Learn Math

6 min read

Integers: Definition, Operations, and Worked Examples

Published: 12.08.2026·Updated: 14.08.2026

Nadia Rahmawati

Math Curriculum Team, Algonova

Integers: Definition, Operations, and Worked Examples

An integer is any number from the set of negative numbers, zero, and positive numbers, with no fractional or decimal part.

Examples: -3, -2, -1, 0, 1, 2, 3, continuing endlessly in both directions. A number such as 2.5 or a half is not an integer because it has a fractional part.

Types of Integer

Type	Members	Examples
Positive integers	Greater than zero	1, 2, 3, 100
Zero	Neither positive nor negative	0
Negative integers	Less than zero	-1, -2, -3, -100

Zero holds a special position: it is the boundary between positive and negative, and belongs to neither.

The Number Line

The number line is the main tool for understanding integers. Zero sits in the middle, positives to the right, negatives to the left. The further right, the greater the value.

From this comes a rule that often confuses: -5 is smaller than -2, even though 5 is bigger than 2. The reason is visible immediately on the line - the position of -5 lies further left.

A way to check through real context: -5 degrees is colder than -2 degrees, and a debt of 5 million is heavier than a debt of 2 million.

Integers in Everyday Life

Air temperature. Minus 3 degrees on a mountain top.
Building floors. Floor -2 means two levels below ground.
Account balance. A negative balance means debt.
Sea depth. A depth of 40 metres is often written as -40 relative to sea level.
Game scores. Points can fall below zero.

Frequently Asked Questions

Does Algonova teach mathematics for primary, junior high, and senior high kids?

Yes, Algonova Indonesia offers a complete math program for kids aged 6 to 17, covering all school levels from primary, junior high, to senior high. Each level has a dedicated curriculum aligned with the child's cognitive stage and the Indonesian school curriculum (Kurikulum Merdeka). For primary school (6-12): basic operations, fractions, simple geometry, and introduction to algebra. For junior and senior high (13-17): algebra, quadratic equations, basic trigonometry, advanced geometry, basic calculus, statistics, UTBK SNBT preparation, and advanced topics. All classes are online live with certified teachers in small groups of up to 10 students per class. Our method is built on visual conceptual understanding, not formula memorisation. Try a free trial class for a child's level diagnostic and recommended learning path.

Is there a free trial class for kids math tutoring?

Yes. For mathematics Algonova Indonesia offers a free diagnostic session of about 60 minutes with no commitment. The format is called Metode Diagnostik Algonova. No credit card is needed and there is no auto subscription afterwards. Note that these roughly 60 minutes are a diagnostic session, not a regular class. A regular math class runs 90 minutes, while the coding and design tracks have their own introductory format, a free 60 minute master class. During the diagnostic a certified teacher maps the child's level: which topics are already solid and where the gaps sit. The child also tries the online learning platform and works through first problems matched to their school level. After the session parents receive a personal learning plan based on the diagnostic result, plus a transparent explanation of program, schedule, and pricing from Rp 102,000 per lesson. To book, fill in the form on the website.

How many students are in one Algonova math class?

Algonova Indonesia math classes come in three formats: 1-on-1 private, a mini-group of 2–4 kids, and a group of up to 10 students with similar ability and school grade levels. This small group format is deliberately chosen because it provides the optimal balance between social interaction with peers and personal teacher attention. In a mini-group, every child averages about 10 minutes of direct teacher interaction in a single session. Compare with traditional offline bimbel typically of 20-40 students per class — direct interaction there is only 1-2 minutes per child, or none at all. For families wanting full attention, one-on-one private class format is also available with one student per teacher. This format is more intensive and suits competition preparation, catching up from severe gaps, or specific topic depth.

How much does kids math tutoring at Algonova Indonesia cost?

Kids math tutoring at Algonova Indonesia starts from Rp 102,000 per lesson. The price includes a live session with a certified teacher, digital learning materials, online platform access, and an official certificate upon completing each program level. The transparent 'starting from' rate is the same across all school levels — the final quote depends only on class format (private, mini-group, or group) and how many sessions per week you choose. Groups are the most affordable option; private classes are more intensive and suit competition prep or closing larger gaps. Full pricing details are shared transparently after the free trial class. No surprise fees — every cost component is explained before formal enrolment. To receive the latest pricing details, fill in the booking form on the website.

Is math tutoring fully available online?

Yes, all Algonova Indonesia math programs are fully available online with live sessions taught by certified teachers — not recorded videos. Kids learn in real time in small groups of up to 10 students, with two-way interaction, live Q&A, and problems worked on alongside the teacher throughout the class. To join online class, a child only needs a computer or laptop with a camera, a stable internet connection, and a headset. The Algonova platform runs directly in the browser so no special software installation is required. Kids can write problems in a regular notebook or on a tablet with stylus. Because every class is fully online, families can join from anywhere in Indonesia and easily fit lessons around school and other activities.

What makes Algonova math tutoring effective for Indonesian kids?

Three main factors make Algonova math tutoring effective for Indonesian kids. First, the curriculum aligns with Kurikulum Merdeka used in national schools, so what is learned at Algonova directly helps with school lessons and exams. Second, the methodology is built on visual conceptual understanding (not formula memorisation). Kids learn to break big problems into small systematic steps — a thinking pattern transferable to other subjects like science and IT. Third, small groups of up to 10 students per class let teachers adjust pace to each child's ability. Slower kids get personal help, while faster kids don't get bored waiting. The result: most Algonova students see math grade improvements at school within the first 2-3 months.

What if my child is behind from earlier math grades?

Algonova Indonesia is specifically designed to help kids behind catch up in a way that doesn't make them feel defeated or ashamed. Every new student starts with a free diagnostic during the trial class to identify exactly where the gap occurred. Based on the diagnostic, the teacher builds a personal learning path that closes the gap from the most basic foundation. For example, a junior high student weak in algebra might actually be behind in primary school fraction operations. We go back to the foundation, then progress gradually without comparison with other peers. Many Algonova students who initially started 1-2 grade levels behind successfully caught up and even surpassed classmates within 3-6 months with weekly classes and consistent homework. It's never too late to start. Try a free trial class for diagnosis without commitment.

What is an integer?

An integer is any number from the set of negative numbers, zero, and positive numbers, with no fractional or decimal part. Examples are -3, -2, -1, 0, 1, 2, 3. A number such as 2.5 is not an integer because it has a fractional part.

Why is -5 smaller than -2?

Because its position on the number line is further left, and further left means smaller. A real-world check: -5 degrees is colder than -2 degrees, and a debt of 5 million is heavier than a debt of 2 million.

What are the sign rules for multiplying integers?

Matching signs give a positive, differing signs give a negative. So negative times negative is positive, while positive times negative is negative. The same rule applies to both multiplication and division.

Why does 5 minus negative 3 equal 8?

Because subtracting a negative is the same as adding. The explanation that makes most sense to a child: cancelling a debt is the same as gaining money. If a debt of 3 thousand is written off, you are 3 thousand better off.

Is zero positive or negative?

Neither. Zero is the boundary between positive and negative numbers and belongs to neither group.

In which year are integers taught?

Negative integers are introduced in Year 6 and deepened in Year 7. The topic matters far beyond primary school, because all of algebra, equations, and calculus stands on fluency with integer operations.

Operations with Integers

Addition and subtraction are easiest to understand as movement along the number line. Adding means moving right, subtracting means moving left.

The hardest part is subtracting a negative. Children struggle to accept that 5 minus negative 3 gives 8, because subtracting ought to make things smaller.

The explanation that makes most sense: cancelling a debt is the same as gaining money. If a debt of 3 thousand is written off, you are 3 thousand better off. That is why subtracting a negative means adding.

Multiplication and division use one sign rule that covers both:

Signs	Result
Positive times positive	Positive
Negative times negative	Positive
Positive times negative	Negative
Negative times positive	Negative

In short: matching signs give a positive, differing signs give a negative. That one sentence replaces the four rows of the table.

The Most Common Mistakes

Treating -5 as greater than -2 because the digit is bigger.
Forgetting to flip the sign when subtracting a negative.
Sign errors in mixed operations with brackets, such as 2 times open bracket x minus 3.
Assuming zero counts as positive.

Mistake number three is the most expensive, because it carries into algebra in Year 7. A student who keeps losing minus signs inside brackets almost always has an integer problem rather than an algebra one.

When It Is Taught at School

Negative integers are introduced in Year 6 and deepened in Year 7. Full topic lists are in Year 6 primary maths and Year 7 secondary maths.

This chapter matters far beyond primary school. All of algebra, equations, and calculus stands on fluency with integers. To check the foundation is solid, a maths assessment of about 60 minutes can show where the gap is.

Blog

More from Blog:

Online Math Tutoring for SMP Students: How to Choose and What to Check in the Trial Class

Learn Math10 min read

Child Behind in Math in Grades 3-6: How to Check and an 8-Week Catch-Up Plan

Parent Guides8 min

Best Classes for Kids by Age: What to Choose at 5, 7, 9 and 12 in Indonesia

Parent Guides11 min read

Algonova worldwide

Algonova Mexico Algonova Malaysia Algonova Global

Contact

Whatsapp: +62 21 50996971

Email: info@algonova.id

Address

Coworking Area, Gedung IT 6 Lantai Dasar, Nongsa Digital Park, Jalan Hang Lekiu, Kelurahan Sambau, Kecamatan Nongsa, Batam, Indonesia Directorate General of Consumer Protection and Trade Compliance – Ministry of Trade of the Republic of Indonesia. WhatsApp Ditjen PKTN: 0853-1111-1010.