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
Week 12 Week 13: Vertically & Crosswise Week 14

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
2
3

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:
2
3
1
4

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

B
D
Step 2: (A×D)+(B×C)

Cross multiplication

A
B

C
D
Step 3: A×C

Tens place result

A
C
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:

  1. The 3-step pattern for 2-digit multiplication
  2. How to multiply vertically (units × units, tens × tens)
  3. How to multiply crosswise and add
  4. Carry management techniques
  5. 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.

About this lesson (Week 13)

Week 13 is part of our free 48-week Vedic Mathematics course for children ages 8–14 at Nikhil Learn Hub. Vedic Maths uses ancient Indian sutras to make mental math faster, clearer, and more fun than traditional methods alone.

For parents & teachers: Read the lesson with your child, try the examples aloud, and use the practice section before moving to Week 14.

Course Hub Week 12 Week 14 Math Puzzles
What is Vedic Mathematics?

A system of mental math techniques from ancient Indian texts, popularized for speed in addition, multiplication, division, squares, and more.

Week 12

Completed: Vertically & Crosswise Introduction

Foundation Multiplication Mastered!
Continue to Week 14

Frequently Asked Questions (Week 13)

Week 13 is one step in our 48-week Vedic Maths path. It includes explanations, worked examples, and practice for this topic. Read the lesson, try every example, then use practice before Week 14.

Plan about 45-60 minutes total, or two shorter sessions of 25-30 minutes. Small, regular practice works best for mental math.

Yes. Week 13 builds on earlier lessons. Finish Week 12 practice first when possible.

It suits curious learners ages 8-14 who know basic school arithmetic. If a step feels hard, review the hub or an earlier week.

Sit together for the first examples, ask your child to explain each trick in their own words, and celebrate correct mental steps. Use the Course Hub link above to jump between weeks.