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Chapter 1: Problem 34

Multiplying Whole Numbers and Area $$ (240)(1)(20) $$

Short Answer

Expert verified
4800

Step by step solution

01

Multiplication with Identity

When multiplying numbers, the identity property of multiplication allows us to multiply any number by 1 without changing its value. So, we can simplify \((240)(1)(20)\) by ignoring the 1. Hence, the expression becomes \((240)(20)\).
02

Multiplying Two Whole Numbers

Now, we multiply the two remaining whole numbers: 240 and 20. First, break it down: multiply 240 by 20. We can write 20 as \(2 \times 10\) and multiply step-by-step. Start by calculating \(240 \times 2 = 480\).
03

Final Multiplication by 10

Next, take the result from Step 2, which is 480, and multiply it by 10 since we initially broke 20 into \(2 \times 10\). So, \(480 \times 10 = 4800\). This gives us the final answer.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Identity Property of Multiplication
In multiplication, there is a special rule called the identity property. This property tells us that any number multiplied by 1 remains unchanged.
For example, if you have the number 5, multiplying it by 1 would still give you 5.
  • This property helps simplify multiplication equations.
  • It works the same way for any whole number, including large numbers like 240, 500, or even 1000.
  • In our exercise, this means we can ignore the 1 in the expression \( (240)(1)(20) \).
This simplification is useful in making problems easier to manage and solve.
Area Calculation
Calculating the area of a rectangle involves multiplying two dimensions: length and width. Although our exercise primarily involves multiplication, the concept of area utilizes similar skills.
  • If our numbers represented dimensions of a rectangle, for example, 240 units in one direction and 20 units in another, multiplying these gives the total area.
  • Thus, the operation \( 240 \times 20 \) would give 4800 square units, symbolizing the total space within the rectangle.
  • This calculation is an everyday use of multiplication in geometry.
The connection between number multiplication and area calculation shows how mathematical operations are applied in practical settings.
Step-by-Step Multiplication Guide
Breaking down multiplication into simpler steps can make calculations easier and less confusing. Here鈥檚 a helpful guide:
  • **Ignore Numbers You Multiply With 1:** Thanks to the identity property, skip multiplying by 1 to simplify your task.
  • **Break Down Multiplication:** Start by breaking the numbers into manageable parts. In our case, turn 20 into \( 2 \times 10 \).
  • **Multiply Step-by-Step:** Compute each part separately. First, multiply 240 by 2 to get 480.
  • **Continue to the Next Step:** Multiply the result by the next factor, which is 10, to finally reach 4800.
By following these steps, complex multiplication becomes straightforward and structured, enhancing accuracy and understanding.

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Most popular questions from this chapter

In Example 12 in this section, we found that the average of \(75,96,81,\) and 88 is \(85 .\) If the number 96 is removed from the list of numbers, does the average increase or decrease? Explain why.

Write each phrase as a variable expression. Use \(x\) to represent "a number." The product of five and a number

Find and correct the error when evaluating each expression for \(x=3\) and \(y=5 .\) \(\begin{aligned} 7 x+y^{2} &=7(3)+5^{2} \\ &=21+10 \\ &=31 \end{aligned}\)

Write each whole number in expanded form. $$99,032$$

Identify which number is the minuend and which number is the subtrahend. $$ \text { Subtract } 7 \text { from } 70 $$
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