Multiplication and Division Chapter Notes | Mathematics for Grade 4 PDF Download

Introduction

Mathematics is like a fun puzzle, and multiplication and division are two exciting pieces that help us solve bigger challenges! In this chapter, we dive into the world of large numbers, learning how to multiply and divide them with ease. From building multiplication tables to breaking down division problems, these skills will make you a math wizard. Let’s explore how to multiply big numbers, divide them accurately, estimate answers quickly, and solve real-world problems using these operations. Get ready for a number adventure!

Multiplication

• Multiplication is adding the same number multiple times.
• It involves a multiplicand (the number being multiplied) and a multiplier (the number of times to multiply).
• The result is called the product.
• To multiply, arrange numbers in columns and start multiplying from the ones place.

Example: Multiply 2,169 by 57.

• Step 1: Multiply 2,169 by 7 (ones place of multiplier): 2,169 × 7 = 15,183.

• Step 2: Multiply 2,169 by 50 (5 tens): 2,169 × 50 = 1,08,450.

• Step 3: Add the products: 15,183 + 1,08,450 = 1,23,633.

Multiplication Tables

• Multiplication tables help us multiply numbers quickly.
• We can create tables for numbers 11 to 20 using methods like repeated addiqtion, skip counting, or adding 1 to 10.
• Repeated addition involves adding a number multiple times to build the table.

Example: Construct the table of 11 using repeated addition.

• Step 1: Add 11 repeatedly for each multiple.
• 1 time: 11 × 1 = 11.
• 2 times: 11 + 11 = 22 (11 × 2 = 22).
• 3 times: 11 + 11 + 11 = 33 (11 × 3 = 33).
• Continue up to 10:11 × 10 = 110.
  

Multiplication of Large Numbers by 2-Digit, 3-Digit and 4-Digit Numbers (Long Multiplication Method)

• Long multiplication is used for numbers larger than 10.
• Write the larger number as the multiplicand and the smaller as the multiplier.
• Multiply the multiplicand by each digit of the multiplier, starting from the ones place.
• Add the partial products to get the final product.

Example: Multiply 4,396 by 158.

• Step 1: Multiply 4,396 by 8: 4,396 × 8 = 35,168.
• Step 2: Multiply 4,396 by 50: 4,396 × 50 = 2,19,800.
• Step 3: Multiply 4,396 by 100: 4,396 × 100 = 4,39,600.
• Step 4: Add: 35,168 + 2,19,800 + 4,39,600 = 6,94,568.

Multiplication by a Multiplier Ending with Zero

• Multiplying by 10, 100, or 1,000 is simpler due to their zeros.
• For 10, add one zero to the multiplicand.
• For multiples of 10, multiply by the non-zero part and add one zero.
• For 100, add two zeros to the multiplicand.
• For multiples of 100, multiply by the non-zero part and add two zeros.
• For 1,000, add three zeros to the multiplicand.
• For multiples of 1,000, multiply by the non-zero part and add three zeros.

Example: Find the products: 
(a) 7,645 × 10, 
(b) 7,215 × 2,000.

• (a) 7,645 × 10: Add one zero to 7,645 = 76,450.
• (b) 7,215 × 2,000: First, 7,215 × 2 = 14,430, then add three zeros = 1,44,30,000.

Lattice Multiplication

• Lattice multiplication uses a grid to multiply large numbers.
• Create a grid with rows for the multiplicand and columns for the multiplier.
• Multiply each pair of digits, write results in the grid, and add along diagonals.
• Sum the diagonal totals to get the final product.

Example: Multiply 5,479 by 678 using lattice multiplication.

• Step 1: Create a grid with 5,479 (4 digits) and 678 (3 digits).
• Step 2: Multiply each digit pair and place results in the grid cells.
• Step 3: Add along diagonals to get partial sums.
• Step 4: Combine sums to get 37,14,762.

• Verify with long multiplication:

  

Multiplication by Expanded Form

• Break both numbers into their place value parts (expanded form).
• Multiply each part of the multiplicand by each part of the multiplier.
• Add all partial products to get the final result.

Example: Multiply 1,618 × 25 using expanded form.

• Step 1: Expand: 1,618 = 1,000 + 600 + 10 + 8, 25 = 20 + 5.
• Step 2: Multiply: (20 × 1,000) + (20 × 600) + (20 × 10) + (20 × 8) + (5 × 1,000) + (5 × 600) + (5 × 10) + (5 × 8).
• Step 3: Calculate: 20,000 + 12,000 + 200 + 160 + 5,000 + 3,000 + 50 + 40 = 40,450.
• Verify with long multiplication:
  

Estimating the Product

• Estimating gives an approximate product by rounding numbers.
• Round both numbers to the nearest 10, 100, or 1,000.
• Multiply the rounded numbers for a quick estimate.
• The result is close but not exact.

Example: Estimate 3,075 × 216 by rounding to the nearest 100.

• Step 1: Round 3,075 to 3,100 and 216 to 200.
• Step 2: Multiply: 3,100 × 200 = 6,20,000.

Word Problems on Multiplication

• Word problems use multiplication to solve real-life scenarios.
• Identify the numbers to multiply based on the problem’s context.
• Multiply the numbers to find the solution.

Example: A factory produces 6,492 cushions in a week. How many in 12 weeks?

• Step 1: Identify numbers: 6,492 cushions per week, 12 weeks.
• Step 2: Multiply: 6,492 × 12 = 77,904.
• Answer: 77,904 cushions.

Framing Word Problems on Multiplication

• Create word problems by describing a scenario needing multiplication.
• Include two numbers and a context where one is multiplied by the other.
• Solve by multiplying the numbers.

Example: Frame two word problems for 2,500 × 31.

• Problem 1: A garden has 2,500 flowers. If there are 31 gardens, how many flowers in all?
• Problem 2: Amaya earns ₹2,500 daily. How much for 31 days?
• Solution: 2,500 × 31 = 77,500 (flowers or rupees).

Division

• Division is repeated subtraction or splitting into equal parts.
• It is the opposite of multiplication.
• Terms: dividend (number to divide), divisor (number to divide by), quotient (result), remainder (leftover).

Example: Divide 225 by 15.

• Step 1: Check if 22 > 15. Divide 22 by 15: 15 × 1 = 15, subtract 22 − 15 = 7.
• Step 2: Bring down 5 to make 75. Divide 75 by 15: 15 × 5 = 75, subtract 75 − 75 = 0.
• Quotient = 15, Remainder = 0.

Division of 3-Digit and 4-Digit Numbers by a 2-Digit Number

• Divide larger numbers using long division.
• Start with the first two digits of the dividend if the divisor is 2-digit.
• Find how many times the divisor fits, subtract, and bring down the next digit.
• Continue until all digits are processed.
• Check: Dividend = (Divisor × Quotient) + Remainder.

Example: Divide 249 by 14.

• Step 1: Divide 24 by 14: 14 × 1 = 14, subtract 24 − 14 = 10.
• Step 2: Bring down 9 to make 109. Divide 109 by 14: 14 × 7 = 98, subtract 109 − 98 = 11.
• Quotient = 17, Remainder = 11.
• Check: (14 × 17) + 11 = 238 + 11 = 249.

Division of a Number by 10, 100 and 1,000

• Dividing by 10: Ones digit is the remainder, rest is the quotient.
• Dividing by 100: Tens and ones digits form the remainder, rest is the quotient.
• Dividing by 1,000: Hundreds, tens, and ones digits form the remainder, rest is the quotient.

Example: Divide 2,046 by 10, 5,048 by 100, 3,204 by 1,000.

• (a) 2,046 ÷ 10: Quotient = 204, Remainder = 6.
• (b) 5,048 ÷ 100: Quotient = 50, Remainder = 48.
• (c) 3,204 ÷ 1,000: Quotient = 3, Remainder = 204.

Division of Numbers when Both the Dividend and Divisor End with Zeros

• Cancel equal numbers of zeros from both dividend and divisor.
• Divide the remaining numbers.
• Add zeros back to the remainder, if any.

Example: Divide 6,300 by 500.

• Step 1: Cancel two zeros: 6,300 ÷ 500 = 63 ÷ 5.
• Step 2: Divide 63 by 5: Quotient = 12, Remainder = 3.
• Step 3: Add two zeros to remainder: Remainder = 300.

Division by Breaking a Number and then Dividing

• Break the dividend into place value parts (expanded form).
• Divide each part by the divisor.
• Add the quotients to get the final quotient.
• Verify using long division.

Example: Divide 8,750 by 25.

• Step 1: Expand 8,750 = 8,000 + 700 + 50.
• Step 2: Divide each: 8,000 ÷ 25 = 320, 700 ÷ 25 = 28, 50 ÷ 25 = 2.
• Step 3: Add quotients: 320 + 28 + 2 = 350.
• Verify:

Estimating the Quotient

• Round the dividend and divisor to the nearest 10.
• Divide the rounded numbers to get an approximate quotient.

Example: Estimate 8,346 ÷ 17.

• Step 1: Round 8,346 to 8,350, 17 to 20.
• Step 2: Divide 8,350 ÷ 20 = 417.

Word Problems on Division

• Identify the total quantity (dividend) and the number of groups or units (divisor).
• Divide to find the amount per group or unit.
• If there’s a remainder, consider if an extra group is needed.

Example: A baker bakes 876 cookies and packs them in boxes of 45. How many boxes?

• Step 1: Divide 876 ÷ 45 = 19, Remainder = 21.
• Step 2: Since 21 cookies remain, add 1 more box.
• Answer: 19 + 1 = 20 boxes.

Framing Word Problems on Division

• Create a scenario where a total is divided into equal parts.
• Include the dividend and divisor in the context.
• Solve by dividing.

Example: Frame a word problem for 6,250 ÷ 25.

• Problem: If 25 school bags cost ₹6,250, how much per bag?
• Solution: 6,250 ÷ 25 = 250.
• Answer: ₹250 per bag.

Word Problems including both Multiplication and Division

• Solve problems requiring both operations.
• First, divide to find a unit rate if needed.
• Then, multiply to find the total for a new quantity.

Example: A baker sells 2,820 buns in 12 days. How many in 26 days?

• Step 1: Find buns per day: 2,820 ÷ 12 = 235.
• Step 2: Multiply for 26 days: 235 × 26 = 6,110.
• Answer: 6,110 buns.

Solving Problems Using the Four Operations

• Use addition, subtraction, multiplication, and division in problems.
• Follow the BODMAS rule: Division, Multiplication, Addition, Subtraction (Brackets and Of are learned later).

Example: Solve 12 ÷ 3 × 2 + 8 − 3.

• Step 1: Divide: 12 ÷ 3 = 4.
• Step 2: Multiply: 4 × 2 = 8.
• Step 3: Add: 8 + 8 = 16.
• Step 4: Subtract: 16 − 3 = 13.
• Answer: 13.