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Chapter 1: Problem 40

Evaluate each expression. $$ -4 \cdot 6+5 $$

Short Answer

Expert verified
The expression evaluates to -19.

Step by step solution

01

Evaluate the Multiplication

Start by evaluating the multiplication part of the expression. The expression is \(-4 \cdot 6 + 5\). First, calculate \(-4 \times 6\). Multiplying, we get \(-24\).
02

Perform the Addition

Next, take the result from the multiplication and add the next term of the expression. We have \(-24 + 5\). Perform the addition to get \(-19\).

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Key Concepts

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

Multiplication
Multiplication is an essential arithmetic operation where numbers are combined or scaled together. In mathematical terms, multiplication is the process of calculating the total of one number added repeatedly based on another number. For example, multiplying -4 by 6 means adding -4 a total of 6 times:
  • -4 + (-4) + (-4) + (-4) + (-4) + (-4)
Instead of repetitive addition, multiplication simplifies this to a single step: -4 \( \times \) 6 = -24. When one or both of the numbers are negative, like in our example, the result follows the rules of multiplication for negative numbers:
  • Positive \( \times \) Positive = Positive
  • Negative \( \times \) Positive = Negative
  • Positive \( \times \) Negative = Negative
  • Negative \( \times \) Negative = Positive
Always remember, when multiplying numbers, first look for signs to determine your answer's sign, and then proceed with the calculation.
Addition
Addition is another fundamental arithmetic operation, connecting values to achieve a total sum. Addition involves calculating the overall value by bringing numbers together. In the context of our exercise, after performing the multiplication and getting -24, we must add 5:
  • Multiply result: -24
  • Next step: Add 5
The addition of -24 and 5 is straightforward, yet it requires careful consideration of signs:
  • When adding a negative and a positive number, subtract their absolute values.
  • The sign of the result will be the same as the sign of the number with the larger absolute value.
For example, -24 and 5 yield -19, because 24 is greater than 5, and 24's sign is negative.
Negative Numbers
Negative numbers express values less than zero, and are essential for depicting deficits or descents. They are symbolized by a minus ( -) sign and follow specific rules in arithmetic operations. Negative numbers are especially significant in multiplication and addition exercises.
To grasp negative numbers in multiplication:
  • When multiplying a negative with a positive number, the resultant product is negative.
  • When both numbers are negative, the outcome is a positive number, owing to the rule of equal signs resulting in a positive effect.
For addition, when working with negative numbers, it's crucial to consider the rules:
  • Adding two negatives results in a larger negative number. For instance, (-4) +(-5) yields -9.
  • Adding a negative and a positive number involves finding the difference between their absolute values, where the answer adopts the larger value's sign.
Recognizing these patterns and rules helps in calculating efficiently and avoiding misunderstandings. Always watch out for those signs!

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Most popular questions from this chapter

In this section, we substituted a number for a variable. List some other uses of the word substitute that you encounter in everyday life.

Is the following statement true or false? Explain. Having a debt of \(\$ 100\) forgiven is equivalent to gaining \(\$ 100\).

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

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