Questions and Answers
What is a characteristic of a rational number?
What is the equation of a linear equation in one variable in general form?
What is the sum of the interior angles of a plane?
What is the method of solving a linear equation by adding or subtracting the same value to both sides of the equation?
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What is the name of the angle that is greater than 90° but less than 180°?
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What is the term for the distance around a shape?
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What is the property of rational numbers that states that the result of adding, subtracting, multiplying, or dividing two rational numbers is always a rational number?
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What is the term for the amount of space inside a shape?
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What is the method of solving a linear equation by multiplying or dividing both sides of the equation by the same value?
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What is the term for shapes that have the same size and shape?
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Study Notes
Rational Numbers
- A rational number is a number that can be expressed as the ratio of two integers, i.e., p/q, where p and q are integers and q ≠ 0.
- Examples: 3/4, 22/7, -5/2
- Properties:
- Closure: The result of adding, subtracting, multiplying, or dividing two rational numbers is always a rational number.
- Commutativity: The order of rational numbers does not change the result of addition or multiplication.
- Associativity: The order in which rational numbers are added or multiplied does not change the result.
- Distributivity: Multiplication of rational numbers is distributive over addition.
Understanding Shapes
-
Points, Lines, and Planes:
- A point has no size, only location.
- A line extends infinitely in two directions.
- A plane is a flat surface that extends infinitely in all directions.
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Types of Angles:
- Acute angle: less than 90°
- Right angle: exactly 90°
- Obtuse angle: greater than 90° but less than 180°
- Straight angle: exactly 180°
-
Properties of Shapes:
- Congruent shapes: have the same size and shape.
- Similar shapes: have the same shape but not necessarily the same size.
- Perimeter: the distance around a shape.
- Area: the amount of space inside a shape.
Linear Equations in One Variable
- A linear equation in one variable is an equation in which the highest power of the variable is 1.
- General form: ax + b = 0, where a and b are constants, and x is the variable.
- Methods for solving linear equations:
- Addition/Subtraction method
- Multiplication/Division method
- Transposition method
- Key concepts:
- Solving for the variable: finding the value of the variable that makes the equation true.
- Checking solutions: verifying that the solution satisfies the equation.
Rational Numbers
- A rational number is a number that can be expressed as the ratio of two integers, p/q, where p and q are integers and q ≠ 0.
- Examples of rational numbers include 3/4, 22/7, and -5/2.
- Rational numbers have the following properties:
- Closure: The result of adding, subtracting, multiplying, or dividing two rational numbers is always a rational number.
- Commutativity: The order of rational numbers does not change the result of addition or multiplication.
- Associativity: The order in which rational numbers are added or multiplied does not change the result.
- Distributivity: Multiplication of rational numbers is distributive over addition.
Understanding Shapes
Points, Lines, and Planes
- A point has no size, only location.
- A line extends infinitely in two directions.
- A plane is a flat surface that extends infinitely in all directions.
Types of Angles
- An acute angle is less than 90°.
- A right angle is exactly 90°.
- An obtuse angle is greater than 90° but less than 180°.
- A straight angle is exactly 180°.
Properties of Shapes
- Congruent shapes have the same size and shape.
- Similar shapes have the same shape but not necessarily the same size.
- The perimeter of a shape is the distance around it.
- The area of a shape is the amount of space inside it.
Linear Equations in One Variable
- A linear equation in one variable is an equation in which the highest power of the variable is 1.
- The general form of a linear equation in one variable is ax + b = 0, where a and b are constants, and x is the variable.
- Methods for solving linear equations include:
- Addition/Subtraction method
- Multiplication/Division method
- Transposition method
- Key concepts in solving linear equations include:
- Solving for the variable: finding the value of the variable that makes the equation true.
- Checking solutions: verifying that the solution satisfies the equation.
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Description
Test your understanding of rational numbers, their properties and operations. Learn about closure, commutativity, and associativity of rational numbers.
