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Chapter 1: Problem 52

Perform each indicated operation. $$ 8-2 \cdot 5 $$

Short Answer

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Step by step solution

01

Identify the order of operations

In mathematical expressions, operations must be performed in a specific order, following the BIDMAS/BODMAS rule: Brackets, Indices (orders, i.e., powers and square roots, etc.), Division and Multiplication (left to right), Addition and Subtraction (left to right). For our expression, we have subtraction and multiplication.
02

Perform the multiplication first

According to the order of operations, perform the multiplication before the subtraction in the expression: \[ 2 \times 5 = 10 \]
03

Perform the subtraction

Now, substitute the result of the multiplication back into the expression and then perform the subtraction: \[ 8 - 10 = -2 \]

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Key Concepts

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

BIDMAS
When solving mathematical expressions, it's crucial to follow the correct order of operations. BIDMAS (Brackets, Indices, Division and Multiplication, Addition and Subtraction) is a useful acronym to remember this order. Also known as BODMAS, depending on the country, it ensures you perform calculations correctly.

Here's how it breaks down:
  • Brackets: Always solve expressions inside brackets first.
  • Indices: Next, calculate powers or square roots.
  • Division and Multiplication: Perform these operations from left to right.
  • Addition and Subtraction: Finally, handle addition and subtraction from left to right.
In the given exercise, BIDMAS informs us to address multiplication before subtraction in the expression: 8 - 2 鈰� 5.
Multiplication
Multiplication is one of the fundamental arithmetic operations and signifies repeated addition. For instance, 2 鈰� 5 means adding 2 five times (2 + 2 + 2 + 2 + 2).

In our exercise, BIDMAS tells us to perform multiplication before any other operations such as addition or subtraction. This means we first calculate:
2 鈰� 5
which results in 10.

It's important to remember that multiplication is done before moving on to addition or subtraction, ensuring our calculations are accurate and follow the correct process.
Subtraction
Subtraction is another key arithmetic operation, often referred to as taking away one quantity from another. In mathematical expressions, after following BIDMAS rules and performing operations like multiplication first, next comes subtraction.

In the exercise, after calculating 2 鈰� 5, we substitute the result back into the original expression:
8 - 10
This means we subtract 10 from 8, yielding:
8 - 10 = -2

Subtraction can result in negative numbers if the number being subtracted is larger than the number from which it is being subtracted. As seen in this exercise, -2 signals that 10 exceeds 8 by 2.

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Most popular questions from this chapter

In 1998 , undergraduate college students had an average (mean) credit card balance of \(\$ 1879 .\) The average balance increased \(\$ 869\) by 2000 , then dropped \(\$ 579\) by \(2004,\) and then increased \(\$ 1004\) by \(2008 .\) What was the average credit card balance of undergraduate college students in \(2008 ?\)

Write a numerical expression for each phrase and simplify. Three subtracted from the product of 4.2 and \(-8.5\)

The operation of division is used in divisibility tests. A divisibility test allows us to determine whether a given number is divisible (without remainder) by another number. An integer is divisible by 8 if its last three digits form a numble by \(8,\) and not otherwise. Show that (a) \(2,923,296\) is divisible by 8 and (b) \(7,291,623\) is not divisible by 8 .

Write each sentence as an equation, using \(x\) as the variable. Then find the solution from the set of integers between \(-12\) and \(12,\) inclusive. The quotient of a number and 4 is \(-1\)

The operation of division is used in divisibility tests. A divisibility test allows us to determine whether a given number is divisible (without remainder) by another number. An integer is divisible by 2 if its last digit is divisible by \(2,\) and not otherwise. Show that (a) \(3,473,986\) is divisible by 2 and (b) \(4,336,879\) is not divisible by 2 .
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