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Chapter 1: Problem 3

Identify each as a sum, difference, product, or quotient. \(\frac{1}{2}\) of \(q\)

Short Answer

Expert verified
The operation is a product.

Step by step solution

01

Analyze the operation

The keyword 'of' in mathematics often implies multiplication. In this case, \(\frac{1}{2}\) 'of' \(q\) represents \(\frac{1}{2} * q\), if we rewrite it in standard mathematical notation.
02

Identify the operation

\(\frac{1}{2} * q\) is a multiplication of two factors, \(\frac{1}{2}\) and \(q\). Therefore, the operation represented is a product.

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Key Concepts

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

Understanding Mathematical Operations
Mathematical operations form the foundation of algebraic expressions. They tell us what to do with numbers and variables. Common operations include addition, subtraction, multiplication, and division. Each operation has specific keywords associated with it. For instance, multiplication often uses "times," "product," or "of." In the exercise, the word "of" signals multiplication between \(\frac{1}{2}\) and \(q\). Recognizing these keywords is essential for converting problem statements into mathematical expressions. This skill helps you work with numbers and variables more effectively, allowing for accurate problem-solving.
Exploring Multiplication
Multiplication is essentially repeated addition. It's one of the four basic operations in mathematics. When you're working with numbers, multiplication combines groups of the same size. For example, \(3 \times 4\) means you have three groups of four, making a total of twelve. When you multiply a number by a fraction like \(\frac{1}{2}\), you're taking "half" of that number. So, multiplying \(\frac{1}{2} \times q\) is the same as finding half of \(q\). By understanding multiplication in this way, you can easily break down and simplify algebraic expressions.
Working with Fractions
Fractions represent a part of a whole. They consist of a numerator (top number) and a denominator (bottom number). The fraction \(\frac{1}{2}\) means one part out of two equal parts. When dealing with multiplication involving fractions, you're essentially distributing a part of a number. In the exercise, multiplying \(\frac{1}{2}\) by \(q\) means taking half of \(q\). To multiply fractions, simply multiply the numerators and then the denominators, though here it's more straightforward as \(q\) is a whole number variable. Understanding fractions helps in managing parts of quantities easily and accurately.

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Most popular questions from this chapter

Each year, a typical dairy cow will eat 12,000 pounds of food that is \(57 \%\) silage. To feed 30 cows, how much silage will a farmer use in a year?

Explain why division is not commutative.

Explain why there is no greatest natural number.

Let \(x=8, y=4,\) and \(z=2 .\) Write each phrase as an algebraic expression, and evaluate it. Assume that no denominators are \(0 .\) What factor is common to all three terms? Consider the algebraic expression \(3 x y z+5 x y+17 x z\)

Suppose there were no numbers other than the odd integers. \(\cdot\) Would the closure property for addition still be true? \(\cdot\) Would the closure property for multiplication still be true? \(\cdot\) Would there still be an identity for addition? \(\cdot\) Would there still be an identity for multiplication?
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