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Chapter 3: Problem 6

Multiply. $$-7 \cdot 3$$

Short Answer

Expert verified
-21

Step by step solution

01

Understand multiplication with negative numbers

Multiplication of a negative number and a positive number always results in a negative number. We can ignore the signs for now and proceed with the multiplication as if both numbers were positive. In the given multiplication -7 \cdot 3, we temporarily treat it as 7 \cdot 3 which equals 21.
02

Apply the negative sign

After the multiplication, apply the negative sign to the result. The negative sign is derived from the fact that one of the factors was a negative number. So, we get the answer as -21. Thus, -7 \cdot 3 = -21.

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Key Concepts

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

Understanding Negative Numbers
When working with negative numbers, it is important to recall that these numbers are less than zero on the number line. Negative numbers have a minus sign (-) in front of them. They often represent a lack of quantity, such as a loss or a debt. In arithmetic:
  • A negative number combined with a positive number can alter the outcome of operations like addition or multiplication.
  • Multiplying a negative number results in different behavior compared to addition or subtraction.
Negative numbers play a crucial role in various real-life situations, such as temperatures below zero or when calculating a financial loss. Understanding how these numbers interact with other integers is essential for solving arithmetic problems correctly.
The Basics of Multiplication
Basic multiplication involves repeating addition. For instance, when you multiply 7 by 3, it is the same as adding 7 together 3 times: 7 + 7 + 7 = 21. In notation, this is written as \( 7 \times 3 = 21 \). Here are some key points to remember about multiplication:
  • It can be visualized using arrays or grouping, making it easier to comprehend.
  • The order of numbers in multiplication (commutative property) does not affect the result, meaning \( a \times b = b \times a \).
This foundational understanding is crucial when combining these operations with negative integers, as the rules slightly change with the introduction of negative numbers.
Operations Involving Integers
Integers include both positive and negative numbers, as well as zero. When performing operations with these numbers, especially multiplication, specific rules apply. Here are the guidelines for integer operations involving multiplication:
  • Multiplying two positive integers yields a positive integer.
  • Multiplying two negative integers gives a positive outcome, because a negative times a negative equals a positive.
  • Multiplying a positive integer with a negative integer results in a negative integer, as demonstrated in \(-7 \cdot 3 = -21\).
Understanding these rules helps in determining the sign of the product in multiplication. Being familiar with integer operations allows you to confidently solve math problems involving various integer combinations.

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Most popular questions from this chapter

Is \(-3\) a solution of the equation \(x-7=-10 ?\)

Mathematics Given the list of numbers at the right, find the largest difference that can be obtained by subtracting one number in the list from a different number in the list. $$5,-2,-9,11,14$$

Subtract. $$(-14)-(-7)$$

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Is \(-8\) a solution of the equation \(1.6=-0.2 z ?\)
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