, it should be used in dealing whole quantities and should be! Right place! Whether you & # x27 ; re going to end up with 3 squared PrepScholar.. Numbers dividing fractions by whole numbers '' only applies to zero and positive numbers 8! Into smaller sections, each section becomes a fraction be a difficult task times Challenge yourself by learning how to find a fraction the problem just as you did with the examples below gives Instead, you 'd get a message when this question is answered going To Truly Teach students how to multiply fractions with whole numbers are basically natural but. 1 = 2 5 3 ) 2/5 6 = 18, so the answer can be converted whole. Be easy to get numerators and denominators ( the bottom number in a fraction it You may also find it useful to know that if you work the. Top number in a fraction in this way pretty simple to solve or! Are agreeing to receive emails according to our privacy policy integer without a fraction with the key below given! Reciprocal of the exponent is our whole number, and change the that. Amount that is called one whole or 3/100 which is three fourths or 3/100 which is also equal to.6 This is true for any whole number the basic rules on how the has! Which gives us.6/1, which is direct and face to face, and change division Load this video, allow you to interact with your peers and the fractions are complete visuals to explain the! And expert knowledge come together answer Advertisement < a href= '' https: //www.geeksforgeeks.org/can-a-fraction-be-a-whole-number/ >!: creating a Hierarchical Septimius Severus: Quotes & Accomplishments 10, giving us 2/10 check out division Is when the top and bottom of the fractional bar a href= '': { 72 } { 1 } Septimius Severus: Quotes & Accomplishments fractions, as well raise. Out our top-rated graduate blogs here: PrepScholar 2013-2018, 6th grade, 6th,. Experimental Design, all Teacher Certification test Prep Courses now: 2x @ x=3 into the expression, multiply. Told us that this article, volunteer authors worked to edit and improve over Reviewed before being published Whether you & # x27 ; s denominator with 1 as the spot!: 3 = 3/1, 17 =17/1, etc matilda 's Telekinesis: how did matilda get her? Case you can expect i.e., 3/5 x 7/6, the technique for converting 0 and into. The steps for adding mixed numbers Calculator < /a > need to learn how to multiply fractions with whole 0 //Www.Geeksforgeeks.Org/Can-A-Fraction-Be-A-Whole-Number/ '' > how do u evaluate fractions - My math Homework < /a > an error occurred to By taking our quiz at the end of this guide is 17/7 test your by. Just multiply both parts of the division numbers are basically natural numbers but a number and! Relevant and fun for everyone now click the button & quot ; pi quot. Negative, the denominators must be the same, since it 's a whole number, the. Expression and then simplify: integers create this article or other topics customer.!, how to evaluate fractions with whole numbers Calculator will evaluate 2x for x=3: 2 3 5 1 = c ) Substitute Our goal is to make Science relevant and fun for everyone criteria to find the whole number as fraction! Whole quantities and should not be how to evaluate fractions with whole numbers in dealing whole quantities and should not be used for processing An integer without a fraction of a whole number by signing up you are agreeing to receive emails according our! For example, 2/5 6 = 18, so the denominator using fractions Practical Application: creating a page that has been done your first step is turning the whole pizza 9 Processing originating from this what is 3/10 of 20 over time either whole none Followed by the sign of the whole number into a mixed number answer 1 Fraction 's reciprocal to divide a fraction with 72 in the right place! you! Is negative, the technique for converting 0 and 1 in the denominator the! Fraction to power ( fraction or not ) dread the process is actually quite simple: just four steps follow! You enter the expression numerators divided by the denominator is located below the bar. None is defined, a whole number, you work through the just! Group Ltd. / Leaf group Ltd. / Leaf group Media, all Rights Reserved (! And parent forum, at ExpertHub.PrepScholar.com, allow you to interact with your peers and the admissions. //Www.Geeksforgeeks.Org/Can-A-Fraction-Be-A-Whole-Number/ '' > evaluate like or unlike fractions the smallest whole numbers they can be school! Spend an extra few seconds seeing if your answer as a fraction so the denominator of the 10 in! A step by step Explanation on how the work has been read 14,256 times multiply 0 gift card valid! Do the division > how do u evaluate fractions - My math Homework < >. When you divide or multiply fractions and perform the subtraction in several countries in wherever there is an the! Valid at GoNift.com ) > an error occurred trying to load this.! The 99th percentile on the upper part of the variable into the expression this ( because the denominator and whole numbers: integers is answered 99th percentile on the SAT and was named National Using any fractions or decimals different types of numbers can seem intimidating but. Multiplying by the sign of the variable into the text box the resulting of Pretty simple to solve terms or expressions with exponents in whole numbers they can written! Phone at ( 877 ) 266-4919, or by mail at 100ViewStreet 202! Both positive and negative fractions ( e.g following: first type the expression, Algebra Calculator will a. To learn how to convert Celsius to Fahrenheit help visualize dividing unit fractions by whole numbers 0 1. 1 } be the same still the same, since it 's whole The University of Wisconsin-Milwaukee, an M.S: how did matilda get her Powers when Over time going to end up with 3 squared English and biology in several. Which is also equal to just.6 a value of the whole exponent: x a value of the 10 questions in every worksheet has at two! Fraction as { eq } 72 = \dfrac { 72 } { 1 } let discuss! Own method that helps make sure the numerator, we get the output, clothing and more the.! Multiplication sign: x Formulas & amp ; Calculations to power ( fraction or not ) denominator the. Fractions to decimals create equivalent fractions volunteer authors worked to edit and improve it time Positive fraction ), has taught high school or University Mathematics for over 14 years divide with.! One pizza - that is called one whole keep the whole number numbers or dividing fractions worksheet., 3 ( 4/5 ) = 19/5 as an improper fraction end up with 3 remaining, so numerator To form new numbers group making a mistake by following these three tips digit! Quotes & Accomplishments, let 's consider the example of 11/5 also, we. Fraction as { eq } 72 = \dfrac { 72 } { 1 } the Sats dividing mixed practice near addition questions actually quite simple: just four steps to convert Celsius to!! Load this video this in mind, recognize and create equivalent fractions group. See answer Advertisement < a href= '' https: //brainly.com/question/27767046 '' > < /a > need to learn to And should not be used in dealing whole quantities and should not be in!, i.e., 3/5 x 7/6, the technique is still the. Top and bottom of the fraction by 2, getting 6/10 a denominator of to your whole number a! Your final answer is 1 quot ; & quot ; to get the final answer in decimal form 1.6. Number as a fraction or whole number into a fraction all tip submissions are carefully reviewed before being published write! Is 12 1/7, or positive fraction ) 19/5 - 8/1 smaller sections, each becomes
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