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Chapter 10: Problem 33

Multiply. \(7 \cdot(-4) \cdot(-3) \cdot 5\)

Short Answer

Expert verified
420

Step by step solution

01

- Multiply the first two numbers

First multiply the numbers 7 and -4. When you multiply a positive number by a negative number, the result is negative: \(7 \times (-4) = -28\)
02

- Multiply the result by the next negative number

Next, multiply the result from Step 1 by the next number, which is -3. Multiplying two negative numbers results in a positive number: \((-28) \times (-3) = 84\)
03

- Multiply the result by the last positive number

Finally, multiply the result from Step 2 by the last number which is 5. Multiplying a positive number by another positive number remains positive: \(84 \times 5 = 420\)

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Key Concepts

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

multiplying integers
When multiplying integers, the process is straightforward. We follow the same basic principles as with smaller numbers.
For positive and positive integers, the result is always positive.
For example: \(2 \times 3 = 6\).
In the case of multiplying a positive integer by a negative integer, the result is negative.
For example: \(2 \times (-3) = -6\).
If both integers are negative, multiplying them gives a positive result.
For example: \((-2) \times (-3) = 6\).
These rules remain the same regardless of the size of the numbers.
negative numbers
Negative numbers are numbers less than zero, such as -1, -2, -3, and so on.
Understanding how they interact when multiplied is crucial in mathematics.
Here are the important rules for multiplication with negative numbers:
  • Multiplying a positive number by a negative number results in a negative number (e.g., \(4 \times (-5) = -20\)).
  • Multiplying two negative numbers yields a positive number (e.g., \((-2) \times (-3) = 6\)).
  • Multiplying negative quantities follows commutative property, meaning the order doesn't change the result (e.g., \((-4) \times 3 = 3 \times (-4) = -12\)).
These properties are essential to solving problems involving multiplication with negative integers.
step by step math solutions
Breaking down math problems step by step can greatly help in understanding and solving them correctly.
Let's revisit the given multiplication problem: \(7 \times (-4) \times (-3) \times 5\).
  • Step 1: Start with the first two numbers. Multiply 7 by -4 to get -28.
  • Step 2: Take the result, -28, and multiply it by the next number, -3. Two negatives make a positive, resulting in 84.
  • Step 3: Multiply the positive result, 84, by the last number, 5, to get 420.
By following each step carefully and applying the rules of multiplication for integers, any math problem can become easier to manage. Step-by-step solutions help clarify complex problems, making them simpler to understand and solve.

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