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Chapter 1: Problem 29

Multiply. $$ -11(11) $$

Short Answer

Expert verified
The product is -121.

Step by step solution

01

Identify the Operation

The operation we need to perform is multiplication between a negative number and a positive number. Specifically, we have \[-11 \times 11\].
02

Apply the Rule of Signs

Remember, when multiplying a negative number by a positive number, the result is negative. Therefore, we should expect a negative result for this multiplication.
03

Multiply the Absolute Values

Ignore the signs for a moment and multiply the absolute values of the numbers: 11 multiplied by 11 is \[121\].
04

Attach the Correct Sign

Based on the rule of signs, attach a negative sign to the result from Step 3, making it \[-121\].

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Key Concepts

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

Negative Numbers
Negative numbers are numbers less than zero. They are usually written with a minus sign in front, like -1, -5, or -11. Imagine them as steps below zero on a number line. The further left you move from zero, the more negative the number becomes. When we multiply two numbers, the signs of the numbers matter. Here鈥檚 a simple way to remember:
  • Negative times Positive = Negative
  • Negative times Negative = Positive
  • Positive times Positive = Positive

In our exercise, since we have one negative (-11) and one positive (11) number, the result is negative.
Positive Numbers
Positive numbers are greater than zero and don't need any sign, but for clarity, you can also write a plus before them, like +5 or +11. On the number line, these are all the numbers to the right of zero. When multiplying positive numbers by any other numbers, they tend to 'keep the peace' with their non-negative nature, affecting the result based on the rules of multiplication:
  • Positive times Positive = Positive
  • Positive times Negative = Negative

In our case, the positive 11 influences the final result's nature when combined with a negative number, giving us a negative result.
Absolute Value
The absolute value of a number is simply the number without its sign. It shows how far the number is from zero, regardless of the direction. For example, both \(-5\) and \(5\) have an absolute value of 5 because they are five steps away from zero on a number line. In math, we write the absolute value using vertical lines, such as \(|-11| = 11\).

When multiplying integers, first find the absolute values of the numbers, multiply them, and consider the signs afterward. For \(-11 \times 11\), the absolute values are \(11\) and \(11\), resulting in \(121\). Then attach the negative sign as per the rule of multiplying a negative by a positive, thus giving \(-121\).

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Most popular questions from this chapter

Perform the following operations. Write answers in lowest terms. $$ \frac{11}{7}-\frac{3}{35} $$

Perform the following operations. Write answers in lowest terms. $$ 2 \frac{3}{5}+4 \frac{7}{10} $$

Perform the following operations. Write answers in lowest terms. $$ \frac{7}{8} \div 3 \frac{1}{4} $$

If \(a\) is a positive number and \(b\) is a negative number, determine whether each statement is true or false. \(a-b\) is always a positive number.

Without calculating, determine whether each answer is positive or negative. Then use a calculator to find the exact difference. \(56.875-87.262\)
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