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Chapter 0: Problem 2

Do each calculation and use a calculator to check your results. a. \(-2 \cdot 5\) b. \(6 \cdot-4\) c. \(-3 \cdot-4\) d. \(-12 \div 3\) e. \(36 \div-6\) f. \(-50 \div-5\)

Short Answer

Expert verified
a. -10, b. -24, c. 12, d. -4, e. -6, f. 10

Step by step solution

01

Calculate -2 multiplied by 5

To solve \(-2 \cdot 5\), multiply -2 and 5 to get \(-10\).
02

Calculate 6 multiplied by -4

To find \(6 \cdot -4\), multiply 6 and -4, resulting in \(-24\).
03

Calculate -3 multiplied by -4

For \-3 \cdot -4\, both numbers are negative, thus the result is positive. Multiply them to get \(+12\).
04

Calculate -12 divided by 3

To solve \(-12 \div 3\), divide -12 by 3, which gives \(-4\).
05

Calculate 36 divided by -6

For \36 \div -6\, divide 36 by -6 to find \(-6\).
06

Calculate -50 divided by -5

In \-50 \div -5\, the negative signs cancel out, resulting in a positive number. Divide 50 by 5 to get \(+10\).

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Key Concepts

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

Multiplication with Negative Numbers
Multiplying with negative numbers can be a bit tricky at first, but with some understanding, it becomes easy. The multiplication of integers involves specific rules, especially when dealing with negative numbers. Here鈥檚 how it works:
  • Positive times Negative: When you multiply a positive number by a negative number, the result is always negative. For instance, \(-2 \cdot 5\) yields \-10\. Similarly, \(6 \cdot -4\) results in \-24\.
  • Negative times Negative: This is where things might seem a little off. When you multiply two negative numbers, the negatives cancel each other and the result is positive. An example is \(-3 \cdot -4\), which equals \+12\.
Whenever you multiply, make sure to carefully count the signs of the numbers to apply the correct rule. These guidelines ensure you always get the right answer, regardless of negative or positive numbers involved.
Division with Negative Numbers
Division with negative numbers follows a similar set of rules as multiplication. Understanding these rules will help you master integer operations. Here鈥檚 a quick guide:
  • Negative divided by Positive: If you divide a negative number by a positive number, the result is negative. For example, when you solve \(-12 \div 3\), you get \(-4\).
  • Positive divided by Negative: Dividing a positive number by a negative number results in a negative outcome, like \(36 \div -6\), which gives \(-6\).
  • Negative divided by Negative: When both numbers are negative, the division results in a positive number. For instance, \(-50 \div -5\) becomes \+10\.
Remember, the negative signs behave like multipliers, affecting the resulting sign of the answer. Just identify and apply the right rule based on the signs of the numbers involved.
Basic Arithmetic Calculations
Basic arithmetic calculations form the foundation for understanding more complex math concepts. These operations include addition, subtraction, multiplication, and division. Let's delve a bit deeper into their basic principles:
  • Addition and Subtraction: These operations are straightforward with integers. Adding two positives or two negatives maintains the sign. Subtracting a number essentially involves adding its opposite.
  • Multiplication: As covered, multiplying integers follows specific sign rules. The product of two numbers can differ based on their signs, leading to positive or negative results.
  • Division: The process of division shares the same fundamental rules regarding the signs of the numbers, leading to either a positive or negative quotient.
Each operation might seem simple on its own, but understanding how they interact, especially with negatives, helps in solving complex problems. Practice regularly, using examples like those from our exercises, to strengthen your arithmetic skills.

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Most popular questions from this chapter

The Stage 0 figure below has a length of 1 . At Stage 1, each segment has a length of \(\frac{1}{4}\). Stage 2 Stage 3 a. Complete a table like the one on the next page by calculating the lengths of the figure at Stages 2 and 3. Give each answer as a fraction in multiplication form, as a fraction in exponent form, and as a decimal rounded to the nearest hundredth. Try to figure out the total lengths at Stages 2 and 3 without counting. (II) \text { b. Which is the first stage to have a length greater than } 3 \text { ? A length greater than } 10 \text { ? }

Write each multiplication expression in exponent form. a. \(5 \times 5 \times 5 \times 5\) (a) b. \(7 \times 7 \times 7 \times 7 \times 7\) c. \(3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3\) d. \(2(2)(2)\)

Do the following calculations. Check your results by entering the expression into your calculator exactly as it is shown. a. \(5 \cdot-4-2 \cdot-6\) b. \(3+-4 \cdot 7\) c. \(-2-5 \cdot(6+-3)\) d. \((-3-5) \cdot-2+9 \cdot-3\)

What is \(4-12 \div 4 \cdot \frac{1}{2}-5^{2}\) ?

Do these calculations. Check your results with a calculator. a. \(-2+5-(-7)\) b. \((-3)^{2}-(-2)^{3}\) c. \(\frac{3}{5}+\frac{-2}{3}\) d. \(-0.2 \cdot 20+15\) e. \(4-6(-2)\) f. \(7-4(2-5)\) g. \(-2 \frac{1}{3}-4 \frac{1}{6}\)
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