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Chapter 2: Problem 37

Simplify using the order of operations. $$90 \div(-3) \cdot(-1) \div(-6)$$

Short Answer

Expert verified
-5

Step by step solution

01

- Apply Division First

First, perform the division from left to right. Start with the first division:\[ 90 \div (-3) = -30 \]
02

- Continue with Multiplication

Next, multiply the result by \(-1 \):\[ -30 \cdot (-1) = 30 \]
03

- Apply Final Division

Lastly, perform the division of the result by \(-6 \):\[ 30 \div (-6) = -5 \]

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Key Concepts

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

Division
Division helps divide a number into specified, equal parts. In the order of operations (PEMDAS/BODMAS), division and multiplication come after parentheses, exponents, but are completed from left to right. For this problem, we start with the division: ewline ewline
  • Choose the first division operation.
    Here: ewline 90 divided by ewline (-3).
  • Solve the division problem:
    \[90 \div (-3) = -30\]
The negative sign appears because the division involved a positive and a negative number. With division remember:
  • A positive number divided by a negative number results in a negative number.
  • A negative number divided by a positive number also results in negative.
  • Two negatives make a positive: a negative number divided by another negative gives you a positive result.
Multiplication
Multiplication follows division in the order of operations, and we handle it next. For this specific problem:
  • Take the previous result, ewline -30. Multiply this by ewline -1.
  • Solve the multiplication problem:
    \[-30 \cdot (-1) = 30\]
Since you are multiplying two negative numbers, they produce a positive result. Key tips:
  • Multiplying two positives gives a positive.
  • Multiplying a positive by a negative or vice versa results in a negative.
  • Multiplying two negative numbers results in a positive.
Remember to always follow left-to-right for division and multiplication if they appear together.
Negative Numbers
Negative numbers use a minus sign (-) and represent values below zero. Understanding negative numbers in operations is crucial. When they interact with division and multiplication:
  • Dividing a positive by a negative, or vice versa, gives a negative result.
  • Dividing two negatives or two positives gives a positive result.
  • When multiplying, negatives behave similarly 鈥� two negatives make a positive, while a negative and a positive make negative.
In our final step:
  • Take 30 and divide it by ewline -6.
  • Perform the division:
    \[30 \div (-6) = -5\]
The positive 30 divided by negative 6 results in -5. This solution combined understanding negative signs during division and multiplication.

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