温馨提示：本站仅提供公开网络链接索引服务，不存储、不篡改任何第三方内容，所有内容版权归原作者所有
AI智能索引来源：http://www.edu.com/math-glossary/Proper-Fraction-Definition-Examples
点击访问原文链接

Proper Fraction: Definition and Example | EDU.COM

进入原网站 导航首页
Proper Fraction: Definition and Example | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">Proper FractionProper Fraction: Definition and ExampleTable of ContentsDefinition of Proper Fractions

A proper fraction is a specific type of fraction where the numerator (the number on top) is less than the denominator (the number on bottom). These fractions always have a value that lies between 0 and 1 because the denominator is larger than the numerator. The numerator tells us how many parts of the whole are being represented, while the denominator indicates how many equal parts the whole is divided into. Some examples of proper fractions include 12\frac{1}{2}21​, 25\frac{2}{5}52​, and 34\frac{3}{4}43​.

Fractions can be categorized based on the relationship between the numerator and denominator. Proper fractions (where numerator 125\frac{12}{5}512​ can be written as the mixed number 225\frac{2}{5}52​, where 25\frac{2}{5}52​ is a proper fraction.

Examples of Proper Fractions Example 1: Identifying Proper Fractions Problem:

Identify whether the following are proper fractions:

a) 1012\frac{10}{12}1210​ b) 1511\frac{15}{11}1115​ c) 1818\frac{18}{18}1818​ Step-by-step solution:

Step 1, recall that in a proper fraction, the numerator must be less than the denominator.

For fraction a): Compare 10 (numerator) and 12 (denominator)

Is 10 less than 12? Yes, because 10

Therefore, 1012\frac{10}{12}1210​ is a proper fraction

For fraction b): Compare 15 (numerator) and 11 (denominator)

Is 15 less than 11? No, because 15 > 11

Therefore, 1511\frac{15}{11}1115​ is not a proper fraction; it's an improper fraction

For fraction c): Compare 18 (numerator) and 18 (denominator)

Is 18 less than 18? No, because 18 = 18

Therefore, 1818\frac{18}{18}1818​ is not a proper fraction; it's an improper fraction (equal to 1)

Example 2: Adding Proper Fractions with Same Denominator Problem:

Add the proper fractions: 1020+1520\frac{10}{20} + \frac{15}{20}2010​+2015​

Step-by-step solution:

Step 1, notice that both fractions have the same denominator (20). This makes addition straightforward!

Step 2, when adding fractions with the same denominator, we keep the denominator the same and add only the numerators: 1020+1520=10+1520=2520\frac{10}{20} + \frac{15}{20} = \frac{10 + 15}{20} = \frac{25}{20}2010​+2015​=2010+15​=2025​

Step 3, simplify the resulting fraction by finding the greatest common factor (GCF) of the numerator and denominator:

The GCF of 25 and 20 is 5 Divide both the numerator and denominator by 5: 25÷520÷5=54\frac{25 ÷ 5}{20 ÷ 5} = \frac{5}{4}20÷525÷5​=45​

Step 4, note that our answer 54\frac{5}{4}45​ is actually an improper fraction because 5 > 4. This makes sense because we added two proper fractions whose sum is greater than 1.

Example 3: Subtracting Fractions with Different Denominators Problem:

Subtract 25−14\frac{2}{5} - \frac{1}{4}52​−41​

Step-by-step solution:

Step 1, notice that the fractions have different denominators (5 and 4). To subtract fractions with different denominators, we need to find equivalent fractions with a common denominator.

Step 2, find the least common multiple (LCM) of the denominators:

List the multiples of 5: 5, 10, 15, 20, 25, 30, ... List the multiples of 4: 4, 8, 12, 16, 20, 24, ... The LCM is 20 (the smallest number that appears in both lists)

Step 3, convert each fraction to an equivalent fraction with the denominator 20:

For 25\frac{2}{5}52​: Multiply both numerator and denominator by 4 2×45×4=820\frac{2 × 4}{5 × 4} = \frac{8}{20}5×42×4​=208​ For 14\frac{1}{4}41​: Multiply both numerator and denominator by 5 1×54×5=520\frac{1 × 5}{4 × 5} = \frac{5}{20}4×51×5​=205​

Step 4, subtract the numerators while keeping the common denominator: 820−520=8−520=320\frac{8}{20} - \frac{5}{20} = \frac{8 - 5}{20} = \frac{3}{20}208​−205​=208−5​=203​

Step 5, the answer 320\frac{3}{20}203​ is already in its simplest form since 3 and 20 have no common factors other than 1.

Comments(9)BBadmintonPlayerScarlettNovember 4, 2025This glossary page on proper fractions is great! I've used it to teach my students, and it made the concept so much easier for them to grasp.

AAgentOscarNovember 4, 2025I've been using this proper fraction def to help my students. It's super clear & the examples really aid understanding. Thanks!

GGuitaristLeoNovember 4, 2025This glossary page on proper fractions is great! It's helped my students grasp the concept easily. Thanks for the clear examples!

NNatureLover25September 17, 2025This Proper Fraction definition was super clear! I used the examples to help my daughter with her homework, and it really clicked for her. Thanks for breaking it down so well!

MCMs. CarterSeptember 10, 2025I’ve been struggling to explain proper fractions to my kids, but this page broke it down so clearly! The examples of adding and subtracting were super helpful. Definitely bookmarking this for homework support!

svg]:px-3 dk:w-auto h-10 dk:h-14 rounded-lg dk:rounded-[15px] px-5 dk:px-7.5 text-sm dk:text-xl text-[#3467FF] bg-white hover:bg-white">Load MoreExplore More TermsDilationGapParts of CircleMultiplying Mixed NumbersRegroupTypes of AnglesView All Math TermsRecommended Interactive LessonsMultiply by 63Math3.OA.C.7Find the value of each digit in a four-digit number3Math3.NBT.AIdentify and Describe Subtraction Patterns3Math3.OA.D.9Find Equivalent Fractions with the Number Line3Math3.NF.A.3.a, 3.NF.A.3.bUse place value to multiply by 103Math3.OA.C.7Word Problems: Addition and Subtraction within 1,0003Math3.NBT.A.2View All Interactive LessonsRecommended VideosOrder Three Objects by Length1Math1.MD.A.1Use The Standard Algorithm To Add With Regrouping1Math1.NBT.C.4Divide by 2, 5, and 103Math3.OA.C.7Measure Length to Halves and Fourths of An Inch3Math3.MD.B.4Divide Whole Numbers by Unit Fractions5Math5.NF.B.7bDivision Patterns of Decimals5Math5.NBT.A.2View All VideosRecommended WorksheetsRead and Make Picture Graphs2Math2.MD.D.10Fractions on a number line: greater than 13Math3.NF.A.2.bUnderstand And Estimate Mass3Math3.MD.A.2Line Symmetry4Math4.G.A.3Understand The Coordinate Plane and Plot Points5Math5.G.A.1Greatest Common Factors6Math6.NS.B.4View All WorksheetsRecommended Coloring PagesCaterpillar on a leaf smilingPre-K – KAll SubjectsUpper and lower case U with an umbrella in front of a house, word 'UMBRELLA' at the top1 – 2All SubjectsVenus with a rocket ship approaching from the right side and a small moon in the background1 – 2All SubjectsWitch hat with a black cat peeking out from under it3 – 4All SubjectsDetailed scene of a golfer with a golf club walking towards a clubhouse with a landscape of the course in the background5 – 6All SubjectsDouble bass in a detailed music shop with various instruments and accessories5 – 6All SubjectsView All Coloring PagesRecommended BlogsTeaching Kanji Stroke Order: A Foundation for Young LearnersNovember 13, 2025Best Reading for Beginners: Building Strong FoundationsNovember 12, 2025What Is Structured Literacy? A Complete Guide for K-6 Teachers and ParentsNovember 9, 2025Simple Thesis Statement Examples for Elementary WritersOctober 14, 2025The Science of Reading: Evidence-Based Strategies for K-6 SuccessSeptember 22, 2025Reading for Beginners: A Data-Driven Guide to Building Strong Literary FoundationsSeptember 17, 2025View All Blog PostsQUICK LINKSAbout UsPrivacy PolicyTerms of ServiceTOOLSHomework HelperGuide DesignerPodcast MakerPlan BuilderRESOURCESMath GlossaryEnglish GlossaryEnglish Language ArtsMathematicsScienceBook InsightsFun with WordsBlog© 2025 EDU.COM. All rights reserved.

智能索引记录