Problem 91 - Algebra 1

Question

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

Step-by-Step Solution

Answer

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

Step 1: 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.

Step 2: 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.

Step 3: 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.

Key Concepts

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’t 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’s 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.