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Chapter 1: Problem 61

Multiply. $$ -(-5.6 y+7) $$

Short Answer

Expert verified
The result is \(5.6y - 7\).

Step by step solution

01

Understand the Expression

The given expression is \(-(-5.6y + 7)\). It represents the multiplication of \(-1\) and \((鈭�5.6y + 7)\).
02

Distribute the Negative Sign

Distribute the negative sign across the terms inside the parentheses. This means multiplying each term inside the parentheses by \(-1\).
03

Multiply Each Term

Multiply \(-1\) by \(鈭�5.6y\) to get \(5.6y\). Multiply \(-1\) by \(7\) to get \(-7\).
04

Write the Result

Combine the results from the multiplication to form the final expression: \(5.6y - 7\).

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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 a fundamental concept in algebra. It allows us to multiply a single term by each term within a set of parentheses. When you see an expression like \(-(-5.6y + 7)\), it might initially look complicated, but the Distributive Property simplifies it. Here's how it works:
  • The concept tells us that when we have a number, such as \(-1\), outside the parentheses, we multiply each term inside the parentheses by this number.
  • In this problem, we distribute the \(-1\) to both \(-5.6y\) and \(+7\).
  • This means you calculate \(-1 \,*\, -5.6y\) and \(-1 \,*\, 7\).
By applying this property, expressions become easier to handle and solve. You essentially "break down" the expression into smaller, simpler parts.
Negative Numbers
Negative numbers can sometimes be tricky, but they are crucial in algebra. When dealing with negative numbers, it's essential to remember how they interact with each other during multiplication and addition.
  • When you multiply two negative numbers, the result is positive. For example, \(-1 \,*\, -5.6y = 5.6y\).
  • Multiplying a negative number by a positive number yields a negative result. In our expression, this rule applies as \(-1 \,*\, 7 = -7\).
  • Understanding these rules helps you predict the sign (positive or negative) of your final answer.
These basics of negative numbers ensure that you can navigate through expressions that feature both positive and negative terms effectively.
Simplifying Expressions
Simplifying algebraic expressions is all about making them as straightforward as possible. After distributing and dealing with negative numbers, it's time to compile and simplify what remains. In our case:
  • We applied the Distributive Property and dealt with negative numbers to arrive at \(5.6y - 7\).
  • The result, \(5.6y - 7\), is simplified because there are no more like terms to combine.
  • Whenever you simplify expressions, you're looking to condense them into the most reduced form, making them easier to understand or use in further calculations.
Remember, simplifying does not change the value of the expression鈥攊t simply makes it easier to work with.

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Most popular questions from this chapter

Using each of the numbers \(2,3,\) and 4 only once, what is the greatest value that the following expression can have?

Explain each error. Then give the correct answer. a. \(9(4 b-2)=36 b-2\) b. \(\quad 3(2 x)=6 \cdot 3 x=18 x\) c. \(-(23 c+2)=-23 c+2\) d. \((5 n+1) 2=5 n+2\)

True or false: \(-4>-5 ?\)

Evaluate: \(\left(\frac{2}{3}\right)^{3}\)

Why is addition of signed numbers taught before subtraction of signed numbers?
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