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Chapter 1: Problem 32

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

Short Answer

Expert verified
The result of the evaluated expression is 4.

Step by step solution

01

Perform Division

Begin by performing the division inside the parentheses. So, \(2.7 \div 0.9 = 3\).
02

Perform Multiplication

Next, multiply the result of the division by 3. So, \(3 \times 3 = 9\).
03

Perform Subtraction

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

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Key Concepts

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

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鈥檚 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.

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Most popular questions from this chapter

CHECKING SOLUTIONS OF INEQUALTTIES Check whether the given number is a solution of the inequality. $$\frac{c+5}{3} \leq 4 ; 3$$

EQUATIONS AND INEQUALITIES Match the verbal sentence with its mathematical representation. The product of 16 and \(x\) is greater than 32.

Compare using \(<,=,\) or \(>.\) $$18.45 \underline{?} 18.5$$

Match the problem with the formula needed to solve the problem. Then use the Guess, Check, and Revise strategy or another problem-solving strategy to solve the problem. Area of a rectangle \(\quad A=l w \quad\) Distance \(\quad d=r t\) Simple interest \(\quad I=P r t \quad\) Volume of a cube Temperature \(\quad C=\frac{5}{9}(F-32)\) Surface area of a cube \(S=6 s^{2}\) A piece of cheese cut in the shape of a cube has a volume of 27 cubic inches. What is the length of each edge of the piece of cheese?

Match the problem with the formula needed to solve the problem. Then use the Guess, Check, and Revise strategy or another problem-solving strategy to solve the problem. Area of a rectangle \(\quad A=l w \quad\) Distance \(\quad d=r t\) Simple interest \(\quad I=P r t \quad\) Volume of a cube Temperature \(\quad C=\frac{5}{9}(F-32)\) Surface area of a cube \(S=6 s^{2}\) You want to construct a patio of 80 square feet with a length of 10 feet. What is the width of the patio?
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