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Chapter 3: Problem 6

\((-3)(-4)=\) ?

Short Answer

Expert verified
The product of \((-3)(-4)\) is 12.

Step by step solution

01

Understand the Signs

When multiplying two negative numbers, remember that the product is always positive. This is because the rule for multiplication of integers states that the product of two numbers with the same sign is positive.
02

Multiply the Absolute Values

Focus on the absolute values of the numbers, ignoring the negative signs for now. Multiply the absolute values: 3 and 4. So, calculate \(3 \times 4\).
03

Calculate the Multiplication

Multiply the absolute values from the previous step: \(3 \times 4 = 12\).
04

Determine the Sign of the Product

As discovered in Step 1, the product of two negative numbers is positive. Therefore, the product of \(-3\) and \(-4\) is a positive 12.

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Key Concepts

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

Multiplying Negative Numbers
When dealing with integer multiplication, especially negative numbers, the rules can sometimes seem confusing. But don't worry! We are here to make it simple. When you multiply two negative numbers, the result is always positive. Why does this happen? It's all about the rules of arithmetic. When the signs of both numbers are the same, whether both are positive or both are negative, their product is positive.
For example:
  • If you have \(-3 \times -4\), the result is positive 12.
  • Similarly, if you have the same numbers but positive, say \(3 \times 4\), the result is also positive 12.
So remember, same signs = positive product.
Absolute Value
Understanding absolute value is key to simplifying multiplication problems involving negative numbers. Absolute value represents the distance a number is from zero on the number line, regardless of direction.
It is always a non-negative number.
For example:
  • The absolute value of \(-3\) is 3.
  • The absolute value of \(-4\) is 4.
When multiplying two negative numbers, focus on their absolute values first. Calculate as if they are positive and apply the result to the multiplication rules of negative numbers, which we explained is a positive product.
Integer Arithmetic
Integer arithmetic forms the basis of most math calculations we perform every day. It's all about using whole numbers, both positive and negative, and their operations.
For multiplication specifically, there are straightforward rules:
  • Two positive numbers multiply to a positive product.
  • A positive and a negative number multiply to a negative product.
  • Two negative numbers come together to give a positive product.
These rules simplify calculations, including zero, which when multiplied with any integer results in zero.
Focusing on these principles makes integer arithmetic a powerful tool for solving various mathematical problems.

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Most popular questions from this chapter

\(\frac{\frac{1}{2}+\frac{7}{4}}{2+\frac{1}{2}}=?\)

\(-5+4=\) ?

\(-4 \div-3=\) ?

Round off the following to two decimal places: (a) \(3.5741\) \(\begin{array}{lll}\text { (b) } 10.1111111 & \text { (c) } 90.0054 & \text { (d) } 9.0009\end{array}\) (e) \(43.52500\)

\(\sqrt{71.234}\)
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