Week 13: Vertically & Crosswise Introduction

Foundation Level • Estimated: 60 minutes

Lesson 13 of 48

Vertically & Crosswise Multiplication

2-digit Multiplication Mental Math Vedic Patterns Cross Multiplication Instant Calculation

The Revolutionary Multiplication Technique

Welcome to Week 13 of your Vedic Mathematics journey! This week, you'll learn one of the most powerful Vedic techniques: Vertically & Crosswise (Urdhva Tiryagbhyam). This method will transform how you multiply forever!

Why This Technique is Magical?

No Carrying Over: Write digits directly in answer
Mental Calculation: Solve without paper and pen
Pattern Based: Follow simple visual patterns

Works for All Digits: 2-digit, 3-digit, even larger
Error Reduction: Fewer steps, fewer mistakes
Speed: 3-5x faster than traditional method

The Sutra: Urdhva Tiryagbhyam

"Vertically and Crosswise"

(Urdhva = Vertical, Tiryagbhyam = Crosswise)

Vertical Multiplication

Multiply units × units (right-most digits)

Result gives right-most digit of answer

Crosswise Multiplication

Cross multiply: tens × units + units × tens

Result gives middle digit of answer

The 3-Step Vertically & Crosswise Framework

Step 1: Vertically (Right)

Multiply the right-most digits (units × units)

Right Digit

Example: 23 × 14

3 × 4 = 12

Write 2, carry 1

Step 2: Crosswise (Middle)

Cross multiply and add (tens×units + units×tens)

Middle Digit

Example: 23 × 14

(2×4) + (3×1) = 8+3 = 11

Add carry from Step 1

Step 3: Vertically (Left)

Multiply the left-most digits (tens × tens)

Left Digit

Example: 23 × 14

2 × 1 = 2

Add carry from Step 2

Example 1: Basic 2-digit Multiplication

Multiply: 23 × 14 Step-by-Step

23 × 14 = ?

Traditional Method:

23 × 14 = ?

23 × 4 = 92

23 × 10 = 230

92 + 230 = 322

Answer: 322

4 steps, requires carrying over

Vedic Vertically & Crosswise:

Step 1 (Right): 3 × 4 = 12

Write 2, carry 1

Step 2 (Crosswise): (2×4) + (3×1) = 8+3 = 11

Add carry 1: 11+1=12

Write 2, carry 1

Step 3 (Left): 2 × 1 = 2

Add carry 1: 2+1=3

Answer: 322 (written from left: 3 2 2)

Visual Pattern:

Step 1: 3 × 4 = 12

Step 2: (2×4) + (3×1) = 8+3 = 11

Step 3: 2 × 1 = 2

Example 2: Managing Carries

Multiply: 47 × 38 Carry Management

47 × 38 = ?

Vedic Solution Step-by-Step:

Step 1 (Right): 7 × 8 = 56

Write 6, carry 5

Answer so far: _ _ 6

Step 2 (Crosswise): (4×8) + (7×3) = 32 + 21 = 53

Add carry 5: 53 + 5 = 58

Write 8, carry 5

Answer so far: _ 8 6

Step 3 (Left): 4 × 3 = 12

Add carry 5: 12 + 5 = 17

Write 17

Final Answer: 1 7 8 6

47 × 38 = 1,786

The Visual Pattern

Pattern Recognition Visual Learning

For multiplication: AB × CD

A B
C D
Step 3 A×C	Step 2 (A×D)+(B×C)
	Step 1 B×D

Step 1: B×D

Units place result

Step 2: (A×D)+(B×C)

Cross multiplication

Step 3: A×C

Tens place result

Pro Tip: Mentally visualize the digits in positions. With practice, you can multiply 2-digit numbers in under 10 seconds!

Practice Arena

Speed Challenge

Try these multiplications using Vertically & Crosswise:

Problem 1

24 × 13

Problem 2

56 × 27

Problem 3

89 × 46

Speed Test

Time yourself: How many can you solve in 2 minutes?

32 × 15

Click for answer

47 × 29

Click for answer

63 × 54

Click for answer

Tips & Patterns

Special Cases

Same Tens Digit: When tens digits are same (e.g., 43×47), pattern simplifies

Ending in 5: Numbers ending in 5 have special patterns

Close to 100: Use base method for numbers close to 100

One number ends in 9: Convert to easier multiplication

This Week's Mastery Goals

Understand the 3-step Vertically & Crosswise pattern
Multiply any 2-digit numbers mentally
Manage carries efficiently
Visualize the multiplication pattern
Solve 10 practice problems with 90% accuracy

Multiplication Master Badge

Unlocks after mastering 2-digit multiplication

Vertically & Crosswise Review

This week you learned:

The 3-step pattern for 2-digit multiplication
How to multiply vertically (units × units, tens × tens)
How to multiply crosswise and add
Carry management techniques
The visual pattern for mental calculation

Multiplication Revolution! You can now multiply 2-digit numbers faster than ever before. Practice daily to build speed and confidence.