Multiplication

In this article, the lesson objectives are: 

1. Multiplication of \(4-\)digit numbers by \(1-\)digit numbers
2. Multiplication by \(10\) and its multiples
3. Multiplication of \(2-\)digit numbers by \(2-\)digit numbers
4. Multiplication of \(3-\)digit numbers by \(2-\)digit numbers

In Primary \(2\) and \(3\), we have learnt the multiplication tables of \(1\) to \(10\). 

Question 1: 

Solve the following multiplication.

\(8 × 9 =\) __________

1. \(54\)
2. \(56\)
3. \(64\)
4. \(72\)

Solution:  

\(8 \times 9 = 72\)

Answer:

\((4) \;72\)

Question 2: 

Solve the following multiplication.

\(18 \times 7 =\) __________

1. \(124\)
2. \(126\)
3. \(134\)
4. \(136\)

Solution:

Answer: 

\((2) \;126\)

1. Multiplication Of 4-Digit Numbers By 1-Digit Numbers

The multiplication of \(4-\)digit numbers by \(1-\)digit numbers is similar to the multiplication of \(3-\)digit numbers by \(1-\)digit numbers.

Example:

\(1936 × 7 =\) __________   

Solution: 

Step 1:

Step 2:

Step 3:

Step 4:

Answer:

\(13 \,552\)

Question 1: 

Solve the following multiplication.

\(3918 \times 5 =\) __________  

Solution:   

Answer:

\(19 \,590\)

2. Multiplication By 10 And Its Multiples

When we multiply a whole number by \(10\), we add one ‘\(0\)’ after the number. 

For instance, 

\(\begin{align*}​ 5 \times 10 &= 50 \\ 15 \times 10 &= 150 \\ 215 \times 10 &= 2150 \end{align*}\)

What do you think happens when we multiply a whole number to a multiple of \(10\)?

We express the multiple as a product of \(10\) and a number.

Let’s try the following.

Example:

\(5 \times 30 =\) __________

Solution:

We express \(30\) as a product of \(3\) and \(10\).

\(\begin{align*}​ 5 \times 30 &= 5 \times 3 \times 10 \\ &= 15 \times 10 \\ &= 150 \end{align*}\)

Answer:

\(150\)

Question 1: 

Solve the following multiplication.

\(22 \times 10 =\) __________

Answer:

\(220\)

Question 2: 

Solve the following multiplication.

\(51 \times 10 =\) __________

Answer: 

\(510\)

Question 3: 

Solve the following multiplication.

\(38 \times 50 =\) __________

Solution:

\(\begin{align*}​ 38 \times 50 &= 38 \times 5 \times10 \\ &= 190 \times 10 \\ &= 1900 \end{align*}\)

Answer: 

\(1900\)

Question 4: 

Solve the following multiplication.

\(94 \times 50 =\) __________

Solution:

\(\begin{align*}​ 94 \times 50 &= 94 \times 5 \times 10 \\ &= 470 \times 10 \\ &=4700 \end{align*}\)

Answer: 

\(4700\)

Question 5: 

Solve the following multiplication.

\(74 \times 60 =\) __________

Solution: 

\(\begin{align*}​ 74 \times 60 &= 74 \times 6 \times 10\\ &= 444 \times 10\\ &= 4440 \end{align*}\)

Answer:

\(4440\)

Question 6: 

Solve the following multiplication. 

\(1059 × 90 =\) __________

Solution:

\(\begin{align*}​ 1059 \times 90 &= 1059 \times 9 \times 10 \\ &= 9531 \times 10 \\ &= 95 310 \end{align*}\)

Answer:

\(95 \,310\)

3. Multiplication Of 2-Digit By 2-Digit Numbers

Now, let’s multiply a \(2-\)digit number by a \(2-\)digit number.

Step 1: 

We multiply the first number by the digit in the ones place of the second number. 

Step 2: 

We multiply the first number by the digit in the tens place of the second number. 

Step 3: 

We add the answers in Step 1 and Step 2.

Question 1: 

Solve the following multiplication. 

\(18 \times 12 =\) __________     

Solution:

Step 1: 

Step 2: 

Step 3:

Think about this! 

You can see \(12 = 10 + 2\). 

\(\begin{align*}​ 18 \times 10 &= 180 \\ 18 \times 2 &= 36 \\ 180 + 36 &= 216 \end{align*}\)

Answer:

\(216\)

Question 2: 

Solve the following multiplication.

\(67 \times 38 =\) __________

Solution:

Answer:

\(2546\)

Question 3: 

Solve the following multiplication.

\(27 \times 31 =\) __________

Solution: 

Answer:

\(837\)

4. Multiplication Of 3-Digit By 2-Digit Numbers

The multiplication of \(3-\)digit numbers by \(2-\)digit numbers is similar to the multiplication of \(2-\)digit numbers by \(2-\)digit numbers.

Step 1: 

We multiply the first number by the digit in the ones place of the second number. 

Step 2: 

We multiply the first number by the digit in the tens place of the second number. 

Step 3: 

We add the answers in Step 1 and Step 2.

Question 1: 

Solve the following multiplication. 

\(132 \times 18 =\) __________

Solution:

Step 1: 

Step 2: 

Step 3:

Think about this! 

You can see, \(18 = 10 + 8\).

\(\begin{align*}​ 132 \times 10 &= 1320 \\ 132 \times 8 &= 1056 \\ 1320 + 1056 &= 2376 \end{align*}\)

Answer:

\(2376 \)

Question 2: 

Solve the following multiplication. 

\(413 \times 26 =\) __________

Solution:

Answer: 

\(10 \,738\)

Question 3: 

Solve the following multiplication. 

\(634 × 38=\) __________   

Solution:

Answer:

\(24 \,092\)