Problem 32 - Algebra 1

Question

Evaluate the expression. $$3(2.7 \div 0.9)-5$$

Step-by-Step Solution

Answer

The result of the evaluated expression is 4.

Step 1: Perform Division

Begin by performing the division inside the parentheses. So, \(2.7 \div 0.9 = 3\).

Step 2: Perform Multiplication

Next, multiply the result of the division by 3. So, \(3 \times 3 = 9\).

Step 3: Perform Subtraction

Finally, subtract 5 from the result of the multiplication. So, \(9 - 5 = 4\).

Key Concepts

Division

Division is the process of distributing a number into equal parts. It is one of the fundamental operations in arithmetic. In our exercise example, division was the first operation performed. The expression began with the division of 2.7 by 0.9.

To solve this, think of division as finding out how many times the divisor fits into the dividend. Here, you're essentially figuring out how many 0.9s fit into 2.7.

This can also be visualized by considering decimals and fractions:

• Convert 2.7 and 0.9 into fractions or divide them directly as decimals.
• Understand that dividing a decimal by another decimal requires aligning the decimal points or simplifying the fraction.

This gives you a clearer view of the operation, resulting in 3, meaning 0.9 fits three times into 2.7.

Multiplication

Multiplication is the process of adding a number to itself a specified number of times. It follows division in the order of operations for our stated problem. Once you have the result from the division step, you multiply that result by another number.

Here, after determining that 2.7 divided by 0.9 equals 3, the next step is to multiply this quotient by 3.

Understand multiplication better with these points:

• It combines multiple occurrences of the same addition into one operation.
• When you multiply 3 by 3, it's like adding 3 three times: 3 + 3 + 3 = 9.

This principle of multiplication simplifies calculations, especially with larger numbers. In this case, multiplying 3 by 3 leads directly to 9, following the correct order of operations.

Subtraction

Subtraction is the operation of removing a number from another number. It is the final step of the given exercise. After calculating multiplication, subtraction finalizes the operation sequence.

To subtract 5 from the result of the earlier multiplication, consider subtraction as taking away from a total. In this problem, after obtaining 9 from the multiplication, you subtract 5.

Here’s a simplified approach to subtraction:

• Visualize subtraction as moving left on a number line or reducing a total amount.
• Understand that subtraction decreases the value of the original number.

This action leaves you with the number 4. Hence, after carrying out the specified order of operations, you arrive at a final result of 4.