Problem 110
Question
Write a numerical expression for each phrase, and simplify the expression. 9 less than -13
Step-by-Step Solution
Verified Answer
-38.7
1Step 1: Identify the key components
First, identify the key components of the phrase:- 'Product of 4.2 and -8.5'- 'Three subtracted' from the product
2Step 2: Write the expression for the product
The product of 4.2 and -8.5 is written as:\(4.2 \times -8.5\)
3Step 3: Calculate the product
Multiply 4.2 by -8.5:\(4.2 \times -8.5 = -35.7\)
4Step 4: Write the complete expression
Combine the result with the subtraction:\(-35.7 - 3\)
5Step 5: Simplify the expression
Subtract 3 from -35.7:\(-35.7 - 3 = -38.7\)
Key Concepts
numerical expressionproductsubtractionmultiplication
numerical expression
A numerical expression is a mathematical phrase that includes numbers and operations. It's like a sentence made up of numbers and symbols instead of words.
For example, in the phrase 'Three subtracted from the product of 4.2 and -8.5,' the numerical expression would be: \( (4.2 \times -8.5) - 3 \).
Each part of the phrase corresponds to an arithmetic operation:
Writing numerical expressions accurately requires identifying the key components and translating them into operations.
For example, in the phrase 'Three subtracted from the product of 4.2 and -8.5,' the numerical expression would be: \( (4.2 \times -8.5) - 3 \).
Each part of the phrase corresponds to an arithmetic operation:
- 'Product of 4.2 and -8.5': multiplication
- 'Three subtracted from': subtraction
Writing numerical expressions accurately requires identifying the key components and translating them into operations.
product
The term 'product' refers to the result of multiplying two or more numbers.
In the given problem, the phrase 'product of 4.2 and -8.5' means we multiply these two numbers together: \(4.2 \times -8.5\).
Multiplying results in finding the product, which in this case is \(-35.7\).
This is a fundamental concept in math and is essential for solving many types of problems efficiently.
In the given problem, the phrase 'product of 4.2 and -8.5' means we multiply these two numbers together: \(4.2 \times -8.5\).
Multiplying results in finding the product, which in this case is \(-35.7\).
This is a fundamental concept in math and is essential for solving many types of problems efficiently.
subtraction
Subtraction is one of the basic arithmetic operations. It involves taking away a number from another.
In our problem, the phrase 'Three subtracted from the product of 4.2 and -8.5' tells us to subtract 3 from \(-35.7\), the product we found earlier.
The subtraction is represented as: \(-35.7 - 3\) and this operation gives us \(-38.7\).
The key here is the correct order: always subtract from the result of the previous operations.
In our problem, the phrase 'Three subtracted from the product of 4.2 and -8.5' tells us to subtract 3 from \(-35.7\), the product we found earlier.
The subtraction is represented as: \(-35.7 - 3\) and this operation gives us \(-38.7\).
The key here is the correct order: always subtract from the result of the previous operations.
multiplication
Multiplication is another basic arithmetic operation. It involves finding the total of one number taken a specific number of times.
In this problem, when we see 'product of 4.2 and -8.5,' we know we need to multiply these two numbers.
Multiplication can often involve both positive and negative numbers. The product of a positive number and a negative number is always negative.
For instance: \(4.2 \times -8.5 = -35.7\).
Understanding multiplication and how to handle negative numbers is crucial for simplifying expressions.
In this problem, when we see 'product of 4.2 and -8.5,' we know we need to multiply these two numbers.
Multiplication can often involve both positive and negative numbers. The product of a positive number and a negative number is always negative.
For instance: \(4.2 \times -8.5 = -35.7\).
Understanding multiplication and how to handle negative numbers is crucial for simplifying expressions.
Other exercises in this chapter
Problem 109
Write a numerical expression for each phrase, and simplify the expression. 8 less than -2
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Write a numerical expression for each phrase, and simplify the expression. The product of 12 and the difference of 9 and -8
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Write a numerical expression for each phrase, and simplify the expression. The sum of 12 and \(-7,\) decreased by 14
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