How to Calculate Ratios: Direct & Inverse Proportion
Published: 21.05.2026·Updated: 15.10.2026
Nadia Rahmawati
Math Curriculum Team, Algonova
How to calculate a ratio: compare two like quantities as a : b, then simplify by dividing both by their GCD. For example 12 : 8 becomes 3 : 2 after dividing by 4. There are two kinds of problems, direct proportion (a/b = c/d) and inverse proportion (a × b = c × d). It is taught from Year 5 to Year 7 and is also used for map scales.
Direct and Inverse Proportion
Direct: both values rise together (more rice, higher price). Inverse: one rises while the other falls (more workers, fewer days). Ask: if the first value goes up, does the second go up or down?
Worked Examples
Simplify 24 : 36 = 2 : 3.
5 kg of rice costs Rp75,000, so 8 kg costs Rp120,000 (direct).
6 workers take 4 days, so 8 workers take 3 days (inverse).
3 taps fill a pool in 12 hours, so 6 taps take 6 hours (inverse).
Rp600,000 shared 2 : 3 gives Rp240,000 and Rp360,000.
Map Scale as a Ratio
Scale = map distance : real distance. At 1 : 500,000, 1 cm on the map is 5 km. A 4 cm map distance is 20 km. Always convert units first: 1 km = 100,000 cm.
Summary
Simplify with the GCD and choose direct or inverse carefully. Algonova has helped more than 1,000,000 students in 97 countries, with a free 45-minute maths diagnostic.
How to Simplify a Ratio
A ratio is simplified by dividing both numbers by their GCD (greatest common divisor). For example, the ratio 12 : 18 has a GCD of 6, so its simplest form is 2 : 3. A simplified ratio is easier to read and to use in problems about scale, recipes, or sharing, and it does not change the value of the original ratio.
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 45 minute diagnostic session 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 45 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 a ratio in mathematics?
A ratio is a way to compare two or more like quantities, written as a:b or a/b. For example, the ratio of 12 apples to 8 oranges is 12:8 = 3:2. Ratios show up every day in recipes, map scales, and speeds.
What is the difference between direct and inverse proportion?
In a direct proportion, when one value increases the other increases too (e.g. more ingredients → more cakes). In an inverse proportion, when one value increases the other decreases (e.g. more workers → fewer days). The formulas differ: direct is a/b = c/d, inverse is a×b = c×d.
How do you simplify a ratio?
To simplify a ratio a:b, find the greatest common divisor (GCD) of a and b, then divide both by it. Example: 24:36 → GCD = 12 → 24÷12 : 36÷12 = 2:3. A ratio is already in simplest form when the only common factor left is 1.
What is a common mistake when calculating ratios?
The biggest mistake is picking the wrong type of proportion. Before calculating, ask: 'If the first value goes up, does the second go up or down?' If up → direct, if down → inverse. Using the wrong formula leads to the wrong answer.
When are ratios taught in school?
The basic idea of ratios is introduced around grades 5–6, then deepened in grade 7 with direct and inverse proportion. From grade 7 onwards, students start solving word problems and applying ratios to real-life contexts such as speed, price, and population.
Where are ratios used in everyday life?
Ratios are everywhere: map scales (1:50,000 means 1 cm on the map = 500 m on the ground), recipes, currency exchange rates, vehicle speeds, and chemical mixtures. Understanding ratios helps you make smarter everyday decisions.
Other Math Topics
Explore other popular math formulas and how-to guides for SD and SMP students in Indonesia:
Want your child to learn math with an experienced mentor? Try a free Master Class at Algonova — a 60-minute session for a level assessment, at no cost.
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.
PT Algonova Indonesia Cerdas
All rights reserved 2026
