School Skills
Abacus and Vedic maths
Calculating quickly in the head with the abacus and the Vedic methods, and checking the answer.
Suits: School children
Duration, fees and batch timings are quoted by the head office or your centre.
The study book of this course
- Abacus and Vedic Maths
- 1Meet the Abacus
- 2Reading and Setting Numbers
- 3Adding on the Abacus
- 4Subtracting and Seeing Beads in Your Mind
- 5Multiplication and Division Ideas
- 6Welcome to Vedic Maths: Tricks with 11 and Squares of 5
- 7Nikhilam: Multiplying Near 100
- 8Urdhva Tiryagbhyam: Vertical and Crosswise
- 9Checking Answers with Digit Sums (Navashesh)
- 10Speed, Accuracy and Mental Maths Games
- Lessons
- 10
- Practice questions
- 40
- Free ebooks
- 0
About the course
What the abacus and Vedic maths course is about
The abacus makes place value something a child can see and touch. The course teaches reading numbers on the abacus and adding and subtracting on it, then moves to doing the same sums in the mind by picturing the beads.
Vedic maths adds shortcut methods for multiplying and squaring, such as the methods for numbers near 100 and numbers ending in 5, and a way to check answers by digit sums. Speed always comes second to accuracy.
What you will practise
Drawn from the lessons of the study books below.
- 01
Read and set numbers on the abacus using place value
- 02
Add and subtract on the abacus and in the mind
- 03
Multiply by 11 and square numbers ending in 5
- 04
Use base methods for numbers near 100
- 05
Use crosswise multiplication for two-digit numbers
- 06
Check answers using digit sums
What you will learn
10 lessons, 30 exercises
Every lesson of the study book that comes with this course in the student portal, with the key points of each lesson and exercises to try. Your centre gives you the syllabus, the duration and the fee.
Study book
Abacus and Vedic Maths
Learn to read, set and calculate on the abacus with friendly rules, then pick up Vedic maths short-cuts such as multiplying by 11, squaring numbers ending in 5, Nikhilam and vertical and crosswise multiplication, with digit-sum checking and mental maths games.
1Meet the Abacus3 min read · 4 key points · 3 exercises
Key points
- An abacus has a frame, rods, beads and a reckoning bar.
- The upper bead is worth 5 and each lower bead is worth 1.
- Beads count only when they touch the bar.
- One rod shows any digit from 0 to 9.
Try this
- Clear your abacus, then set 3, 5, 7 and 9 on one rod, one after another.
- Draw an abacus rod on paper with a bar, and colour the beads that show the number 8.
- Tell a friend or family member the value of an upper bead and a lower bead, using your own words.
2Reading and Setting Numbers3 min read · 4 key points · 3 exercises
Key points
- The right-most rod is the ones rod, then tens, hundreds and so on.
- The same bead is worth more on a rod further to the left.
- An empty rod shows zero and keeps the other digits in the right place.
- Read a number by adding the beads touching the bar on each rod.
Try this
- Set these numbers on the abacus and say them aloud: 18, 46, 305, 607, 3042.
- Ask a friend to set a number secretly and read it. Swap roles.
- Write the Indian-style number 1,25,000 in words, then show its digits on six rods.
3Adding on the Abacus4 min read · 4 key points · 3 exercises
Key points
- Push beads straight to the bar when there are enough of them.
- Small friends use 5: +4 means +5 - 1.
- Big friends use 10: +9 means +10 - 1, carrying to the next rod.
- Check a sum by adding the numbers in the other order.
Try this
- Do these on the abacus: 3 + 4, 2 + 4, 6 + 3, 7 + 9, 8 + 6.
- Do 36 + 27 and 48 + 35 on the abacus. Check with pencil and paper.
- Write the small-friend and big-friend rules in your notebook as a chart you can look at while you practise.
4Subtracting and Seeing Beads in Your Mind4 min read · 4 key points · 3 exercises
Key points
- To subtract, move beads away from the bar, using 5 or 10 when beads are missing.
- -4 means -5 + 1, and -7 means -10 + 3 (borrowing from the next rod).
- Check a subtraction by adding the answer back to the smaller number.
- Mental abacus means picturing the beads and moving your fingers in the air.
Try this
- Do these on the abacus: 8 - 3, 6 - 4, 13 - 7, 52 - 27, 100 - 36.
- Check each answer by adding it back, for example 25 + 27 = 52.
- Close your eyes and picture the number 47 on the abacus. Describe aloud which beads are touching the bar.
5Multiplication and Division Ideas4 min read · 4 key points · 3 exercises
Key points
- Multiplication is repeated addition; division is equal sharing.
- Splitting a number into tens and ones makes multiplication and division easy.
- Multiplying by 5 is halving then multiplying by 10; multiplying by 25 is dividing by 4 then multiplying by 100.
- Multiplication and division check each other.
Try this
- Use the split method to work out 23 × 4, 46 × 3 and 52 × 6. Check with a calculator or paper.
- Do 84 ÷ 4, 96 ÷ 6 and 72 ÷ 3 by splitting.
- Write the 9 times table up to 9 × 10 and circle the digit-sum pattern.
6Welcome to Vedic Maths: Tricks with 11 and Squares of 54 min read · 4 key points · 3 exercises
Key points
- Vedic maths gives short-cut ways to calculate, collected as sutras.
- To multiply by 11: first digit, sum of the two digits, last digit (carry if needed).
- To square a number ending in 5: multiply the front digits by the next number, then write 25.
- Always check a trick answer with another method at first.
Try this
- Use the 11 trick for 23, 45, 62, 78 and 99.
- Square 25, 45, 55, 65 and 95 with the 5 trick and check two of them by long multiplication.
- Explain to a friend, in your own words, why you carry 1 when the middle sum is 10 or more.
7Nikhilam: Multiplying Near 1004 min read · 4 key points · 3 exercises
Key points
- Nikhilam works by using the distance of each number from a base such as 100.
- Below the base: subtract crosswise and multiply the deficits.
- Above the base: add crosswise and multiply the excesses.
- In base 100 the right part must have two digits, so add a leading zero when needed.
Try this
- Work out 97 × 96, 98 × 94 and 95 × 97 with Nikhilam and check each by another method.
- Do 104 × 107 and 102 × 103 using the excess method.
- Make up three of your own multiplications near 100 and swap them with a friend for checking.
8Urdhva Tiryagbhyam: Vertical and Crosswise4 min read · 4 key points · 3 exercises
Key points
- Urdhva Tiryagbhyam means vertically and crosswise and works for any numbers.
- For two digits: ones times ones, then the cross products added, then tens times tens.
- Carry the tens digit of each step into the next step.
- Choose the method to suit the numbers: near 100, ending in 5, or general.
Try this
- Use the method for 23 × 14, 12 × 13, 31 × 42 and 25 × 16. Check each with the long method.
- Write the three steps in your own words on a small card to keep in your pencil box.
- Pick three pairs of two-digit numbers, multiply them, then ask a partner to check with a calculator.
9Checking Answers with Digit Sums (Navashesh)3 min read · 4 key points · 3 exercises
Key points
- The digit sum is found by adding digits until one digit remains.
- For multiplication, multiply the digit sums, reduce, and compare with the digit sum of the answer.
- A mismatch means the answer is definitely wrong; a match means probably right.
- The check cannot catch swapped digits or mistakes that are multiples of 9.
Try this
- Find the digit sums of 456, 678, 1234 and 9999.
- Use the digit-sum check on 23 × 14 = 322, 12 × 13 = 156 and 31 × 42 = 1302.
- Make up three sums with a deliberate mistake, swap with a friend and see who finds them first.
10Speed, Accuracy and Mental Maths Games4 min read · 4 key points · 3 exercises
Key points
- Accuracy comes before speed, and speed follows from good habits.
- Estimate first, write neatly and check every answer.
- Doubling and halving, rounding and adjusting and friendly numbers speed up mental sums.
- Games and daily short practice keep skills sharp.
Try this
- Estimate and then calculate 49 × 21, 98 + 47 and 49 × 6.
- Play "Beat the table" with a partner for five minutes and note your score.
- Make a weekly practice chart with ten minutes a day for seven days and tick each day you finish.
Glossary: 25 key terms of Abacus and Vedic Maths
- Abacus
- A frame with rods and beads used to show numbers and do sums.
- Rod
- A thin upright stick on the abacus that stands for one place value.
- Bead
- A round piece that slides on a rod and counts when it touches the bar.
- Reckoning bar
- The bar across the middle of the abacus that separates upper and lower beads.
- Upper bead
- The single bead above the bar, worth 5.
- Lower bead
- One of the four beads below the bar, each worth 1.
- Place value
- The value of a digit that depends on its place: ones, tens, hundreds and so on.
- Digit
- One of the numerals 0 to 9.
- Small friends
- Abacus moves that use 5 when lower beads are not enough, such as +4 = +5 - 1.
- Big friends
- Abacus moves that use 10 and a carry, such as +9 = +10 - 1.
- Mental abacus
- Picturing the abacus in your mind and moving imaginary beads to calculate.
- Product
- The answer to a multiplication.
- Quotient
- The answer to a division.
- Remainder
- What is left over after dividing as equally as possible.
- Vedic mathematics
- A set of short-cut calculation methods collected as sutras.
- Sutra
- A short sentence or rule that holds a big idea.
- Ekadhikena Purvena
- The sutra "one more than the one before", used for squaring numbers ending in 5.
- Nikhilam
- The sutra "all from 9 and the last from 10", used to multiply numbers near a base.
- Base
- A round number such as 10, 100 or 1000 that numbers are compared with.
- Deficit
- How far a number is below the base.
- Excess
- How far a number is above the base.
- Urdhva Tiryagbhyam
- The sutra "vertically and crosswise", a method to multiply any numbers.
- Digit sum
- The single digit you get by adding the digits of a number again and again.
- Navashesh
- The nine-remainder or digit-sum method of checking calculations.
- Estimate
- A quick, rounded guess that is close to the real answer.
Practice and study material
Study books and timed practice tests in the student portal
Students sign in to read the study books lesson by lesson, print them, mark lessons as done and test themselves with timed practice tests, every answer explained.
- 1study book
- 10lessons
- 40practice questions
- 25glossary terms
How the practice tests work
- Fresh questions each time
Up to 20 questions are picked at random from the subject’s question bank.
- One minute per question
A timer counts down. When it reaches zero, your answers are sent automatically.
- Move around freely
Skip a question, flag it, and come back to change your answer before you submit.
- Learn from every answer
At the end you see the right answer and an explanation for each question.
- Read, print and keep track
Each study book has its lessons, key points, exercises and a glossary. Print a lesson, or mark it as done.
Your centre gives you your login when you enrol.
Try 3 practice questions
Real questions from this course’s question banks. Pick an answer to see the explanation.
What should you do before calculating a long sum?
Show the answer
Answer: A. Make a quick estimate
An estimate tells you whether your final answer is sensible.
How do you add 9 using a big friend?
Show the answer
Answer: C. Add 10 and take away 1
+9 is the same as +10 - 1.
What is 35 × 35?
Show the answer
Answer: B. 1225
3 × 4 = 12, then 25 gives 1225.
Careers
Careers this course leads towards
The kind of work these skills are used for. Each guide explains what the job involves, the skills it asks for and how to get started.
Accounts assistant (Tally)
Entering sales, purchases and payments, keeping GST records and preparing the reports a business owner or accountant asks for.
Free calculators
Useful calculators
Free tools that go with this course. They work in your browser, on a phone or a computer.
Percentage and marks calculator
Work out the percentage of your marks in a test or across a whole marksheet.
How admission works
From your first question to your certificate.
The usual steps, at the head office in Delhi or at an authorised member centre.
- Who can join
- School children
- Where
- The Delhi head office and authorised member centres.
- Fees and timings
- On WhatsApp at +91 97116 99511, or by phone on 011 2721 1512.
- 1
Ask about the course
Call or WhatsApp the head office, or visit your nearest member centre. Ask for the duration, the fee and the batch timings in writing.
- 2
Fill the admission form
Admission forms are supplied by the head office to every centre.
- 3
Learn in class
Attend your batch at the centre, with the course material and study notes, and sign in to the student portal for the study books and practice tests.
- 4
Take the exam
The institute prefers written exams, taken in front of a teacher.
- 5
Receive your certificate
Students who pass get a Gurukul Technicals Institute certificate and marksheet. Employers can verify it with the head office.
Who can join the abacus and Vedic maths course?
School children. Ask the head office or your nearest member centre which group your child should join, and what they already know will help them start in the right place.
How long is the course and what is the fee?
Duration, fees and batch timings depend on the course and the centre. Ask the head office or your nearest member centre, and get the details in writing before you pay.
Where are the classes?
At the head office in Delhi (A-10, Chief Commissioner Colony, opposite Rana Pratap Bagh) and at authorised member centres. Call or WhatsApp the head office to find the nearest centre.
What do I need to use the study books and practice tests?
A phone or a computer with an internet connection, and the login your centre gives you at enrolment. The student portal opens in an ordinary web browser, so there is nothing to install. Student login.
How do the practice tests work?
Sign in to the student portal and choose a subject. Each test picks up to 20 questions at random from that subject’s question bank and gives you one minute per question, with a timer that sends your answers automatically when it reaches zero. You can skip a question, flag it and come back before you submit, and at the end you see the right answer and an explanation for every question. This course has 40 practice questions across 1 subject, and you can take the tests as often as you like.
Is there an exam and a certificate?
Yes. The institute prefers written exams, taken in front of a teacher. Students who pass receive a Gurukul Technicals Institute certificate and marksheet.
How is a Gurukul Technicals Institute certificate verified?
On the verify certificate page, anyone can enter a certificate number and check it against the institute’s online register, which covers certificates issued through the portal. For older certificates, or if there is any doubt, send a copy to the head office by email or WhatsApp; the reply comes within 2 working days.
Ready to start the abacus and Vedic maths course?
Ask the head office for the duration, the fee, the batch timings and your nearest member centre.