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Chapter 2: Problem 91

Evaluate the expression. $$ (27 \div 9) \div(7-5) $$

Short Answer

Expert verified
The answer to the expression \((27 \div 9) \div(7-5)\) is 1.5.

Step by step solution

01

Perform the first operation

According to the order of operations, the first operation to perform is the division in the parentheses which is \(27 \div 9\). This yields a result of 3.
02

Perform the second operation

The next operation to perform is the subtraction in the parentheses which is \(7 - 5\). This yields a result of 2.
03

Perform the final operation

Now we can proceed and perform the final operation, dividing the results from step 1 and step 2 which is \(3 \div 2\). The result is 1.5.

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Key Concepts

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

Understanding Division
Division is a fundamental arithmetic operation that involves splitting a number into equal parts. In our original exercise, we first divide 27 by 9. When you divide 27 by 9, you're asking how many times 9 can fit into 27. The answer, which is 3, is called the quotient. This is an integral part of the expression evaluation.
  • The number being divided is called the dividend, which is 27 in this case.
  • The number you are dividing by is the divisor, which is 9 here.
  • The outcome of the division is the quotient.
Remember, division can sometimes result in a decimal or fraction if the numbers don鈥檛 divide evenly. Our final division in the exercise, 3 divided by 2, results in a decimal quotient of 1.5. Understanding how to handle both exact and non-exact division is crucial in mathematical calculations.
Basics of Subtraction
Subtraction is the process of removing objects from a collection. It is the opposite of addition. In our exercise, after handling the initial division, we have a subtraction operation within the parentheses: 7 minus 5. This step simply involves taking 5 away from 7, which results in 2.
  • The number from which we subtract is the minuend, which is 7 in this problem.
  • The number being subtracted is the subtrahend, which is 5.
  • The result of subtraction is known as the difference.
A key point to remember is that subtraction, unlike addition, is not commutative, meaning changing the order of the numbers changes the result. Practicing subtraction in various contexts strengthens problem-solving skills.
Principles of Expression Evaluation
Expression evaluation is all about finding the value of a mathematical phrase. To correctly evaluate an expression, it's vital to follow the order of operations. This ensures that calculations are performed in the correct sequence to obtain the right result.
  • Parentheses and brackets are used to indicate operations that should be performed first.
  • Operations within these are evaluated following the standard order: division and multiplication before addition and subtraction.
In our exercise, we started by resolving what鈥檚 inside the parentheses:
  • First performing the division: 27 divided by 9;
  • Then the subtraction: 7 minus 5.
Finally, we divide the outcomes of these operations to reach the overall solution, demonstrating how systematic and step-by-step calculation leads to accurate results.

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Most popular questions from this chapter

EXPRESSIONS WITH FRACTION BARS Evaluate the expression. $$ \frac{6+7^{2}}{3^{3}-9-7} $$

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