Which Choice Shows The Product Of 22 And $39$?A. $(22)(39) = 858$B. \$22 \times 39 = 748$[/tex\]C. $22 + 39 = 61$D. $22 \cdot 39 = 648$
Introduction
Multiplication is a fundamental operation in mathematics that involves finding the product of two or more numbers. In this article, we will focus on the multiplication of large numbers, specifically the product of 22 and 39. We will explore the different methods of multiplication and provide a step-by-step guide on how to calculate the product of these two numbers.
Understanding the Problem
The problem requires us to find the product of 22 and 39. To do this, we need to understand the concept of multiplication and how it applies to large numbers. Multiplication is a shortcut for repeated addition. For example, the product of 22 and 39 can be calculated by adding 22 together 39 times.
Method 1: Multiplication using Repeated Addition
One way to calculate the product of 22 and 39 is by using repeated addition. This method involves adding 22 together 39 times.
Step 1: Multiply 22 by 10
First, we multiply 22 by 10, which gives us 220.
Step 2: Multiply 22 by 30
Next, we multiply 22 by 30, which gives us 660.
Step 3: Add the Results
Now, we add the results of the two multiplications: 220 + 660 = 880.
Step 4: Multiply 22 by 9
Finally, we multiply 22 by 9, which gives us 198.
Step 5: Add the Results
We add the result of the last multiplication to the previous result: 880 + 198 = 1078.
Method 2: Multiplication using the Standard Algorithm
Another way to calculate the product of 22 and 39 is by using the standard algorithm for multiplication.
Step 1: Multiply 20 by 39
First, we multiply 20 by 39, which gives us 780.
Step 2: Multiply 2 by 39
Next, we multiply 2 by 39, which gives us 78.
Step 3: Add the Results
Now, we add the results of the two multiplications: 780 + 78 = 858.
Step 4: Multiply 22 by 10
Finally, we multiply 22 by 10, which gives us 220.
Step 5: Multiply 22 by 30
We multiply 22 by 30, which gives us 660.
Step 6: Add the Results
We add the results of the two multiplications: 220 + 660 = 880.
Step 7: Multiply 22 by 9
We multiply 22 by 9, which gives us 198.
Step 8: Add the Results
We add the result of the last multiplication to the previous result: 880 + 198 = 1078.
Method 3: Multiplication using the Commutative Property
The commutative property of multiplication states that the order of the factors does not change the product. We can use this property to calculate the product of 22 and 39.
Step 1: Multiply 39 by 20
First, we multiply 39 by 20, which gives us 780.
Step 2: Multiply 39 by 2
Next, we multiply 39 by 2, which gives us 78.
Step 3: Add the Results
Now, we add the results of the two multiplications: 780 + 78 = 858.
Step 4: Multiply 20 by 22
Finally, we multiply 20 by 22, which gives us 440.
Step 5: Multiply 2 by 22
We multiply 2 by 22, which gives us 44.
Step 6: Add the Results
We add the results of the two multiplications: 440 + 44 = 484.
Step 7: Add the Results
We add the result of the last multiplication to the previous result: 484 + 374 = 858.
Conclusion
In conclusion, the product of 22 and 39 is 858. We have explored three different methods of multiplication to calculate this product. The standard algorithm for multiplication is the most efficient method, but the commutative property of multiplication can also be used to calculate the product. We hope that this article has provided a clear understanding of the concept of multiplication and how it applies to large numbers.
Answer
Q: What is multiplication?
A: Multiplication is a mathematical operation that involves finding the product of two or more numbers. It is a shortcut for repeated addition.
Q: How do I multiply two numbers?
A: To multiply two numbers, you can use the standard algorithm for multiplication, which involves multiplying the numbers together and then adding the results. Alternatively, you can use the commutative property of multiplication, which states that the order of the factors does not change the product.
Q: What is the commutative property of multiplication?
A: The commutative property of multiplication states that the order of the factors does not change the product. For example, 2 x 3 = 3 x 2 = 6.
Q: How do I multiply large numbers?
A: To multiply large numbers, you can use the standard algorithm for multiplication, which involves multiplying the numbers together and then adding the results. Alternatively, you can use the commutative property of multiplication, which states that the order of the factors does not change the product.
Q: What is the difference between multiplication and addition?
A: Multiplication is a shortcut for repeated addition. For example, 2 x 3 = 2 + 2 + 2 = 6.
Q: Can I multiply fractions?
A: Yes, you can multiply fractions. To multiply fractions, you multiply the numerators together and the denominators together.
Q: Can I multiply decimals?
A: Yes, you can multiply decimals. To multiply decimals, you multiply the numbers together and then add the results.
Q: What is the product of 22 and 39?
A: The product of 22 and 39 is 858.
Q: How do I calculate the product of 22 and 39?
A: To calculate the product of 22 and 39, you can use the standard algorithm for multiplication, which involves multiplying the numbers together and then adding the results. Alternatively, you can use the commutative property of multiplication, which states that the order of the factors does not change the product.
Q: What are some real-world applications of multiplication?
A: Multiplication has many real-world applications, including:
- Calculating the cost of items in a store
- Determining the area of a room
- Finding the volume of a container
- Calculating the interest on a loan
Q: Can I use a calculator to multiply numbers?
A: Yes, you can use a calculator to multiply numbers. However, it's always a good idea to double-check your work to make sure you get the correct answer.
Conclusion
In conclusion, multiplication is a fundamental mathematical operation that involves finding the product of two or more numbers. It has many real-world applications and can be used to calculate the cost of items, determine the area of a room, find the volume of a container, and calculate the interest on a loan. We hope that this article has provided a clear understanding of the concept of multiplication and how it applies to different types of numbers.