2-Digit by 1-Digit Multiplication & Division
Let's learn about...
- Multiplication & Division
- Multiplication Strategies for Multiplying 2-Digit By 1-Digit Numbers
- Division Strategies for Dividing 2-Digit By 1-Digit Numbers
What is Multiplication & Division?
Multiplication
Division
Division is the method of breaking a number into equal parts or groups.
Multiplication is the method of finding the product of two or more numbers.
In a division sentence, the first number is called the dividend, the second number is called the divisor, and the answer is called the quotient.
In a multiplication sentence, the numbers that are being multiplied are called factors, and the answer is called the product.
9 ÷ 3 = 3
3 x 6 = 18
Did You Know?
Multiplication and division are:
- both basic arithematic operations,
- involve two or more numbers, and
- inverse operations, meaning they are opposites.
dividend
product
factors
quotient
divisor
Let's Talk About Multiplication Strategies!!!
Multiply using Standard Algorithm
2-Digit by 1-Digit Numbers
Step 1: Write the two factors to be multiplied on top of each other, with the digits lined up according to their place value (ones, tens, hundreds, etc.). Step 2: Multiply the ones digit of the bottom factor by the ones digit of the top factor. Write the product under the ones column. (NOTE: Sometimes, the product of the digits in ones place of both factors can equal a two-digit number. In this case, you would write the ones digit of the product under the ones column and write the tens digit of the product above the tens column.)
Multiply using Standard Algorithm
2-Digit by 1-Digit Numbers
Step 3: Multiply the tens digit of the top factor by the ones digit of the bottom factor. Write the product under the tens column and to the left of the number from step 2. Multiply the tens digit of the top factor by the ones digit of the bottom factor. If applicable, add the digit above the tens digit of the top number by the product of the tens digit of the top by the ones digit of the bottom. Write the product under the tens column and to the left of the number from step 2. (NOTE: Sometimes, the product of the digits in tens place of the top factor and the ones place of the bottom factor can equal a two-digit number. In this case, you would write the product to the left of the product of Step #2.)
Multiply using Standard Algorithm
2-Digit by 1-Digit Numbers
+3
Examples:
24 x 2
48 x 4
48
192
Multiplying using Repeated Addition/Skip Counting
Example: 56 x 456 + 56 + 56 + 56 = ______
56+ 56
224
112+ 56
OR
112 + 112
168+ 56
224
224
Step 1: Add the first factor as many times as indicated by the second factor.
Multiplying using Equal Groups
= 70
Example: 35 x 2
Step 1: Draw the number of rectangles to represent the number of groups indicated by the divisor. Step 2: Draw the number of circles within the rectangles indicated by the dividend. Step 3: Count the number of circles in each group then add the totals. The sum of the group is the answer.
Therefore, 35 x 2 = 70.
Multiplying using a Number Line
Example: 79 x 3
79
+ 79
+ 79
158
237
316
Step 1: Mark your number line starting with 0 using the multiples of the dividend.
Step 2: Starting at 0, move over the number of spaces indicated by the divisor. Once you have reached the number of moved spaces, that will be your answer.
Therefore, 79 x 3 = 237.
Let's Practice...
Directions: Using the multiplication strategy map, multiply using the corresponding multiplication strategy.
- (Standard Algorithm) 80 x 5
- (Repeated Addition) 29 x 2
- (Equal Groups) 18 x 3
- (Number Line) 27 x 7
Let's Practice...
Directions: Check your answers!
= 54 = 189 = 400 = 58
Let's Talk About Division Strategies!!!
Divide using Standard Algorithm
2-Digit by 1-Digit Numbers
Example:88 ÷ 2
88
Step 1: Write the dividend (the number being divided) inside the division symbol, with the divisor (the number doing the dividing) outside the symbol.
Divide using Standard Algorithm
2-Digit by 1-Digit Numbers
Example:88 ÷ 2
88
Step 2: Start with the leftmost digit of the dividend, and divide it by the divisor. Write the quotient (the answer) above the dividend, and write the remainder (what's left over) next to the next digit of the dividend.
-8
8 ÷ 2 = 4
Divide using Standard Algorithm
2-Digit by 1-Digit Numbers
Example:88 ÷ 2
88
-8
Step 3: Bring down the next digit of the dividend next to the remainder to create a new one- or two-digit number.
Divide using Standard Algorithm
44
2-Digit by 1-Digit Numbers
Example:88 ÷ 2
88
-8
Step 4: Repeat step 2 using the newly-created one- or two-digit number and the divisor.
8 ÷ 2 = 4
Divide using Standard Algorithm
44
2-Digit by 1-Digit Numbers
Example:88 ÷ 2
88
Step 5: Repeat step 2 using the newly-created one- or two-digit number and the divisor. Continue bringing down digits and dividing until you've gone through all the digits of the dividend.
-8
8 ÷ 2 = 4
-8
Divide using Standard Algorithm
2-Digit by 1-Digit Numbers
Example:72 ÷ 8
72
Step 1: Write the dividend (the number being divided) inside the division symbol, with the divisor (the number doing the dividing) outside the symbol.
Divide using Standard Algorithm
2-Digit by 1-Digit Numbers
Example:72 ÷ 8
72
Step 2: Start with the leftmost digit of the dividend, and divide it by the divisor. Write the quotient (the answer) above the dividend, and write the remainder (what's left over) next to the next digit of the dividend. (NOTE: Sometimes, the leftmost digit cannot be divided by the divisor. So, in this case, you would move over to the next digit to the right and divide the new 2-digit number.)
-72
Therefore, 72 ÷ 8 = 9.
Division using Repeated Subraction/Skip Counting
Example: 32 ÷ 832 - 8 = 24 - 8 = 16 - 8 = 8 - 8 =
32- 8
24 16 8 0
24 - 8
OR
16 - 8
Note: When using repeated subtraction, subtract the divisor until you get "0". The amount of times you subtract your divisor is your answer.
8 - 8
Therefore, 32 ÷ 8 = 4
Division using Equal Groups
Example: 36 ÷ 9
Step 1: Draw the number of circles indicated by the dividend. Step 2: Use bigger circles or rectangles, and circle the number of circles in each group indicated by the divisor. Step 3: Count the number of groups made, and the total will be the quotient.
36 circles
Therefore, 36 ÷ 9 = 4.
Dividing using a Number Line
Example: 68 ÷ 4
68
64
60
52
44
32
20
16
12
24
28
36
40
48
56
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
Step 1: Starting with 0, mark your number line using the multiples of your divisor. Step 2: Starting from your dividend, subtract by your divisor until you have reached 0.
Therefore, 68 ÷ 4 = 17
Step 3: Count the number of jumps made to reach 0, and that number will be your quotient.
Let's Practice...
Directions: Using the division map, divide using the corresponding division strategy.
- (Standard Algorithm) 49 ÷ 7
- (Repeated Subtraction) 51 ÷ 3
- (Equal Groups) 30 ÷ 5
- (Number Line) 56 ÷ 2
Let's Practice...
Directions: Check your answers.
= 7 = 17 = 6 = 28
2-Digit by 1-Digit Multiplication & Division
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Transcript
2-Digit by 1-Digit Multiplication & Division
Let's learn about...
What is Multiplication & Division?
Multiplication
Division
Division is the method of breaking a number into equal parts or groups.
Multiplication is the method of finding the product of two or more numbers.
In a division sentence, the first number is called the dividend, the second number is called the divisor, and the answer is called the quotient.
In a multiplication sentence, the numbers that are being multiplied are called factors, and the answer is called the product.
9 ÷ 3 = 3
3 x 6 = 18
Did You Know?
Multiplication and division are:
dividend
product
factors
quotient
divisor
Let's Talk About Multiplication Strategies!!!
Multiply using Standard Algorithm
2-Digit by 1-Digit Numbers
Step 1: Write the two factors to be multiplied on top of each other, with the digits lined up according to their place value (ones, tens, hundreds, etc.). Step 2: Multiply the ones digit of the bottom factor by the ones digit of the top factor. Write the product under the ones column. (NOTE: Sometimes, the product of the digits in ones place of both factors can equal a two-digit number. In this case, you would write the ones digit of the product under the ones column and write the tens digit of the product above the tens column.)
Multiply using Standard Algorithm
2-Digit by 1-Digit Numbers
Step 3: Multiply the tens digit of the top factor by the ones digit of the bottom factor. Write the product under the tens column and to the left of the number from step 2. Multiply the tens digit of the top factor by the ones digit of the bottom factor. If applicable, add the digit above the tens digit of the top number by the product of the tens digit of the top by the ones digit of the bottom. Write the product under the tens column and to the left of the number from step 2. (NOTE: Sometimes, the product of the digits in tens place of the top factor and the ones place of the bottom factor can equal a two-digit number. In this case, you would write the product to the left of the product of Step #2.)
Multiply using Standard Algorithm
2-Digit by 1-Digit Numbers
+3
Examples:
24 x 2
48 x 4
48
192
Multiplying using Repeated Addition/Skip Counting
Example: 56 x 456 + 56 + 56 + 56 = ______
56+ 56
224
112+ 56
OR
112 + 112
168+ 56
224
224
Step 1: Add the first factor as many times as indicated by the second factor.
Multiplying using Equal Groups
= 70
Example: 35 x 2
Step 1: Draw the number of rectangles to represent the number of groups indicated by the divisor. Step 2: Draw the number of circles within the rectangles indicated by the dividend. Step 3: Count the number of circles in each group then add the totals. The sum of the group is the answer.
Therefore, 35 x 2 = 70.
Multiplying using a Number Line
Example: 79 x 3
79
+ 79
+ 79
158
237
316
Step 1: Mark your number line starting with 0 using the multiples of the dividend.
Step 2: Starting at 0, move over the number of spaces indicated by the divisor. Once you have reached the number of moved spaces, that will be your answer.
Therefore, 79 x 3 = 237.
Let's Practice...
Directions: Using the multiplication strategy map, multiply using the corresponding multiplication strategy.
Let's Practice...
Directions: Check your answers!
= 54 = 189 = 400 = 58
Let's Talk About Division Strategies!!!
Divide using Standard Algorithm
2-Digit by 1-Digit Numbers
Example:88 ÷ 2
88
Step 1: Write the dividend (the number being divided) inside the division symbol, with the divisor (the number doing the dividing) outside the symbol.
Divide using Standard Algorithm
2-Digit by 1-Digit Numbers
Example:88 ÷ 2
88
Step 2: Start with the leftmost digit of the dividend, and divide it by the divisor. Write the quotient (the answer) above the dividend, and write the remainder (what's left over) next to the next digit of the dividend.
-8
8 ÷ 2 = 4
Divide using Standard Algorithm
2-Digit by 1-Digit Numbers
Example:88 ÷ 2
88
-8
Step 3: Bring down the next digit of the dividend next to the remainder to create a new one- or two-digit number.
Divide using Standard Algorithm
44
2-Digit by 1-Digit Numbers
Example:88 ÷ 2
88
-8
Step 4: Repeat step 2 using the newly-created one- or two-digit number and the divisor.
8 ÷ 2 = 4
Divide using Standard Algorithm
44
2-Digit by 1-Digit Numbers
Example:88 ÷ 2
88
Step 5: Repeat step 2 using the newly-created one- or two-digit number and the divisor. Continue bringing down digits and dividing until you've gone through all the digits of the dividend.
-8
8 ÷ 2 = 4
-8
Divide using Standard Algorithm
2-Digit by 1-Digit Numbers
Example:72 ÷ 8
72
Step 1: Write the dividend (the number being divided) inside the division symbol, with the divisor (the number doing the dividing) outside the symbol.
Divide using Standard Algorithm
2-Digit by 1-Digit Numbers
Example:72 ÷ 8
72
Step 2: Start with the leftmost digit of the dividend, and divide it by the divisor. Write the quotient (the answer) above the dividend, and write the remainder (what's left over) next to the next digit of the dividend. (NOTE: Sometimes, the leftmost digit cannot be divided by the divisor. So, in this case, you would move over to the next digit to the right and divide the new 2-digit number.)
-72
Therefore, 72 ÷ 8 = 9.
Division using Repeated Subraction/Skip Counting
Example: 32 ÷ 832 - 8 = 24 - 8 = 16 - 8 = 8 - 8 =
32- 8
24 16 8 0
24 - 8
OR
16 - 8
Note: When using repeated subtraction, subtract the divisor until you get "0". The amount of times you subtract your divisor is your answer.
8 - 8
Therefore, 32 ÷ 8 = 4
Division using Equal Groups
Example: 36 ÷ 9
Step 1: Draw the number of circles indicated by the dividend. Step 2: Use bigger circles or rectangles, and circle the number of circles in each group indicated by the divisor. Step 3: Count the number of groups made, and the total will be the quotient.
36 circles
Therefore, 36 ÷ 9 = 4.
Dividing using a Number Line
Example: 68 ÷ 4
68
64
60
52
44
32
20
16
12
24
28
36
40
48
56
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
Step 1: Starting with 0, mark your number line using the multiples of your divisor. Step 2: Starting from your dividend, subtract by your divisor until you have reached 0.
Therefore, 68 ÷ 4 = 17
Step 3: Count the number of jumps made to reach 0, and that number will be your quotient.
Let's Practice...
Directions: Using the division map, divide using the corresponding division strategy.
Let's Practice...
Directions: Check your answers.
= 7 = 17 = 6 = 28