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Chapter 7: Problem 43

Multiply. $$ 2000 \cdot \frac{3}{10} \cdot 2 $$

Short Answer

Expert verified
The result of the multiplication is 1200.

Step by step solution

01

Start with the Fractional Part

First, multiply 2000 by \( \frac{3}{10}\). To do this, multiply the 2000 by the numerator which is 3: \(2000 \times 3 = 6000\). Then divide the result by the denominator of the fraction which is 10: \(\frac{6000}{10} = 600\).
02

Multiply by the Whole Number

Now take the result from Step 1, which is 600, and multiply it by the 2. This is done by simply multiplying the numbers: \(600 \times 2 = 1200\).
03

Confirm the Result

Finally, double-check the result to ensure it is correct. You have performed the operations correctly in sequential steps, leading to a final answer of 1200.

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Key Concepts

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

Fraction Multiplication
When multiplying a fraction by a number, follow these simple steps to simplify your work:
  • Start by multiplying the numerator of the fraction by the number. This gives you an intermediary product.
  • Next, divide the intermediary product by the denominator of the fraction. This will provide you with the final result after multiplying with the fraction.
Let's take an example from our exercise: Suppose you have 2000 and you need to multiply it by \( \frac{3}{10} \). Here's how you'd do it:1. **Multiply the numerator by 2000**: \( 2000 \times 3 = 6000 \).2. **Divide by the denominator**: \( \frac{6000}{10} = 600 \).By proceeding in this way, you easily manage fraction multiplication and avoid confusion.
Step-by-step Multiplication
A step-by-step strategy can make complex multiplication simpler. This strategy involves breaking down the problem into manageable chunks:
  • First, handle any fractional parts separately. As we did in our exercise, tackle \( 2000 \times \frac{3}{10} \) before moving on.
  • Next, take the result from your initial calculation and multiply it by the next component in the expression. This ensures you work methodically and produce a correct final result.
For instance, after computing \( 2000 \times \frac{3}{10} = 600 \) in Step 1 of our example, proceed to:1. **Multiply 600 by 2**: \( 600 \times 2 = 1200 \).Breaking steps this way removes a lot of stress from dealing with longer multiplication equations, as each step carries less cognitive load and focuses on a smaller, specific task.
Whole Number Multiplication
Multiplying whole numbers often comes instinctively, but it can be advantageous to think of it as involving a streamlined process:
  • Identify the numbers to be multiplied, which in our case was 600 and 2.
  • Simply align the numbers vertically or multiply them directly when appropriate.
  • Carry over numbers as necessary if you're not using a calculator or digital device.
In our exercise, once you have completed dealing with the fractional multiplication and resolved the intermediary product, the next step looked like this:1. **Multiply 600 by 2** directly: \( 600 \times 2 = 1200 \).This step reinforces straightforward math and concludes the calculation process, validating the ease of whole number multiplication.

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Most popular questions from this chapter

Solve. 9.18 is \(6.8 \%\) of what number?

Perform each indicated operation. See Sections 4.3 through \(4.5,4.7,\) and 5.2 through \(5.4 .\) $$9.2+1.98$$

Write a word statement for the proportion \(\frac{x}{28}=\frac{25}{100} .\) Use the phrase "what number" for " \(x\),"

Recall that \(1=100 \% .\) This means that 1 whole is \(100 \%\). The top four components of bone are below. Find the missing percent. 1\. Minerals \(-45 \%\) 2\. Living tissue \(-30 \%\) 3\. Water \(-20 \%\) 4\. Other-?

Perform each indicated operation. See Sections 4.3 through \(4.5,4.7,\) and 5.2 through \(5.4 .\) $$29.4 \div 0.7$$
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