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Chapter 1: Problem 55

Perform each indicated operation. $$ -7(3-8) $$

Short Answer

Expert verified
35

Step by step solution

01

- Simplify the expression in the parentheses

First, solve the expression inside the parentheses. The expression is $$3 - 8$$. Perform the subtraction: $$3 - 8 = -5$$
02

- Multiply by -7

Now, multiply the result from Step 1 by -7. Using the expression: $$-7(-5)$$. Since multiplying two negative numbers gives a positive result: $$-7 \times -5 = 35$$

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Key Concepts

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

Parentheses Simplification
When working with algebraic expressions, it's important to simplify expressions inside the parentheses first. Parentheses indicate which operations should be performed first according to the order of operations, which is also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

In the given problem, we have the expression \(-7(3-8)\). The expression inside the parentheses is \(3-8\).

To simplify it:
  • Perform the subtraction: \(3-8\)
  • This calculation equals \(-5\)

Now, we have \(-7(-5)\), this makes our expression easier to handle moving forward.
Negative Numbers
Understanding negative numbers is crucial in algebra, as they frequently appear in various operations. When dealing with negative numbers, it's helpful to remember the rules of multiplication and addition involving these numbers.

For instance, in our problem, we simplified the expression inside the parentheses to get \(-5\). It is important to understand that \(-5\) is a negative number. When we move to the next step, we need to use another vital rule of algebra:
  • Multiplying a negative by a negative results in a positive, \(a \times b = -a \times -b = +ab\)
So, \( -7(-5)\) when multiplied gives us a positive number.
By incorporating these rules, we can avoid mistakes with negative numbers and ensure our solution is correct.
Multiplication
Multiplication is one of the fundamental operations in algebra. In the given exercise, after simplifying the expression inside the parentheses, we need to multiply the resultant number with the given coefficient.

In our case, the expression is now \(-7 \times -5\). As mentioned earlier, when multiplying two negative numbers, the product is positive: \(-7 \times -5 = 35\).
  • Remember to apply the correct multiplication rules for negative numbers.
  • Always conduct the multiplication step methodically to avoid errors.
This ensures that our final answer is accurate and free from mistakes. Through regular practice, you will find handling these operations much simpler.

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Most popular questions from this chapter

Write a numerical expression for each phrase and simplify. \(20 \%\) of the product of \(-5\) and 6

The operation of division is used in divisibility tests. A divisibility test allows us to determine whether a given number is divisible (without remainder) by another number. An integer is divisible by 12 if it is divisible by both 3 and \(4,\) and not otherwise. Show that (a) \(4,249,474\) is not divisible by 12 (b) \(4,253,520\) is divisible by 12 and

Write a numerical expression for each phrase and simplify. The product of \(-\frac{1}{2}\) and \(\frac{3}{4},\) divided by \(-\frac{2}{3}\)

Evaluate each expression for \(x=6, y=-4,\) and \(a=3\) $$ \left(\frac{1}{3} x-\frac{4}{5} y\right)\left(-\frac{1}{5} a\right) $$

Decide whether each statement is an example of the commutative, associative, identity, inverse, or distributive property. See Examples \(1,2,3,5,6,7,\) and \(9 .\) $$6(5 t)-6(7 r)=6(5 t-7 r)$$
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