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Chapter 7: Problem 44

Simplify. $$ 1000 \div 100 \div 2 \cdot 5 $$

Short Answer

Expert verified
The simplified result is 25.

Step by step solution

01

- First Division

Start by dividing 1000 by 100. \[ 1000 \times (100)^{-1} = 10 \]
02

- Second Division

Next, divide the result from step 1 by 2. \[ 10 \times (2)^{-1} = 5 \]
03

- Multiplication

Finally, multiply the result from step 2 by 5. \[ 5 \times 5 = 25 \]

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Key Concepts

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

Division
Division is a fundamental operation in mathematics where you split a number into equal parts. In the problem, you first divide 1000 by 100 to get 10. Division can be represented as multiplication with the reciprocal. For instance, dividing by 100 is the same as multiplying by \[ \frac{1}{100} \].

Here's a quick tip: When sequentially dividing, you can combine multiple division steps into one by keeping the order in mind. This is crucial for understanding the result accurately.

Practicing division with simpler numbers like 10, 100, or 1000 can make the concept clearer.
Multiplication
Multiplication is essentially repeated addition. When you multiply 5 by 5 in the final step, you're adding 5 to itself five times. This operation is often easier for students to grasp as it builds on basic addition skills they already have.

Multiplication can also be seen in many real-life scenarios, such as calculating the total cost when buying multiple items or determining an area.

A good trick to remember is that anything multiplied by 1 stays the same and multiplying by 0 makes the product zero. This makes it much easier to handle multiplication in more extensive calculations.
Simplification
Simplification involves taking a complex expression and breaking it down into simpler steps. Begin each simplification task by identifying the operations involved and follow the order of operations (PEMDAS/BODMAS).

For this problem, the steps show how to approach an expression with both division and multiplication:
  • First, complete the divisions from left to right
  • Then, finally handle the multiplication


Simplification makes it easier to understand and solve problems step by step. The goal is to make complex expressions more manageable and straightforward.

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