How to Multiply 2-Digit Numbers Mentally – Step-by-Step Guide for Kids

Ever wanted to impress everyone by solving complex multiplication problems in your head, without needing a pencil or paper? It's not magic; it's mental math—a superpower you can learn! This article is your step-by-step guide to mastering mental multiplication of two-digit numbers. While it might seem challenging initially, a few simple tricks and consistent practice will transform you into a math whiz. Prepare to enhance your brainpower, accelerate problem-solving, and simplify daily calculations. Let's unleash your mental math superpower together!

Tricks to Multiply 2-digit in Mind

There are several ways in which we can multiple a 2 digit number easily. Follow the methods given below along with examples

Method 1: The "Breaking Apart" or Distributive Property Method

This is often the most intuitive starting point. It uses the distributive property of multiplication (ax(b+c)=(axb)+(axc)). You break one of the numbers into its tens and ones components, multiply each part by the other number, and then add the results.

Best for: Most general 2-digit multiplications, especially when one number has small digits (e.g., 12,21,32).

Step-by-Step with Example: 14x32

1. Break Apart One Number: Choose one of the numbers to break into its tens and ones. It's often easier to break apart the smaller number or the one with a 1 or 2 in the tens place.

• Let's break 14 into 10 and 4.

• Our problem becomes: (10+4)x32

2. Multiply the Tens Part: Multiply the "tens" part of the broken number by the other number.

• 10x32=320

• Mentally note: "First part is 320."

3. Multiply the Ones Part: Multiply the "ones" part of the broken number by the other number.

• 4x32

• Break this down further if needed: 4x30=120

• And 4x2=8

• Add them: 120+8=128

• Mentally note: "Second part is 128."

4. Add the Partial Products: Add the results from Step 2 and Step 3.

• 320+128

• Think: 320+100=420

• Then 420+20=440

• Then 440+8=448

Here’s your result: 14x32=448

Also Read - Abacus vs Vedic Math: Which One is Better for Mental Development?

Method 2: The "Cross-Multiplication" (Vertical and Crosswise) Method

Students must know that this method is more advanced and requires good working memory for carry-overs, but it's incredibly fast once mastered. It directly calculates the ones, tens, and hundreds/thousands digits of the answer.

Best for: Experienced mental calculators; very efficient for all 2-digit multiplications.

Step-by-Step with Example: 27x34

Multiply the Ones Digits (Right Side): Multiply the digits in the ones column. This gives you the ones digit of your answer, plus any carry-over.

• 7x4=28

• Mentally note: The last digit is 8. Carry-over 2.

2. Cross-Multiply and Add (The Middle Part): This is the core step. Multiply the outer digits, multiply the inner digits, and add those two products together. Then, add any carry-over from Step 1. This result gives you the tens digit of your answer, plus any new carry-over.

• Outer digits: 2x4=8

• Inner digits: 7x3=21

• Add these products: 8+21=29

• Add the carry-over from Step 1 (2): 29+2=31

• Mentally note: The tens digit is 1. Carry-over 3.

3. Multiply the Tens Digits (Left Side): Multiply the digits in the tens column. Then, add any carry-over from Step 2. This gives you the hundreds/thousands digits of your answer.

• 2x3=6

• Add the carry-over from Step 2 (3): 6+3=9

• Mentally note: The hundreds digit is 9.

4. Combine the Digits: Read the digits from left to right (hundreds, tens, ones).

• Hundreds: 9

• Tens: 1

• Ones: 8

You got your result: 27x34=918

Method 3: Rounding and Adjusting

This method is fantastic when one or both numbers are close to a multiple of 10 (e.g., 19,21,48,52). You round, multiply, and then adjust by adding or subtracting the "extra" multiplication.

Best for: Numbers ending in 8,9,1,2.

Step-by-Step with Example: 38x7 (You can use this for 2-digit x 1-digit too, as a building block for 2-digit x 2-digit)

1. Round One Number: Round one of the numbers to the nearest multiple of 10.

• Round 38 up to 40. (38 is 40−2)

2. Multiply the Rounded Number: Multiply the rounded number by the other number.

• 40x7=280

3. Adjust: Determine how much you over-multiplied (or under-multiplied) and adjust the product.

• Since you multiplied by 40 instead of 38, you multiplied 7 by 2 too many times.

• Calculate this "extra" amount: 2times7=14

• Subtract this extra amount from your product: 280−14=266

Result: 38x7=266

Example for Two 2-Digit Numbers: 49x23

1. Round One Number: Round 49 up to 50. (49 is 50−1)

2. Multiply the Rounded Number:

• 50times23

• Think: 5x23=115

• Add a zero: 1150

3. Adjust:

• You multiplied by 50 instead of 49, so you multiplied 23 by 1 too many times.

• Calculate this "extra": 1x23=23

• Subtract from your product: 1150−23=1127

Your result is: 49x23=1127

Method 4: Doubling and Halving

This strategy is brilliant when one number is even and the other is easily doubled or when you want to create numbers that are easier to multiply (like multiples of 10 or 25).

Best for: When one number is even, especially if halving it multiple times leads to a simpler number, or if doubling the other number creates a multiple of 10 or 100.

Step-by-Step with Example: 16x25

1. Identify Even Number and Halve It: Find an even number and halve it.

• 16 is even. Halve it: 16/2=8

2. Double the Other Number: Double the other number.

• 25x2=50

3. Multiply the New Pair: You now have an equivalent problem that's often easier.

• 8x50=400

4. Repeat if Necessary: If the new pair still has an even number, you can repeat the process.

• (e.g., if you had 8x50, you could do 4x100, then 2x200, etc.)

Result: 16x25=400

Whether you prefer breaking apart numbers or mastering the cross-multiplication trick, the key to becoming a mental math wizard is practice, practice, practice! Don't get discouraged if it feels challenging at first. Embrace the fun of mental math! It's a fantastic skill that not only makes you quicker with numbers but also sharpens your overall problem-solving abilities. Keep practicing, keep challenging yourself, and you'll soon be impressing everyone with your incredible mental math magic!