Problem 109 - Beginning and Intermediate Algebra

Question

Write a numerical expression for each phrase, and simplify the expression. 8 less than -2

Step-by-Step Solution

Answer

-13.8

Step 1: Identify the components

First, identify the components of the phrase. The phrase mentions 'the product of 1.5 and -3.2' and 'nine subtracted from' it.

Step 2: Formulate the product

Calculate the product of 1.5 and -3.2. \[1.5 \times -3.2 = -4.8\]

Step 3: Form the expression

Now, form the expression for nine subtracted from the product of 1.5 and -3.2. \[-4.8 - 9\]

Step 4: Simplify the expression

Simplify the expression by performing the subtraction. \[-4.8 - 9 = -13.8\]

Key Concepts

numerical expression

A numerical expression is a mathematical phrase that includes numbers and operations like addition, subtraction, multiplication, and division. It does not contain any variables. In the given problem, we need to write and simplify a numerical expression based on the phrase 'Nine subtracted from the product of 1.5 and -3.2'.

To create a numerical expression:

• Identify the numbers and operations mentioned in the phrase.
• Combine them to form the correct mathematical expression.

In our case:

• The product of 1.5 and -3.2
• Subtract 9 from this product

By following these rules, you can convert any phrase into a numerical expression.

subtraction

Subtraction is one of the basic arithmetic operations. It represents the operation of removing objects from a collection. In simpler terms, it is taking one number away from another. The symbol for subtraction is '-'.

When we say 'Nine subtracted from the product of 1.5 and -3.2', it means:

• First, calculate the product of 1.5 and -3.2 which is -4.8.
• Then, subtract 9 from this number.

So, the subtraction part is -4.8 - 9. Remember that when dealing with negative numbers, subtraction can be tricky. The result of -4.8 - 9 is -13.8.

product

In mathematics, the product is the result of multiplying two or more numbers together. The product is key to understanding expressions involving multiplication.

In the problem given, the phrase 'the product of 1.5 and -3.2' specifies a multiplication operation. To find this product, you need to multiply:

• 1.5
• -3.2

So, the product would be calculated as: \[1.5 \times -3.2 = -4.8\] This step is crucial as it provides the value we need for further operations. Once we have this product, we can then proceed to the subtraction step to complete the expression.