Introduction
Translating verbal expressions into mathematical expressions is a vital skill in algebra, key to simplifying problems and enhancing problem-solving capabilities. Understanding the relation between words and their mathematical counterparts can make complex problems manageable. In this article, we will cover various expressions and demonstrate how to convert them into their mathematical forms step-by-step.
Understanding Key Terms
Before jumping into examples, let’s clarify some fundamental terms:
- Quotient: Refers to the result of division.
- Sum: Indicates addition.
- Difference: Refers to subtraction.
- Product: Indicates multiplication.
- Total: Similar to sum, indicates addition.
- Twice: Means double the value.
- Fraction: Represents division, often depicted as a numerator over a denominator.
Example Translations
Let's now dive into the examples:
1. The Quotient of n in the Sum of n and Six
The expression states, "the quotient of n in the sum of n and six".
-
Quotient means division, hence the expression can be represented as:
$$\frac{n}{n + 6}$$
Here, the numerator is n and the denominator is the sum (n + 6).
2. The Sum of Five and the Product of Four and n
This expression translates to "the sum of five in the product of four and n".
-
The product of four and n can be expressed as 4n.
-
Therefore, the sum translates to:
$$5 + 4n$$
This indicates adding five to the product of four and n.
3. The Difference Between Eight and Twice t
In this case, you need to interpret "the difference between 8 and twice t".
-
The phrase twice t indicates 2t.
-
Thus, the expression translates to:
$$8 - 2t$$
This signifies subtracting 2t from 8.
4. The Product of Three and the Difference Between z and Four
This expression reads, "the product of three and the difference between z and four".
-
Here, you have to identify the difference between z and four, indicating the expression (z - 4).
-
Thus, you arrive at:
$$3(z - 4)$$
This states that three is multiplied by the quantity (z - 4).
5. The Quotient of Five and the Product of Seven and x
The phrase states, "the quotient of five and the product of seven and x".
-
The product is expressed as 7x,
-
Therefore, the expression translates to:
$$\frac{5}{7x}$$
This represents dividing five by the product of seven and x.
6. The Total of a Number in the Square of the Number
We’ll express "the total of a number in the square of the number" using a variable, say n.
-
Total denotes addition, hence you get:
$$n + n^2$$
This translates to the sum of n and its square.
7. The Product of a Number and One Half of the Number
In this phrase, "the product of a number and one half of the number", we can denote the unknown number as n.
-
One half of n is represented as (1/2)n,
-
Therefore, the product, as you might expect, is:
$$n \times \frac{1}{2} n = \frac{1}{2} n^2$$
This clears up any confusion regarding multiplication with fractions!
Additional Expressions and Keywords
In learning how to translate verbal expressions, familiarize yourself with commonly used terms:
- Addition: more than, the sum of, total of, increased by
- Subtraction: less than, difference between, decreased by
- Multiplication: times, product of, of, twice
- Division: divided by, the quotient of, the ratio of.
Conclusion
Understanding how to convert verbal expressions into mathematical expressions is a critical mathematical skill that can improve your problem-solving aptitude. Familiarizing yourself with terms like sum, difference, product, and quotient makes mathematics more approachable. Practice these translations frequently to enhance your mathematical fluency, and soon you'll navigate between words and equations with ease!
section 11.5 translating verbal expressions into mathematical expressions
number one translate the quotient of n in the sum of n and six into a mathematical expression
start with the word quotient the word quotient means division you can write it as a horizontal
division with a division symbol or you can write it as a fraction as you see here
so we are going to have the quotient of n which will be our numerator and the sum of n and six the sum of n
and six itself will be the denominator of the fraction
or of the quotient sum means to add so the quantity n plus six is our denominator number two translate
the expression the sum of five in the product of four and
n so it's really an addition problem because it's the sum of five and four n the product
means to multiply 4 times n which can be expressed as 4n so our final answer is
5 plus 4n number 3 the difference between 8 and twice t this problem is essentially a
subtraction problem we're subtracting eight minus two t the phrase twice t means two times
whatever it's being multiplied by number four translate the product of three
and the difference between z and four so we have two parts we have three and then we have a product so
times then we have a quantity the difference between z and four
notice that i put the quantity z minus four in parentheses that's because we are multiplying that
entire quantity by three so it's three times the quantity z minus four
again the word product means to multiply and the word difference means to subtract
number five translate the quotient of five and the product of seven and x
so this is essentially a division problem where the numerator is five and the denominator is the
product of seven and x so we have five over seven times x or five over seven x
number six translate the total of a number in the square of the number you can pick
any letter of the alphabet that you'd like to represent your unknown value or your number
the word total means to add think about it this way anytime you're trying to find a total or you're totaling numbers
together you're going to add them to get a final answer so in this case it's the total of
a number we'll call it n and the square of the same number so it's n plus n squared
finally number seven translate the product of a number and one half of the number
i chose and again you can choose whatever letter you want from the alphabet
so this is essentially a product meaning multiplication so it's n times one half n the word
of so one half of the number also means to multiply so essentially what you're doing with
that one-half n is multiplying so it's really n times one-half
times n so n times one-half n if you'd like you could also write with parentheses which also denotes
multiplication n times one-half n in general you want to be comfortable when reading
expressions knowing what they mean so starting with addition some expressions you may see
are more than or the sum of or the total of or increased by there are
others as well in terms of subtraction you may see less than or the difference between or decreased
by in terms of multiplication you may see times
or the product of or the word of which i just mentioned or twice
amongst other examples and then finally division divided by or the quotient of or the
ratio of remember the word ratio also can denote a fraction
Heads up!
This summary and transcript were automatically generated using AI with the Free YouTube Transcript Summary Tool by LunaNotes.
Generate a summary for freeRelated Summaries

Mastering Order of Operations: Simplifying Complex Expressions
Learn how to simplify complex expressions using the order of operations with clear examples and step-by-step instructions.

Understanding the Order of Operations in Mathematics
Learn the importance of the Order of Operations and how to solve math problems accurately.

How to Simplify Algebraic Expressions: A Step-by-Step Guide
Learn how to simplify algebraic expressions with easy steps and clear examples.

Understanding the Distributive Property and Key Algebra Terms
Learn about the distributive property and important algebra terms like terms, coefficients, and constants.

Mastering Square Roots of Rational Numbers: A Comprehensive Guide
Learn how to easily calculate square roots of rational numbers with practical examples and tips.
Most Viewed Summaries

A Comprehensive Guide to Using Stable Diffusion Forge UI
Explore the Stable Diffusion Forge UI, customizable settings, models, and more to enhance your image generation experience.

Pamaraan at Patakarang Kolonyal ng mga Espanyol sa Pilipinas
Tuklasin ang mga pamamaraan at patakarang kolonyal ng mga Espanyol sa Pilipinas at ang mga epekto nito sa mga Pilipino.

Pamamaraan at Patakarang Kolonyal ng mga Espanyol sa Pilipinas
Tuklasin ang mga pamamaraan at patakaran ng mga Espanyol sa Pilipinas, at ang epekto nito sa mga Pilipino.

Kolonyalismo at Imperyalismo: Ang Kasaysayan ng Pagsakop sa Pilipinas
Tuklasin ang kasaysayan ng kolonyalismo at imperyalismo sa Pilipinas sa pamamagitan ni Ferdinand Magellan.

Ultimate Guide to Installing Forge UI and Flowing with Flux Models
Learn how to install Forge UI and explore various Flux models efficiently in this detailed guide.