62. Subtract \[$4 + 3y\$\] From \[$8 - 5y\$\].63. Simplify: \[$3.4m - 4 - 3.4m - 7\$\].64. Simplify: \[$2.8w - 0.9 - 0.5 - 2.8w\$\].65. Simplify: \[$\frac{1}{3}(7y - 1) + \frac{1}{6}(4y + 7)\$\].66. Simplify:
Introduction
Algebraic expressions are a fundamental concept in mathematics, and simplifying them is a crucial skill to master. In this article, we will explore the process of simplifying various types of algebraic expressions, including linear expressions, expressions with variables, and expressions with fractions.
Subtracting Algebraic Expressions
62. Subtract ${4 + 3y\$} from ${8 - 5y\$}
To subtract one algebraic expression from another, we need to combine like terms. In this case, we have two expressions: ${4 + 3y\$} and ${8 - 5y\$}. To subtract the first expression from the second, we need to distribute the negative sign to the terms in the first expression.
${$8 - 5y - (4 + 3y)$]
Using the distributive property, we can rewrite the expression as:
[$8 - 5y - 4 - 3y$]
Now, we can combine like terms:
[$8 - 4 - 5y - 3y$]
Simplifying further, we get:
[$4 - 8y$]
Therefore, the result of subtracting [4 + 3y\$} from ${8 - 5y\$} is ${$4 - 8y$].
63. Simplify: [3.4m - 4 - 3.4m - 7\$}
To simplify this expression, we need to combine like terms. We have two terms with the variable {m$}$, and two constant terms.
${$3.4m - 4 - 3.4m - 7$]
Combining like terms, we get:
[-4 - 7}$
Simplifying further, we get:
${-11$]
Therefore, the result of simplifying the expression is [-11$].
64. Simplify: [2.8w - 0.9 - 0.5 - 2.8w\$}
To simplify this expression, we need to combine like terms. We have two terms with the variable {w$}$, and two constant terms.
${$2.8w - 0.9 - 0.5 - 2.8w$]
Combining like terms, we get:
[-0.9 - 0.5$]
Simplifying further, we get:
[-1.4$]
Therefore, the result of simplifying the expression is [-1.4$].
65. Simplify: [\frac{1}{3}(7y - 1) + \frac{1}{6}(4y + 7)\$}
To simplify this expression, we need to distribute the fractions to the terms inside the parentheses.
{\frac{1}{3}(7y - 1) + \frac{1}{6}(4y + 7)$]
Distributing the fractions, we get:
[\frac{7y}{3} - \frac{1}{3} + \frac{4y}{6} + \frac{7}{6}}$
Combining like terms, we get:
Simplifying further, we get:
Combining like terms, we get:
Simplifying further, we get:
Therefore, the result of simplifying the expression is .
66. Simplify: {\frac{1}{2}(3x + 2) - \frac{1}{4}(2x - 3)$}$
To simplify this expression, we need to distribute the fractions to the terms inside the parentheses.
{\frac{1}{2}(3x + 2) - \frac{1}{4}(2x - 3)$]
Distributing the fractions, we get:
[\frac{3x}{2} + \frac{2}{2} - \frac{2x}{4} + \frac{3}{4}}$
Combining like terms, we get:
Simplifying further, we get:
Combining like terms, we get:
Simplifying further, we get:
Therefore, the result of simplifying the expression is .
Conclusion
Q&A: Simplifying Algebraic Expressions
Q: What is the first step in simplifying an algebraic expression? A: The first step in simplifying an algebraic expression is to combine like terms. Like terms are terms that have the same variable raised to the same power.
Q: How do I combine like terms? A: To combine like terms, you need to add or subtract the coefficients of the like terms. For example, if you have the expression $2x + 3x\$}, you can combine the like terms by adding the coefficients$.
Q: What is the distributive property? A: The distributive property is a rule that allows you to multiply a single term to multiple terms inside parentheses. For example, if you have the expression $2(x + 3)\$}, you can use the distributive property to multiply the 2 to each term inside the parentheses$.
Q: How do I simplify an expression with fractions? A: To simplify an expression with fractions, you need to combine the fractions by finding a common denominator. For example, if you have the expression {\frac1}{2} + \frac{1}{3}$}$, you can find a common denominator of 6 and rewrite the fractions{6} + \frac{2}{6} = \frac{5}{6}$}$.
Q: What is the difference between a linear expression and a quadratic expression? A: A linear expression is an expression with one variable raised to the power of 1, while a quadratic expression is an expression with one variable raised to the power of 2. For example, ${2x + 3\$} is a linear expression, while {x^2 + 2x + 1$}$ is a quadratic expression.
Q: How do I simplify an expression with parentheses? A: To simplify an expression with parentheses, you need to follow the order of operations (PEMDAS): parentheses, exponents, multiplication and division, and addition and subtraction. For example, if you have the expression $2(x + 3)\$}, you need to multiply the 2 to each term inside the parentheses$.
Q: What is the difference between a variable and a constant? A: A variable is a letter or symbol that represents a value that can change, while a constant is a value that does not change. For example, {x$}$ is a variable, while ${3\$} is a constant.
Q: How do I simplify an expression with absolute value? A: To simplify an expression with absolute value, you need to consider two cases: when the expression inside the absolute value is positive, and when it is negative. For example, if you have the expression {|x + 3|$}$, you need to consider two cases: {x + 3 \geq 0$}$ and {x + 3 < 0$}$.
Conclusion
Simplifying algebraic expressions is an essential skill in mathematics. By combining like terms, distributing fractions, and following the order of operations, you can simplify complex expressions and make them easier to work with. In this article, we have explored the process of simplifying various types of algebraic expressions, including linear expressions, expressions with variables, and expressions with fractions. By following the steps outlined in this article, you can simplify even the most complex algebraic expressions and become a master of algebraic manipulation.