Multiplication of One-Digit by Two-Digit Numbers

Preparation

This will be a preparation for problems such as 5 x 10, 10 x 5, 3 x 20, and 20 x 3.

Method 1: For problems such as 5 x 10, whenever a number is being multiplied by ten, that number simply gets a zero written on to the end of it. This is the same as increasing the place value of that number. So, 5 x 10 = 50.
Method 2: For problems such as 10 x 5, the Commutative Property of Multiplication can be used to switch the 5 and 10 around. Now this problem can be solved using Method 1. 10 x 5 = 5 x 10 = 50.
Method 3: For problems such as 3 x 20; 20 is equal to 2 tens, or 2 x 10. Multiply 3 by 2, and the multiply the product of that by 10 to get the answer. This is the System of Numeration. 3 x 20 = 3 x 2 x10 = 6 x 10 = 60.
Method 4: For problems such as 20 x 3 use the Commutative Property just like in Method 2 and then solve using Method 3. 20 x 3 = 3 x 20 = 60.

Multiplication of One Digit by Two Digit Numbers
Without Regrouping

Method 1: For a problem such as 3 x 32 split the 2-digit number into ones and tens and multiply each by the 1-digit number. Then add the results to get the product.
3 x 32 = [3 x 30] + [3 x 2] = [90] + [6] = 96
So, 3 x 32 = 96

Practice these problems using method 1:
Practice 1:
2 x 43
43 = 40 + (3)
2 x 40 = (80)
2 x (3) = (6)
(80) + (6) = (86)

Practice 2:
3 x 23
23 = (20) + (3)
3 x (20) = (60)
3 x (3) = (9)
(60) + (9) = (69)

Method 2: For problems such as 12 x 3, use the Commutative Property to switch the numbers and solve using Method 1.

Solve Mentally:
1. 34 x 2
2. 13 x 3
3. 42 x 2
4. 12 x 4
5. 33 x 3
6. 22 x 4