Multiplication Chapter Notes | Mathematics Class 4 ICSE PDF Download

Introduction

Multiplication is like a magic trick in mathematics that helps us combine groups of numbers quickly! Imagine you have several boxes, each containing the same number of candies. Instead of counting each candy one by one, multiplication allows us to find the total number of candies in a snap. This chapter will take you on an exciting journey through multiplication tables, grids, and methods like lattice multiplication, making it easy to solve real-world problems, such as calculating the total number of items in multiple groups. Get ready to discover how multiplication makes math fun and efficient!

Constructing Tables

• Multiplication tables can be built using different methods like repeated addition, skip counting, or adding numbers from 1 to 10.
• Repeated addition involves adding a number to itself multiple times to find the product.
• Skip counting means counting by a specific number to create the table.
• Adding 1 to 10 involves using the table of a previous number and adding the next numbers to get the new table.

Multiplication Tables in a Grid

• A multiplication grid helps find the product of two numbers by locating their intersection.
• Numbers from 1 to 10 are written horizontally (top row) and vertically (first column).
• Steps to fill the grid:
  • Step 1: Take the multiplier from the first column and the multiplicand from the first row, multiply, and write the product where they intersect.
• 
  • Step 2: Repeat for the next multiplier and multiplicands to fill the next column.
  • Step 3: Continue until all columns are filled by multiplying each pair of numbers.

• The product of any two numbers (1 to 10) can be found at their intersection point.

Multiplication Facts

• Numbers can be multiplied in any order, and the product remains the same (commutative property).
• Multiplying any number by 0 gives 0.
• Multiplying any number by 1 gives the number itself.

Multiplication by Numbers Ending with Zero

Multiplication by a Number Ending with One Zero

• To multiply by 10, add one zero to the multiplicand.
• For numbers like 20, 30, 40, etc., add a zero to the multiplicand, then multiply by the non-zero digit(s) and place the result before the zero.

Multiplication by a Number Ending with Two or Three Zeros

• To multiply by 100, add two zeros to the multiplicand.
• For numbers like 200, 300, 400, etc., add two zeros, then multiply by the non-zero digit(s) and place the result before the zeros.

Multiplication of Numbers (without carry over)

Steps to multiply without carry over

• Step 1: Multiply the multiplicand by the ones digit of the multiplier.
• Step 2: Multiply the multiplicand by the tens digit of the multiplier, adding a zero to the result.
• Step 3: Add the products from steps 1 and 2 to get the final result.

Multiplication of Numbers (with carry over)

• Multiplication with carry over involves handling digits that exceed 9 in a place value, carrying over the excess to the next place.
• Steps:
  • Step 1: Multiply the multiplicand by the ones digit of the multiplier, carrying over any tens to the next place value.
  • Step 2: Multiply the multiplicand by the tens digit of the multiplier, adding a zero to the result, and carry over any tens as needed.
  • Step 3: Add the products from steps 1 and 2 to get the final result.

Lattice Multiplication

• Lattice multiplication uses a grid to break multiplication into smaller steps.
• Steps:
  • Step 1: Draw a grid based on the number of digits in the multiplicand and multiplier.
  • Step 2: Write the multiplicand on top and the multiplier on the right side of the grid.
  • Step 3: Multiply each digit of the multiplicand by each digit of the multiplier, placing the tens digit above and the ones digit below the diagonal in each cell.
  • Step 4: Add the numbers diagonally, carrying over tens to the next diagonal if needed.
  • Step 5: Read the sum from left to right to get the final product.

Solving Word Problems

• Word problems involve translating real-life situations into multiplication problems.
• Steps:
  • Step 1: Identify the numbers to multiply (e.g., quantity per group and number of groups).
  • Step 2: Multiply the numbers to find the total.
  • Step 3: Write the final answer with proper units.

Framing Word Problems

• Create word problems by describing a situation that involves multiplication.
• Include the numbers to be multiplied and a context that makes sense for the calculation.

Mixed Problems

• Mixed problems combine multiplication with other operations like subtraction to solve real-life scenarios.
• Steps:
  • Step 1: Identify the total quantity and the part that involves multiplication.
  • Step 2: Perform the multiplication to find the partial quantity.
  • Step 3: Subtract the partial quantity from the total to find the remaining amount.

Multiplication by Expanded Form

• Expanded form breaks a number into its place values (e.g., hundreds, tens, ones) before multiplying.
• Steps:
  • Step 1: Write the multiplicand in expanded form.
  • Step 2: Multiply each part by the multiplier.
  • Step 3: Add the products to get the final result.

Estimating Product of Two Numbers

• Estimation involves rounding numbers to the nearest 10, 100, or 1,000 to find an approximate product.
• Steps:
  • Step 1: Round both numbers to the nearest 10, 100, or 1,000.
  • Step 2: Multiply the rounded numbers to get the estimated product.
  • Step 3: Compare with the actual product for verification.