Question:The quotient of a number and 2 is the same as the difference of the number doubled and 3. what is the number? Show
Algebraic ExpressionsWe have to translate the words given into two algebraic expressions. Both these expressions will be equal to each other. This allows us to form an equation that can be solved to find the required number. Answer and Explanation: 1Let the number be x. The quotient of x and 2 will be x/2. The difference of the double of x and 3 and 2x-3. As the above two quantities are equal, we get the following equation: $$\begin{align} \frac{x}{2}&=2x-3\\ x&=2(2x-3)\\ x&=4x-6\\ x-4x&=-6\\ x&=\frac{-6}{-3}\\ x&=2 \end{align} $$ Thus, the number is 2. Learn more about this topic:Solving Problems Using Rational Equations from Chapter 11 / Lesson 8 Rational equations are equations with fractions that are just numbers or have both numbers and letters. Explore the definition of rational equations, and the process of finding the solution that will solve these types of problems. Related to this QuestionExplore our homework questions and answers libraryMath, like any other language, has a way of communicating ideas. An algebraic expression is a concise way of describing mathematical objects through the use of numbers, variables (letters), and arithmetic operations such as addition, subtraction, multiplication, and division. The three main components of algebraic expressions are numbers, variables, and arithmetic operations.
Examples: 1, 6, 8, 27, 32, etc.
Examples: x, y, a, h, p, etc.
Examples: + (addition), - (subtraction) , \times (multiplication) , ÷ (division) The following are easy examples that can help you get familiar with the operations of addition, subtraction, multiplication, and division.
the sum of x and 5 → x+5
the difference of y and 3 → y-3
the product of n and 2 → 2n
the quotient of k and 7 → \Large{{k \over 7}} Writing Algebraic Expressions Step-by-Step ExamplesLet’s go over more examples. Example 1: The sum of twice a number and 3 Answer: Let variable x be the unknown number. So twice a number means 2x. The sum (use plus symbol) of twice a number and 3 can be written as 2x+3. Example 2: The difference of triple a number and 5 Answer: Let variable y be the unknown number. So triple a number means 3y. Thedifference(use minus symbol) of triple a number and 5 should be written as 3y - 5. Example 3: The sum of the quotient of m and 2, and the product of 4 and n. Answer: In this case, the unknown numbers are already provided as m and n. That’s one less thing to worry about. The key is to recognize that we are going to add a quotient and a product.
Therefore, the sum of the quotient and product is {\Large{{m \over 2}}} + 4n. Example 4: The difference of the product of 7 and w, and the quotient of 2 and v. Answer: In this case, the unknown numbers have been assigned with corresponding variables which are w and v. The key is to recognize that we are going to subtract the product by the quotient of some expressions.
Therefore, the difference of the product and quotient is 7w - {\Large{{2 \over v}}}. Common Words or Terms to Mean Addition, Subtraction, Multiplication, and DivisionLet’s go over some common words or phrases that describe the four arithmetic operations. It is critical that you understand these words or phrases in order to successfully write or interpret any given algebraic expression. Math Phrases into Algebraic ExpressionsThe key to learning is to study a LOT of examples!
You might also be interested in: Algebraic Expressions Worked Examples Algebraic Sentences Word Problems What is the algebraic expression for a number divided by 4?Math Phrases into Algebraic Expressions. How do you write the quotient of four and a number?Step 1: Consider the unknown number to be x. Step 2: The word "quotient" indicates division. So, x/4.
Is 4 a algebraic expression?Is 4 an algebraic expression? No, 4 is not an algebraic expression because an expression should have at least one variable and one operation to be algebraic.
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