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/Interval-Definition-Examples
点击访问原文链接

Interval: Definition and Example | EDU.COM

进入原网站 导航首页
Interval: Definition and Example | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">IntervalInterval: Definition and ExampleTable of ContentsDefinition of interval

An interval in mathematics represents a set of numbers that includes all real numbers between two endpoints. These endpoints can be included or excluded from the interval, depending on how the interval is defined. Interval notation provides a simplified way to describe these ranges using square brackets [ ] to include endpoints and round brackets ( ) to exclude them. For example, the interval [6, 20] includes all real numbers from 6 to 20, including both 6 and 20 themselves, while (6, 20) includes all numbers between 6 and 20 but not the endpoints.

There are three main types of intervals in mathematics: open intervals, closed intervals, and half-open/half-closed intervals. An open interval, denoted by round brackets like (5, 10), does not include either endpoint. A closed interval, written with square brackets like [4, 9], includes both endpoints. A half-open and half-closed interval includes only one endpoint, represented as either (6, 16] (including the right endpoint only) or [6, 16) (including the left endpoint only). Time intervals are a specific application, representing the duration between two events measured along a timeline.

Examples of intervals Example 1: Calculating a Time Interval Problem:

Calculate the interval between 2 p.m. and 6:45 p.m.

Step-by-step solution: Step 1, Identify what we're looking for: the total time that passes between these two points on a timeline. Step 2, Set up the subtraction to find the difference: 6:45 p.m. - 2:00 p.m. Step 3, When subtracting times, think of them in hours and minutes: From 2:00 p.m. to 6:00 p.m. is 4 hours From 6:00 p.m. to 6:45 p.m. is 45 minutes Step 4, Combine these amounts to get the complete interval: 4 hours + 45 minutes = 4 hours and 45 minutes Example 2: Representing Age Restrictions as an Interval Problem:

Students between the ages of 12 and 17 can be on the school soccer team. Express this as a mathematical interval.

Step-by-step solution: Step 1, Identify the minimum and maximum ages allowed: 12 years and 17 years. Step 2, Determine if these endpoints should be included in the interval. Since students who are exactly 12 years old and students who are exactly 17 years old can join the team, both endpoints need to be included. Step 3, We use square brackets to indicate inclusion of both endpoints: [12, 17] This notation means all ages from 12 up to and including 17 are eligible for the soccer team. Example 3: Expressing a Threshold as an Interval Problem:

To pass a math exam, students need to score above 65 marks out of a total of 100. Express this condition as an interval.

Step-by-step solution: Step 1, Identify the relevant range of passing scores: above 65 and up to 100. Step 2, Consider whether the endpoints should be included: 65 itself is not a passing score (the requirement states "above 65"), so 65 should be excluded. 100 is definitely a passing score, so it should be included. Step 3, We use a round bracket on the left (to exclude 65) and a square bracket on the right (to include 100): (65, 100] This notation means all scores greater than 65 and less than or equal to 100 will result in passing the exam. Comments(6)MCMs. CarterSeptember 17, 2025I’ve been using this page to help my kids with math homework, and the clear examples of open and closed intervals made it so much easier for them to understand. Great resource!

MMsTraveler25September 10, 2025I loved how clear the interval definitions were! My kids finally understood the difference between open and closed intervals. We even used the examples to solve some age-related math problems together. Super helpful resource!

NNatureLover89August 28, 2025I’ve used the interval definition and examples from this page to help my kids understand math ranges better. The clear explanations and real-life examples made it so much easier for them to grasp the concept!

NNatureLover84August 20, 2025I’ve been using this page to help my kids understand intervals for their math homework. The examples with bracket notation made it so much easier to explain open and closed intervals. Super helpful resource!

MMathWhizMomAugust 6, 2025I’ve been using this page to help my 7th grader understand number ranges. The examples and step-by-step explanations are so clear—it’s been a game-changer for his homework!

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 TermsCorresponding TermsHalf ofMeterMoreCommon NumeratorCube NumbersView All Math TermsRecommended Interactive LessonsUnderstand the Commutative Property of Multiplication3Math3.OA.B.5Find the value of each digit in a four-digit number3Math3.NBT.AUse Base-10 Block to Multiply Multiples of 103Math3.NBT.A.3Divide by 73Math3.OA.C.7Use the Rules to Round Numbers to the Nearest Ten3Math3.NBT.A.1Understand Equivalent Fractions with the Number Line3Math3.NF.A.3.a, 3.NF.A.3.bView All Interactive LessonsRecommended VideosMeasure Lengths Using Like Objects1Math1.MD.A.2Identify Quadrilaterals Using Attributes3Math3.G.A.1The Distributive Property3Math3.OA.B.5Convert Units Of Time4Math4.MD.A.1，4.MD.A.2Find Angle Measures by Adding and Subtracting4Math4.MD.C.7Area of Rectangles With Fractional Side Lengths5Math5.NF.B.4bView All VideosRecommended WorksheetsCompare and order four-digit numbers3Math3.NBT.AThe Distributive Property3Math3.OA.B.5Divide by 6 and 73Math3.OA.C.7Identify and write non-unit fractions3Math3.NF.A.1Divisibility Rules4Math4.OA.B.4Subtract Mixed Number With Unlike Denominators5Math5.NF.A.1View All WorksheetsRecommended Coloring PagesAmphibious aircraft landing on waterPre-K – KAll SubjectsGarland with bows and ribbonsPre-K – KAll SubjectsA cylinder standing on a flat surface with a circle shadow1 – 2All SubjectsFour small kittens in a row with a simple park background (grass and flowers)1 – 2All SubjectsA dragon with five heads, each head expressing a different emotion, surrounded by small stars.1 – 2All SubjectsWolf family (parents and pups) in a den with detailed surroundings5 – 6All SubjectsView All Coloring PagesRecommended BlogsWhat's a Perfect SAT Score? A Guide for K-6 FamiliesNovember 4, 2025Understanding All Five ACT Sections for K-12 Success: A Guide for Parents, Teachers, and KidsOctober 17, 2025ACT Prep Plan: Creating a Personalized Strategy for High School SuccessOctober 10, 2025ACT vs SAT: Key Differences Parents and Students Should KnowOctober 9, 2025Mastering the ACT: Smart Time Management Tips for Test SuccessOctober 9, 2025Army ASVAB Composite Scores: A Parent's Guide to Military Career PathsOctober 7, 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