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Chapter 1: Problem 82

Evaluate the given expression. Remember to follow the order of operations. $$32+16 \div 8-6$$

Short Answer

Expert verified
The expression evaluates to 28.

Step by step solution

01

Division

Identify the division operation in the expression. According to the order of operations (PEMDAS/BODMAS), division is performed before addition and subtraction. Compute the division part: \[16 \div 8 = 2\]
02

Rewrite the Expression

Replace the division part with its result to simplify the expression. Now the expression should look like this: \[ 32 + 2 - 6 \]
03

Addition

Next, perform the addition operation as it comes before subtraction according to the order of operations. Compute the addition part: \[ 32 + 2 = 34 \]
04

Subtraction

Finally, perform the subtraction operation to get the final result. Compute the subtraction part: \[ 34 - 6 = 28 \]

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Key Concepts

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

Division in Arithmetic
Division in arithmetic is one of the four basic mathematical operations. When you divide, you are essentially splitting a number into equal parts. For instance, in the expression \(16 \div 8\), 16 is being divided into 8 equal parts, resulting in 2.

Here's why understanding division is important:
  • Division is used for fair sharing.
  • It's essential for more complex math topics, like fractions and ratios.
Remember, in the order of operations, division takes precedence over both addition and subtraction. This means you always do division before tackling addition or subtraction when simplifying an expression.
Addition in Arithmetic
Addition is another fundamental arithmetic operation. It's the process of combining two or more numbers to get a total.

Take the expression \(32 + 2\), for example. This means you are combining the numbers 32 and 2 to get 34.

Addition is useful for everyday activities:
  • Combining groups of items.
  • Calculating totals in money transactions.
According to the order of operations rule, addition is performed after any multiplication or division but before any subtraction.
Subtraction in Arithmetic
Subtraction is the process of taking one number away from another. In the expression \(34 - 6\), you are taking away 6 from 34 to get 28.

Subtraction has practical uses:
  • Determining differences between numbers.
  • Calculating change.
As with division and addition, subtraction follows specific rules in the order of operations. Subtraction should be the last operation you perform in an expression after completing any division and addition steps.

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Most popular questions from this chapter

Compute the given expression. Round off your answer to two decimal places where necessary. $$0.28(56)-0.36(63)$$

Evaluate the given expression. Remember to follow the order of operations. $$\frac{7 \cdot 2+4 \cdot 5-2 \cdot 2}{9 \cdot 3-2 \cdot 6-3 \cdot 3}$$

In Exercises \(73-84\), evaluate the given expression. $$|10-7|-|7-10|$$

Consider the following statements. If the statement is true, explain why. If the statement is false, explain why and/or give an example illustrating why. (a) Every rational number is an integer. (b) Every integer is a rational number. (c) \(-15\) is greater than \(-10\) (d) The absolute value of \(-15\) is greater than the absolute value of \(-10 .\) (e) A rational number must be positive. (f) An integer must be positive. (g) Every real number is a rational number. (h) Every rational number is a real number.

Evaluate the given expression. Remember to follow the order of operations. $$30-(5 \cdot 4)-2$$
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