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Chapter 2: Problem 50

Simplify each of the numerical expressions. $$-5(0.9)-0.6+4.1(6)-0.9$$

Short Answer

Expert verified
The simplified expression is 18.6.

Step by step solution

01

Apply the Distributive Property

First, distribute the multiplier across each term inside the parentheses. For \(-5(0.9)\), calculate: \(-5 \times 0.9 = -4.5\) For \(4.1(6)\), calculate: \(4.1 \times 6 = 24.6\). Replacing these into the expression gives: \ \(-4.5 - 0.6 + 24.6 - 0.9\).
02

Simplify the Expression by Combining Like Terms

Now, add and subtract the numbers in the expression: \ \(-4.5 - 0.6 = -5.1 \) Next, combine with the term \(-0.9\): \ \( -5.1 - 0.9 = -6\) Finally, add the positive term: \(-6 + 24.6 = 18.6\).

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Key Concepts

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

Distributive Property
The Distributive Property is like a superpower that helps you simplify expressions by breaking them down into smaller parts. Imagine you have a big task and you want to make it easier; you divide it into several smaller tasks. This is exactly how the distributive property works! It allows you to multiply a sum by multiplying each addend separately and then adding the products.
For example, in the expression \(-5(0.9)\), you multiply \(-5\) by \(0.9\) to get \(-4.5\). Similarly, with \(4.1(6)\), you multiply \(4.1\) by \(6\) and obtain \(24.6\).
  • Step 1: Break down the expressions inside the parentheses.
  • Step 2: Multiply each term by the number outside.
This technique makes it much simpler to handle complex numbers, making your calculations accurate and quick.
Simplifying Expressions
Simplifying expressions involves making them easier to work with, by turning a long and confusing expression into a simpler, more manageable form. Think of it like cleaning up your room - you are organizing things so that it looks neat!
After distributing the numbers, what's left is an expression that needs tidying: \(-4.5 - 0.6 + 24.6 - 0.9\).
  • First, group the similar kinds of numbers together.
  • Then perform sequential operations to minimize them further.
It鈥檚 a valuable skill that allows you to solve equations more efficiently and with fewer errors, ensuring that each step makes the expression more straightforward.
Combining Like Terms
Combining like terms is a great strategy to simplify expressions even further.It's all about grouping together the numbers or variables that are similar, so you can do calculations easily.
In the original expression after applying the distributive property, you have \(-4.5 - 0.6 + 24.6 - 0.9\).
Here's how you simplify it:
  • Start by combining \(-4.5\) and \(-0.6\) to get \(-5.1\).
  • Then, take your result \(-5.1\) and combine it with \(-0.9\) to get \(-6\).
  • Finally, finish by adding \(-6\) to the positive term, \(24.6\), and you end up with \(18.6\).
This process is a great example of how combining like terms can quickly simplify expressions, making complex calculations much more accessible.

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Most popular questions from this chapter

Perform the indicated operations. $$6.6-(-1.2)$$

A triangular plot of ground measures \(14 \frac{1}{2}\) yards by \(12 \frac{1}{3}\) yards by \(9 \frac{5}{6}\) yards. How many yards of fencing are needed to enclose the plot?

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At this time how would you describe the difference between arithmetic and algebra?
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