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Chapter 4: Problem 87

Write four phrases that translate into the expression \(d-16\)

Short Answer

Expert verified
The expression \(d-16\) translates into the following phrases: 1. 16 less than a certain number \(d\), 2. Subtract 16 from a certain number \(d\), 3. A certain number \(d\) decreased by 16, 4. A certain number \(d\) minus 16.

Step by step solution

01

Understand the expression

Here, the expression given is \(d-16\). It represents the mathematical operation of subtraction. In this case, the number 16 is subtracted from a variable \(d\). The variable could be any real number.
02

Translate into a phrase - Phrase 1

One possible translation could be '16 less than a certain number \(d\)'. This describes the operation of subtraction by referring to the number 16 being less than the variable \(d\).
03

Translate into a phrase - Phrase 2

Another way to phrase it could be 'Subtract 16 from a certain number \(d\)'. This phrase clearly and directly refers to our mathematical operation.
04

Translate into a phrase - Phrase 3

'A certain number \(d\) decreased by 16'. This expression indicates the number \(d\) being decreased or subtracted by 16.
05

Translate into a phrase - Phrase 4

Final translation can be 'A certain number \(d\) minus 16'. This is perhaps the simplest and most direct translation of the original mathematical expression.

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Key Concepts

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

Translation of Expressions
Translating mathematical expressions into phrases is an important skill. This involves converting numerical operations and symbols into everyday language. For the expression \(d-16\), we observe it consists of two main components: the variable \(d\) and the constant 16, where the operation between them is subtraction.

Here are ways to express \(d-16\) through language:
  • '16 less than a certain number \(d\)': This translation helps us visualize 16 units being taken away from something represented by \(d\).
  • 'Subtract 16 from a certain number \(d\)': Here, the emphasis is on the action of subtraction, illustrating the operation directly.
  • 'A certain number \(d\) decreased by 16': This phrase highlights the reduction of the value \(d\) by 16.
  • 'A certain number \(d\) minus 16': This provides a straightforward translation that mirrors the expression's structure.
Each phrase provides a different perspective on the same mathematical concept, aiding comprehension by catering to varied modes of understanding.
Subtraction in Mathematics
Subtraction is one of the fundamental operations in mathematics. It involves "taking away" or "removing" a certain amount from another. In our expression \(d-16\), the subtraction tells us to remove 16 from whatever the value of \(d\) might be.

In everyday life, subtraction can illustrate various scenarios, such as:
  • Calculating the remaining amount after an expense
  • Determining how much more is needed to reach a goal
  • Evaluating the difference between two quantities
In algebra, subtraction helps in simplifying expressions and solving equations. By translating subtraction into language, we gain better insight into its application. For example, when we express \(d-16\) in words as discussed earlier, it clarifies the process happening behind the subtraction symbol.
Variables in Equations
Variables are symbols used to represent numbers whose exact values are not known. In the expression \(d-16\), \(d\) is a variable, often representing a number that can change based on context. This makes variables crucial for forming and solving equations.

Here's why variables are pivotal:
  • They allow general mathematical formulas and expressions to be applied to a wide range of situations.
  • Variables enable us to describe relationships between numbers without knowing their specific values.
  • They are foundational in algebra, serving as the tools that help in constructing equations.
By understanding variables, like \(d\) in \(d-16\), we can explore how different values affect expressions and solve for unknowns, a key part of both algebraic thinking and problem-solving.

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