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:

$24 \,092$