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Questions and Answers
Which mathematical principle is primarily demonstrated by the equation $5(7 + 3)$?
Which mathematical principle is primarily demonstrated by the equation $5(7 + 3)$?
What is the result of simplifying the expression $12 - 4 + 3$?
What is the result of simplifying the expression $12 - 4 + 3$?
If $x = 3$ and $y = 4$, what is the value of the expression $2x + 3y$?
If $x = 3$ and $y = 4$, what is the value of the expression $2x + 3y$?
Which equation represents the inverse operation for addition?
Which equation represents the inverse operation for addition?
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What is the correct interpretation of the expression $3(x + 4)$?
What is the correct interpretation of the expression $3(x + 4)$?
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The ______ of an equation shows how two expressions are equivalent.
The ______ of an equation shows how two expressions are equivalent.
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A ______ is a mathematical statement that asserts the equality of two expressions.
A ______ is a mathematical statement that asserts the equality of two expressions.
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To ______ an equation means to isolate the variable on one side.
To ______ an equation means to isolate the variable on one side.
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In mathematics, a ______ is any numeral or symbol that represents a value.
In mathematics, a ______ is any numeral or symbol that represents a value.
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The ______ of addition is subtraction.
The ______ of addition is subtraction.
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Study Notes
Distributive Property
- The equation 5(7+3)5(7 + 3)5(7+3) demonstrates the distributive property of multiplication over addition.
- The distributive property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products.
Order of Operations
- To simplify the expression 12−4+312 - 4 + 312−4+3, we follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
- Therefore, we first perform the subtraction: 12−4=812 - 4 = 812−4=8, and then the addition: 8+3=118 + 3 = 118+3=11.
Evaluating Expressions
- Given x=3x = 3x=3 and y=4y = 4y=4, we substitute these values into the expression 2x+3y2x + 3y2x+3y.
- This gives: 2(3)+3(4)=6+12=182(3) + 3(4) = 6 + 12 = 182(3)+3(4)=6+12=18.
Inverse Operation
- The inverse operation for addition is subtraction.
- Subtraction "undoes" addition, meaning that adding a number and then subtracting the same number results in the original number.
Interpreting Expressions
- The expression 3(x+4)3(x + 4)3(x+4) represents multiplying the quantity (x+4)(x + 4)(x+4) by 3.
- This means that we distribute the multiplication to both terms inside the parentheses: 3(x+4)=3x+123(x + 4) = 3x + 123(x+4)=3x+12.
The Distributive Property
- The equation $5(7 + 3)$ demonstrates the distributive property of multiplication over addition. This property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products.
Order of Operations
- To simplify $12 - 4 + 3$, follow the order of operations, which is often remembered by PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction):
- $12 - 4 + 3 = 8 + 3 = 11$
Evaluating Expressions
- If $x = 3$ and $y = 4$, substitute these values into the expression $2x + 3y$ and evaluate:
- $2(3) + 3(4) = 6 + 12 = 18$
Inverse Operations
- The equation representing the inverse operation for addition is subtraction:
- $a + b = c$ is equivalent to $c - b = a$
Simplifying Expressions
- The expression $3(x + 4)$ is a combination of multiplication and addition. It can be interpreted as:
- Multiplying the sum of $x$ and $4$ by $3$, or
- Distributing the $3$ to both terms inside the parentheses: $3x + 12$
Equations
- The equal sign of an equation shows how two expressions are equivalent.
- An equation is a mathematical statement that asserts the equality of two expressions.
- To solve an equation means to isolate the variable on one side by performing inverse operations on both sides.
Mathematical Terms
- In mathematics, a constant is any numeral or symbol that represents a value.
- The inverse of addition is subtraction, meaning they undo each other.
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Description
This quiz covers fundamental concepts in algebra, including mathematical principles, simplification of expressions, and the evaluation of algebraic expressions. Test your understanding of key operations such as addition and distribution.
