Mastering Algebraic Expressions

Table of Contents:

1. Introduction
2. Expressions with One Operation
   • 2.1. Product of Nine and m
   • 2.2. Number x Divided by Twelve
   • 2.3. Seven Less Than r
   • 2.4. Sum of w and Fifty-Five
   • 2.5. Difference of c and Thirty-Eight
   • 2.6. Number y Increased by Ten
   • 2.7. Twenty-One Times a Number g
   • 2.8. Quotient of Forty-Six and x
3. Expressions with Two Operations
   • 3.1. Sum of a Number x and Eight, then Multiply by Ten
   • 3.2. Quotient of Twenty-Five and a Number y Increased by a Number m
   • 3.3. Subtract a Number w from Eighty-One, then Divide by Two
   • 3.4. Five Times the Difference of Thirty-Three and a Number x
4. Conclusion

How to Write Algebraic Expressions

In this article, we will explore how to write algebraic expressions. Algebraic expressions are essential in mathematics as they allow us to represent and solve various situations using variables and operations. By understanding and being able to write algebraic expressions correctly, You can develop a solid foundation in algebra and enhance your problem-solving skills.

2. Expressions with One Operation

Let's begin by looking at expressions that involve a single operation.

2.1. Product of Nine and m

The first example we will discuss is the product of nine and m. The keyword "product" indicates multiplication. Therefore, we can write this expression as 9 * m or 9m. It is important to avoid using "x" as it can lead to confusion with variables.

2.2. Number x Divided by Twelve

Next, we have an expression where a number x is divided by twelve. Here, "divided by" indicates division. We can write the expression as x / 12 or x ÷ 12. Using a slash or a fraction symbol is also acceptable.

2.3. Seven Less Than r

In this case, we need to express the phrase "seven less than r." The keyword "less than" suggests subtraction. We switch the order and write the expression as r - 7. It is crucial to pay Attention to the wording to determine the correct order of variables.

2.4. Sum of w and Fifty-Five

Our next expression involves finding the sum of w and fifty-five. The keyword "sum" indicates addition. We can write this expression as w + 55.

2.5. Difference of c and Thirty-Eight

Here, we want to express the difference between c and thirty-eight. The keyword "difference" implies subtraction. Therefore, we write the expression as c - 38. Note that the order remains the same since there is no keyword indicating a change in order.

2.6. Number y Increased by Ten

In this expression, we need to represent the phrase "number y increased by ten." The keyword "increased" signifies addition. Thus, the expression becomes y + 10.

2.7. Twenty-One Times a Number g

We now consider an expression where we have to find the product of twenty-one and a number g. The keyword "times" indicates multiplication. We represent this expression as 21g. Using a number next to a variable signifies multiplication.

2.8. Quotient of Forty-Six and x

Lastly, let's discuss the expression "quotient of forty-six and x." The keyword "quotient" represents division. We write this expression as 46 / x or 46 ÷ x using a fraction format.

3. Expressions with Two Operations

Moving on, we will explore expressions involving two operations.

3.1. Sum of a Number x and Eight, then Multiply by Ten

In this example, we need to find the sum of a number x and eight, then multiply the result by ten. The first operation is addition, indicated by the keyword "sum." We write this as (x + 8). Due to the order of operations, we enclose the addition in parentheses. The Second operation is multiplication. We represent the entire expression as (x + 8) * 10 or 10(x + 8).

3.2. Quotient of Twenty-Five and a Number y Increased by a Number m

Here, we want to find the quotient of twenty-five and a number y, increased by a number m. The keyword "quotient" denotes division. We write this expression as (25 / y) + m or (25 ÷ y) + m. Note that we can represent division as a fraction or using a slash. By following the order of operations, we perform division first and then addition.

3.3. Subtract a Number w from Eighty-One, then Divide by Two

In this case, we need to subtract a number w from eighty-one, then divide the result by two. The keyword "subtract" implies subtraction, and "divide" indicates division. The expression becomes (81 - w) / 2. Using parentheses helps indicate the order of operations, ensuring we perform subtraction before division.

3.4. Five Times the Difference of Thirty-Three and a Number x

Our final example involves finding the product of five and the difference between thirty-three and a number x. The keyword "difference" indicates subtraction. Therefore, the expression is 5 * (33 - x). By enclosing the subtraction in parentheses, we ensure that it is performed first, followed by multiplication.

Conclusion

In this article, we explored how to write algebraic expressions with one and two operations. By understanding the keywords relating to different operations and following the order of operations, you can accurately represent mathematical situations using variables and operations. By practicing and familiarizing yourself with writing algebraic expressions, you can develop your problem-solving skills and build a solid foundation in algebra.