UK K12 GCSE/A-Level: Year 5 KS2 Mathematics - Multiplication, Long Multiplication

Learning objectives

By the end of this topic, students will be able to:

• Understand the concept of long multiplication and its application in real-life situations
• Recall the correct order of operations in long multiplication (multiplying digits, multiplying numbers, and adding)
• Apply long multiplication to solve problems involving multi-digit numbers and decimals
• Identify and correct common errors in long multiplication
• Explain the concept of the multiplication symbol (?) and its role in long multiplication

Core concepts

Long multiplication is a method of multiplying multi-digit numbers. It involves breaking down the numbers into their place values and multiplying each digit by the other number, then adding the results. The correct order of operations is:

1. Multiply the digits in the ones place
2. Multiply the digits in the tens place
3. Multiply the digits in the hundreds place
4. Multiply the digits in the thousands place
5. Add the results of each multiplication

The multiplication symbol (?) is used to represent the multiplication operation. For example, 4 × 5 = 4-5.

Worked examples

Example 1: Multiplying two single-digit numbers

To multiply 4 and 5, we follow the order of operations:

1. Multiply the digits in the ones place: 4 × 5 = 20
2. Multiply the digits in the tens place: 0 × 5 = 0
3. Add the results: 20 + 0 = 20

Therefore, 4 × 5 = 20.

Example 2: Multiplying a multi-digit number by a single-digit number

To multiply 43 by 5, we follow the order of operations:

1. Multiply the digits in the ones place: 3 × 5 = 15
2. Multiply the digits in the tens place: 4 × 5 = 20
3. Multiply the digits in the hundreds place: 0 × 5 = 0
4. Add the results: 15 + 20 + 0 = 35

Therefore, 43 × 5 = 215.

Example 3: Multiplying two multi-digit numbers

To multiply 43 by 25, we follow the order of operations:

1. Multiply the digits in the ones place: 3 × 5 = 15
2. Multiply the digits in the tens place: 4 × 5 = 20
3. Multiply the digits in the hundreds place: 0 × 5 = 0
4. Multiply the digits in the thousands place: 0 × 5 = 0
5. Add the results: 15 + 20 + 0 + 0 = 35

Therefore, 43 × 25 = 1075.

Common misconceptions

• Students may confuse the order of operations in long multiplication, resulting in incorrect answers.
• Students may forget to multiply the digits in each place value, resulting in incorrect answers.
• Students may not understand the concept of the multiplication symbol (?) and its role in long multiplication.

Exam tips

• Make sure to follow the correct order of operations in long multiplication.
• Double-check your calculations to ensure accuracy.
• Use the multiplication symbol (?) to represent the multiplication operation.
• Practice, practice, practice! Long multiplication takes practice to master.

MCQs with explanations

Question 1: [F]

What is the result of multiplying 4 by 5?

A) 15 B) 20 C) 25 D) 30

Correct answer: B) 20

Why the distractors fail: A) 15 is the result of multiplying 3 by 5, not 4 by 5. C) 25 is the result of multiplying 5 by 5, not 4 by 5. D) 30 is the result of multiplying 6 by 5, not 4 by 5.

Question 2: [H]

What is the result of multiplying 43 by 25?

A) 1075 B) 1070 C) 1080 D) 1090

Correct answer: A) 1075

Why the distractors fail: B) 1070 is the result of multiplying 43 by 20, not 25. C) 1080 is the result of multiplying 43 by 30, not 25. D) 1090 is the result of multiplying 43 by 35, not 25.

Question 3: [F]

What is the result of multiplying 4 by 0?

A) 0 B) 4 C) 10 D) 20

Correct answer: A) 0

Why the distractors fail: B) 4 is the result of multiplying 1 by 4, not 4 by 0. C) 10 is the result of multiplying 2 by 5, not 4 by 0. D) 20 is the result of multiplying 4 by 5, not 4 by 0.

Question 4: [H]

What is the result of multiplying 43 by 5?

A) 215 B) 210 C) 220 D) 230

Correct answer: A) 215

Why the distractors fail: B) 210 is the result of multiplying 40 by 5, not 43 by 5. C) 220 is the result of multiplying 45 by 5, not 43 by 5. D) 230 is the result of multiplying 50 by 5, not 43 by 5.

Question 5: [F]

What is the result of multiplying 3 by 5?

A) 10 B) 15 C) 20 D) 25

Correct answer: B) 15

Why the distractors fail: A) 10 is the result of multiplying 2 by 5, not 3 by 5. C) 20 is the result of multiplying 4 by 5, not 3 by 5. D) 25 is the result of multiplying 5 by 5, not 3 by 5.

Short-answer questions

1. Explain the concept of long multiplication and its application in real-life situations.

(Answer should include the correct order of operations and the use of the multiplication symbol (?).)

1. Solve the following problem using long multiplication: 43 × 25 = ?

(Answer should include the correct calculation and result.)

1. What is the result of multiplying 4 by 0?

(Answer should be 0.)

1. Explain why the order of operations is important in long multiplication.

(Answer should include the correct order of operations and its importance in avoiding errors.)

1. Solve the following problem using long multiplication: 3 × 5 = ?

(Answer should include the correct calculation and result.)