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Chapter 6: Problem 7

Simplify. $$(0.4)^{2}-2.8 \div 0.2(1.6)$$

Short Answer

Expert verified
Question: Simplify the expression \((0.4)^{2} - 2.8 \div 0.2 * 1.6\). Answer: -22.24

Step by step solution

01

Evaluate Exponent

Evaluate \((0.4)^{2}\). $$(0.4)^{2} = 0.4 * 0.4 = 0.16$$
02

Division

Now, let's perform the division: \(2.8 \div 0.2\). $$2.8 \div 0.2 = \frac{2.8}{0.2} = \frac{28}{2} = 14$$
03

Multiplication

Next, we multiply the result from step 2 by \(1.6\). $$14 * 1.6 = 22.4$$
04

Subtraction

Finally, let's perform the subtraction using the results from steps 1 and 3. $$0.16 - 22.4 = -22.24$$ So, the simplified expression is $$-22.24$$.

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Key Concepts

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

Understanding Exponents
Exponents play a critical role in simplifying algebraic expressions. An exponent indicates how many times we multiply a number by itself. In our exercise, we evaluate \((0.4)^2\), which means multiplying 0.4 by itself.
When solving, you multiply the base number (0.4) by itself:
  • Calculate \(0.4 \times 0.4 = 0.16\).
Understanding this principle is crucial for tasks involving powers and roots, ensuring a proper grasp of algebraic manipulation.
Division in Algebra
Division in algebra involves distributing a number into equal parts and is represented using the division symbol \(\div\) or a fraction. In our equation, we divide \(2.8\) by \(0.2\).
Here's how you simplify it:
  • Rewrite the division as a fraction: \(\frac{2.8}{0.2}\).
  • Multiply both numerator and denominator by 10 to get \(\frac{28}{2}\).
  • Simplify to get 14.
Being able to switch between these representations makes it easier to solve and simplify expressions.
Multiplication in Algebra
Multiplication is a basic operation that combines numbers to form a product, denoted by symbols like \(*\) or brackets. After performing division in our step-by-step process, we proceed to multiplication. We multiply the quotient from division (14) by \(1.6\).
  • Perform the multiplication: \(14 \times 1.6 = 22.4\).
This operation helps consolidate the results from previous calculations, forming part of the final solution.
Subtraction in Algebra
Subtraction involves deducting one quantity from another, and it is critical when simplifying expressions. For our task, the final step is subtraction where we subtract the multiplied value (22.4) from the squared value (0.16).
Here's how it's done:
  • Write the expression: \(0.16 - 22.4\).
  • Perform the subtraction to get \(-22.24\).
Mastering subtraction allows us to complete expressions by uniting all operations into a singular simplified result.

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