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Chapter 3: Problem 64

Simplify. $$ 5 \cdot 2^{2} \div 10 \quad[1.9 \mathrm{c}] $$

Short Answer

Expert verified
2

Step by step solution

01

- Evaluate the Exponent

First, evaluate the exponent in the expression. Calculate the value of \( 2^2 \). Since \( 2^2 = 4 \), the expression now becomes \( 5 \times 4 \div 10 \).
02

- Perform the Multiplication

Next, perform the multiplication. Multiply 5 by 4 to get \( 20 \). The expression is now \( 20 \div 10 \).
03

- Perform the Division

Finally, perform the division. Divide 20 by 10 to get \( 2 \).

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Key Concepts

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

Exponents
Exponents are a way to express repeated multiplication of the same number. For example, in the expression \(2^2\), 2 is the base, and 2 is the exponent. This means you multiply 2 by itself, which gives you 4:
\(2^2 = 2 \times 2 = 4\).
Key points to remember:
  • Always evaluate exponents before other operations like multiplication or division.
  • Exponents can greatly change the value of a number, so getting them correct is crucial.
Multiplication and Division
After dealing with exponents, the next step is to perform multiplication and division. These operations are performed from left to right, following the order of operations (often remembered by the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).
In the given example, once you've evaluated the exponent and have the expression \(5 \times 4 \div 10\):
Performing Multiplication:
  • 5 multiplied by 4 equals 20.

Now the expression becomes \(20 \div 10\).
Performing Division:
  • 20 divided by 10 equals 2.

Understanding these steps will help simplify any math problem that involves these operations.
Mathematical Simplification
Mathematical simplification involves performing all the necessary operations to reduce an expression to its simplest form. The goal is to make the math expression as simple and straightforward as possible.
Here are the steps we followed:
  • Start by solving exponents.
  • Next, carry out multiplication and division from left to right.
  • Finally, ensure all operations are performed correctly to arrive at a simple, final answer.
    For example, simplifying the given expression \( 5 \cdot 2^{2} \div 10 \) involves correctly following these rules to ultimately reach the answer: \(2\).

By understanding these concepts deeply, you can simplify complex expressions effectively and accurately.

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Most popular questions from this chapter

A guitarist's band is booked for Friday and Saturday nights at a local club. The guitarist is part of a trio on Friday and part of a quintet on Saturday. Thus, the guitarist is paid one-third of one-half the weekend's pay for Friday and one-fifth of one-half the weekend's pay for Saturday. What fractional part of the band's pay did the guitarist receive for the weekend's work? If the band was paid \(\$ 1200\), how much did the guitarist receive?

Subtract and simplify. $$ \frac{3}{4}-\frac{1}{8} $$

Find the average of \(\frac{1}{6}, \frac{1}{8},\) and \(\frac{3}{4}\).

Simplify. $$ \frac{\frac{7}{12}}{\frac{5}{8}-\frac{1}{4}} $$

Simplify. $$ \left(\frac{3}{4}\right)^{2}+3 \frac{1}{2} \div 1 \frac{1}{4} $$
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