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Chapter 1: Problem 17

Use mathematical symbols to translate each phrase. Six less than half of a number

Short Answer

Expert verified
\( \frac{x}{2} - 6 \)

Step by step solution

01

Identify the unknown variable

Let the unknown number be represented by the variable \( x \).
02

Translate 'half of a number'

Half of the number \( x \) can be represented as \( \frac{x}{2} \).
03

Translate 'six less than'

To express 'six less than' a value, subtract 6 from that value.
04

Combine the translations

Combine the expressions to get 'six less than half of a number,' which translates to \( \frac{x}{2} - 6 \).

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Key Concepts

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

Unknown Variable
In algebra, an unknown variable represents a number we don't yet know. We use letters like x to stand for this mysterious number. This makes it easier to write and solve equations.
For example, if we don't know a number, we just call it x. Then, if we're given hints or equations involving x, we can figure out what x is.
So in the problem 'Six less than half of a number,' we start by letting our unknown number be x. This sets the stage for us to translate the entire phrase into algebraic expressions.
Fractional Expressions
Fractional expressions involve parts of a whole and are common in algebra. When we see a phrase like 'half of a number', it's talking about dividing that number by 2.
Using our unknown variable x, 'half of a number' is represented as \(\frac{x}{2} \). This is because dividing by 2 splits the number into two equal parts.
Fractions in algebra often make equations more flexible and understandable, especially when dealing with portions of quantities. When you encounter such phrases, always think about what fractional expression will best represent the idea.
Subtraction in Algebra
Subtraction is another key operation in algebra and life. If we say 'six less than a number', we're talking about taking 6 away from that number.
In algebraic terms, if you have a number a, 'six less than' that number is represented as a - 6.
So when we combine everything from the previous steps:
  • Our unknown number is x
  • Half of that number is \(\frac{x}{2}\)
  • Six less than that half is \(\frac{x}{2} - 6\)

This shows how to put together different parts of a phrase to form a complete algebraic expression. Always break down the problem step-by-step.

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Most popular questions from this chapter

Find an equivalent expression by factoring. $$ 9 p-3 $$

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Write an equivalent expression using an associative law. $$ (3 x) y $$

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