Problem 11 - Algebra A Combined Function

Question

Multiply. 5(-1.4)

Step-by-Step Solution

Answer

The product of 5 and -1.4 is -7.0.

Step 1: Understand the Problem

We need to multiply two numbers: 5 and -1.4. Multiplication involves combining parts to find the whole. In this case, we have to multiply a positive by a negative number.

Step 2: Determine the Sign of the Answer

A positive number multiplied by a negative number will yield a negative result. Therefore, the result of multiplying 5 by -1.4 will be negative.

Step 3: Multiply the Absolute Values

First, ignore the negative sign of -1.4 and multiply the absolute values of the numbers: 5 x 1.4.

Step 4: Perform the Multiplication

Multiply 5 by 1.4:\(5 imes 1.4 = 7.0\)

Step 5: Apply the Negative Sign

Since we determined in Step 2 that the result is negative, apply the negative sign to the product: The answer is -7.0.

Key Concepts

Understanding Negative Numbers

Negative numbers are numbers with a value less than zero. They are represented with a minus sign (-). In mathematics, they indicate a decrease or movement in the opposite direction on a number line compared to positive numbers.
It's important to learn how they interact with other numbers in arithmetic operations, especially in multiplication.

• When you multiply two negative numbers, the result is positive.
• When you multiply a positive number by a negative number, the result is negative.
• Negative numbers are essential in various real-life situations, such as debts or temperatures below zero.

Understanding negative numbers is crucial when dealing with real-world scenarios and more complex math problems later in your studies.

Grasping the Absolute Value

The concept of absolute value is straightforward. The absolute value of a number is its non-negative value. It's the distance of a number from zero on the number line, regardless of direction. To use absolute value:

• Ignore the negative sign of a negative number.
• For positive numbers, the absolute value is the number itself.
• The notation for absolute value is two vertical bars, like this: \(|x|\).

For example, the absolute value of -1.4 is 1.4, just as the absolute value of 1.4 is also 1.4.
Absolute values help simplify calculations, especially when determining the magnitude of numbers without worrying about their signs.

Exploring Multiplication Properties

Multiplication has several properties that can make calculations simpler and help understand mathematical operations better. These properties include:

• Commutative Property: Changing the order of numbers does not change the result (e.g., \(a \times b = b \times a\)).
• Associative Property: Changing the grouping of numbers does not change the result (e.g., \((a \times b) \times c = a \times (b \times c)\)).
• Multiplicative Identity Property: Any number multiplied by 1 remains unchanged (e.g., \(a \times 1 = a\)).
• Multiplicative Property of Zero: Any number multiplied by zero is zero (e.g., \(a \times 0 = 0\)).

When multiplying a positive number by a negative number, like in the exercise, the sign of the result is negative. It follows the rules of arithmetic, combining these properties with the knowledge of negative numbers to solve problems effectively.