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Write to explain how you can use an array to break apart 18 x 12 to find the product and check if the product is reasonable.

Write to explain how you can use an array to break apart 18 x 12 to find the product and check if the product is reasonable.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Using an Array to Multiply** In this task, you're asked to explore how arrays can be used to break apart and simplify multiplication problems. Specifically, you will work with the multiplication problem 18 × 12. ### Instructions: 1. **Understanding Arrays**: Arrays are visual representations that help illustrate multiplication. They consist of rows and columns, where the number of rows corresponds to one factor, and the columns correspond to the other factor. 2. **Breaking Apart the Problem**: - The first step is to decompose the numbers 18 and 12 into parts that are easier to multiply. - For example, you can break apart 18 into 10 and 8, and 12 into 10 and 2. 3. **Using the Array**: - Create an array grid based on the breakdown: - For 18, make a row for 10 and a row for 8. - For 12, make a column for 10 and a column for 2. 4. **Multiply the Parts**: - Multiply each part separately: - \(10 \times 10 = 100\) - \(10 \times 2 = 20\) - \(8 \times 10 = 80\) - \(8 \times 2 = 16\) 5. **Add the Results**: - Combine all the partial products to find the total: - \(100 + 20 + 80 + 16 = 216\) 6. **Check Reasonableness**: - Verify if the result is reasonable by estimating or using a calculator. The breakdown helps confirm that the calculated product makes sense by offering smaller, more manageable numbers to work with. This method is beneficial for understanding how multiplication works and for solving problems more efficiently.
Transcribed Image Text:**Using an Array to Multiply** In this task, you're asked to explore how arrays can be used to break apart and simplify multiplication problems. Specifically, you will work with the multiplication problem 18 × 12. ### Instructions: 1. **Understanding Arrays**: Arrays are visual representations that help illustrate multiplication. They consist of rows and columns, where the number of rows corresponds to one factor, and the columns correspond to the other factor. 2. **Breaking Apart the Problem**: - The first step is to decompose the numbers 18 and 12 into parts that are easier to multiply. - For example, you can break apart 18 into 10 and 8, and 12 into 10 and 2. 3. **Using the Array**: - Create an array grid based on the breakdown: - For 18, make a row for 10 and a row for 8. - For 12, make a column for 10 and a column for 2. 4. **Multiply the Parts**: - Multiply each part separately: - \(10 \times 10 = 100\) - \(10 \times 2 = 20\) - \(8 \times 10 = 80\) - \(8 \times 2 = 16\) 5. **Add the Results**: - Combine all the partial products to find the total: - \(100 + 20 + 80 + 16 = 216\) 6. **Check Reasonableness**: - Verify if the result is reasonable by estimating or using a calculator. The breakdown helps confirm that the calculated product makes sense by offering smaller, more manageable numbers to work with. This method is beneficial for understanding how multiplication works and for solving problems more efficiently.
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