Problem 82 - Prealgebra

Question

Perform the indicated operations. $$(8 \cdot 5) \div 4$$

Step-by-Step Solution

Answer

The result is 10.

Step 1: Perform the Multiplication

First, multiply the numbers inside the parentheses: \(8 \times 5 = 40\).

Step 2: Perform the Division

Next, take the result from Step 1 and divide it by 4: \(40 \div 4 = 10\).

Key Concepts

Multiplication

Multiplication is one of the basic arithmetic operations and is essentially repeated addition. When you multiply two numbers, you're adding a number (the multiplicand) to itself a certain number of times (the multiplier). For example, in the expression \(8 \cdot 5\), 8 is added to itself 5 times, resulting in 40.

Here are some key points about multiplication to remember:

• Multiplication is commutative, meaning \(a \times b = b \times a\).
• It is associative, so \((a \times b) \times c = a \times (b \times c)\).
• Multiplication by zero always results in zero, and multiplication by one leaves the number unchanged.

Understanding these basics will help you solve problems where multiplication is an initial step.

Division

Division is another fundamental arithmetic operation that breaks a number (the dividend) into a specified number of equal parts (the divisor). In other words, it helps to determine how many times a number can fit into another. For instance, in the division problem \(40 \div 4\), you are figuring out how many times 4 can fit into 40, which is 10 times.

Important details about division include:

• Division is not commutative, so \(a \div b eq b \div a\) generally.
• Division by zero is undefined, so it's crucial to ensure the divisor is never zero.
• The quotient, or result of division, may not always be a whole number and can sometimes be a fraction or decimal.

By mastering these concepts, you will be able to tackle a wide range of division problems effectively.

Arithmetic Operations

Arithmetic operations such as addition, subtraction, multiplication, and division are the building blocks of mathematics. Their proper use is guided by an important set of rules known as the order of operations.

The order of operations is often remembered by the acronym PEMDAS:

• Parentheses
• Exponents (or powers)
• Multiplication and Division (from left to right)
• Addition and Subtraction (from left to right)

This means that in an expression like \((8 \cdot 5) \div 4\), you first perform the operation inside the parentheses: multiply 8 and 5. Then, take the result and divide it by 4. Following these steps ensures accurate results, especially as arithmetic problems become more complex.Understanding and applying these rules consistently allows for error-free calculation and problem-solving across all levels of math.