Simple Multiplication Near Base Numbers Vedic Maths Tricks for Class 5

What is Near Base multiplication?

The base in Vedic maths is the landmark number, which is a power of 10 (e.g., 10, 100, or higher). This technique uses specific calculation parameters to perform multiplication between numbers located just below or above other reference points. Avoid performing "long multiplication" – the typical step-by-step method you may know for dealing with large digits – but focus entirely on how far each number is from its nearest base.

In this manner, it directly employs a well-known Vedic Maths sutra called 'Nikhilam Navatashcaramam Dashatah', which means 'all from 9 and the last from 10'. By employing these rapid calculation strategies, students divide a seemingly complicated multiplication problem into two very simple steps: adding or subtracting small numbers and single-digit multiplication. 

Simple Multiplication Near Base Vedic Maths Tricks

For example, to learn simple multiplication tricks in near-base Vedic maths, divide the numbers based on their relative positions with respect to the nearest power of 10. Class 5 pupils regularly encounter two kinds of numbers: those less than the base and those greater than it.

Numbers Below the Base (e.g., Base 100)

Let us explore how to multiply two numbers that are slightly less than 100, such as 95 and 96.

Example: Multiply 95 by 96

Step 1: Identify the Base and Find Deviations

• The nearest power of 10 for both numbers is 100. Now, find out how much each number is short of 100.

• 95 is 5 short of 100, so its deviation is -5.

• 96 is 4 short of 100, so its deviation is -4.

Step 2: Divide Your Answer Space

Imagine a column in your mind, splitting your answer into a left-hand side (LHS) and a right-hand side (RHS).

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Step 3: Calculate the Right-Hand Side (RHS)

• Multiply the two deviations together.

• Multiply -5 by -4, which equals 20.

• Because base 100 has exactly two zeros, the RHS must occupy two digit places. Here, 20 fits perfectly.

Step 4: Calculate the Left-Hand Side (LHS)

• Cross-subtract the deviation of the second number from the first number, or vice versa. The result is always the same.

• Subtract 4 from 95 to get 91. Alternatively, subtract 5 from 96 to get 91.

Step 5: Combine the Parts

• Join the LHS and the RHS together to get the final result.

• Combining 91 and 20 gives 9120. Therefore, 95 multiplied by 96 equals 9120.

Read More - Mental Division Tricks for Class 5

Numbers Above the Base (e.g., Base 100)

So now, how can we deal with the numbers that exceed our base? So now, the process remains almost exactly the same for multiplication; we just cross-add our deviations instead of subtracting them.

Example: Multiply 104 by 108

Step 1: Identify the Base and Find Deviations

• The closest power of 10 is 100. Find out how much higher each number is.

• 104 is 4 above 100, so its deviation is +4.

• 108 is 8 above 100, so its deviation is +8.

Step 2: Calculate the Right-Hand Side (RHS)

• Multiply the positive deviations together.

• Multiply 4 by 8, which equals 32.

• As base 100 has two zeros, our two-digit RHS is 32.

Step 3: Calculate the Left-Hand Side (LHS)

• Cross-add the deviation of one number to the alternate number.

• Add 8 to 104 to get 112. You can also add 4 to 108 to get 112.

Step 4: Combine Both Parts

• Combine 112 and 32 to get your final answer.

• The final product is 11232.

Read More - Fractions to Decimals in Seconds for Class 5

Practise Sheet for Simple Multiplication Near Base Vedic Maths Tricks

The best way to master these Vedic maths tricks of Class 5 is by consistent, daily practice. Use the structured exercises below to develop speed and accuracy. See how many answers you can figure out yourself, doing all the sums using only your brain and mental maths multiplication tricks before looking at the solutions.

Section A: Problems Below Base 100

• Question 1: 97 x 98
  Deviation check: (-3) and (-2). RHS = 06. Remember to maintain two digits for base 100. LHS = 97 - 2 = 95.
  Answer: 9506

• Question 2: 92 x 95
  Deviation check: (-8) and (-5). RHS = 40. LHS = 92 - 5 = 87.
  Answer: 8740

• Question 3: 89 x 97
  Deviation check: (-11) and (-3). RHS = 33. LHS = 89 - 3 = 86.
  Answer: 8633

Section B: Problems Above Base 100

• Question 4: 102 x 105
  Deviation check: (+2) and (+5). RHS = 10. LHS = 102 + 5 = 107.
  Answer: 10710

• Question 5: 103 x 107
  Deviation check: (+3) and (+7). RHS = 21. LHS = 103 + 7 = 110.
  Answer: 11021

• Question 6: 112 x 104
  Deviation check: (+12) and (+4). RHS = 48. LHS = 112 + 4 = 116.
  Answer: 11648

Section C: Advanced Problems (Base 10)

• Question 7: 9 x 8
  Deviation check from Base 10: (-1) and (-2). RHS = 2. Only one digit is needed for base 10 because it has one zero. LHS = 9 - 2 = 7.
  Answer: 72

• Question 8: 13 x 15
  Deviation check from base 10: (+3) and (+5). RHS = 15. Because base 10 allows only one digit on the RHS, keep the 5 and carry the 1 to the LHS. LHS = 13 + 5 = 18. Add the carried digit: 18 + 1 = 19.
  Answer: 195

Benefits of Simple Multiplication Near Base Vedic Maths Tricks

For primary school children, the advantage of moving from fixed textbook steps to continuous Vedic systems is instantaneous.

• Increases Overall Calculation Speed: With these fast calculation methods, kids can answer hard multi-digit questions much faster than traditional methods.

• Minimises Rough Paperwork: Students calculate the answer directly in their heads, without messy margins or cluttering exam paper.

• Enhances Concentration and Memory: When you visualise the deviations while cross-adding numbers, both hemispheres of your brain are in use, which strengthens elementary cognitive skills.

• Boosts Exam Accuracy: When we do traditional borrowing and carrying, it sometimes leads to very few small mistakes. Base methods are more reliable because they are stepwise and allow very little room for mistakes.

• Builds Maths Positivity: When you find easy maths shortcuts, it makes maths feel less like an academic nightmare and more like a fun game. 

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