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Questions and Answers
What is the result of 2 × (3 + 4) using the Distributive Property?
What is the result of 2 × (3 + 4) using the Distributive Property?
What type of angle is formed by two lines that intersect at exactly 90 degrees?
What type of angle is formed by two lines that intersect at exactly 90 degrees?
Which of the following is an example of a Congruent Shape?
Which of the following is an example of a Congruent Shape?
What is the value of x in the equation 2x + 5 = 11?
What is the value of x in the equation 2x + 5 = 11?
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What is the definition of a Point in geometry?
What is the definition of a Point in geometry?
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Which of the following shapes has all sides and angles equal?
Which of the following shapes has all sides and angles equal?
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What is the result of 5 - 2 + 1 using the Associative Property?
What is the result of 5 - 2 + 1 using the Associative Property?
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What is the definition of a Polygon?
What is the definition of a Polygon?
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Study Notes
Arithmetic
Numbers and Operations
- Whole numbers: positive integers, e.g., 1, 2, 3, ...
- Fractions: part of a whole, e.g., 1/2, 3/4
- Decimals: fractional parts of a whole, e.g., 0.5, 0.25
- Percentages: fractions of 100, e.g., 25%, 50%
Basic Operations
- Addition: combining numbers, e.g., 2 + 3 = 5
- Subtraction: finding the difference, e.g., 5 - 2 = 3
- Multiplication: repeated addition, e.g., 2 × 3 = 6
- Division: sharing into equal parts, e.g., 6 ÷ 2 = 3
Properties of Operations
- Commutative Property: order of numbers doesn't change the result, e.g., 2 + 3 = 3 + 2
- Associative Property: order of operations doesn't change the result, e.g., (2 + 3) + 4 = 2 + (3 + 4)
- Distributive Property: multiplying a number by a sum is the same as multiplying by each addend, e.g., 2 × (3 + 4) = 2 × 3 + 2 × 4
Geometric Shapes
Points, Lines, and Planes
- Point: a location in space, represented by a set of coordinates (x, y, z)
- Line: a set of points extending infinitely in two directions
- Plane: a flat surface extending infinitely in all directions
Types of Angles
- Acute Angle: less than 90 degrees
- Right Angle: exactly 90 degrees
- Obtuse Angle: greater than 90 degrees
- Straight Angle: exactly 180 degrees
Properties of Shapes
- Congruent Shapes: same size and shape, e.g., two identical triangles
- Similar Shapes: same shape but different sizes, e.g., two triangles with same angles but different side lengths
- Regular Shapes: all sides and angles are equal, e.g., equilateral triangle, square
Basic Shapes
- Triangle: three sides and three angles
- Quadrilateral: four sides and four angles
- Polygon: five or more sides and angles
- Circle: a set of points equidistant from a central point (center)
Arithmetic
- Number Types: Whole numbers are positive integers (e.g., 1, 2, 3,...), Fractions are parts of a whole (e.g., 1/2, 3/4), Decimals are fractional parts of a whole (e.g., 0.5, 0.25), and Percentages are fractions of 100 (e.g., 25%, 50%).
Basic Operations
- Addition: Combining numbers to get a total or a sum (e.g., 2 + 3 = 5).
- Subtraction: Finding the difference between two numbers (e.g., 5 - 2 = 3).
- Multiplication: Repeated addition of a number (e.g., 2 × 3 = 6).
- Division: Sharing a number into equal parts (e.g., 6 ÷ 2 = 3).
Properties of Operations
- Commutative Property: The order of numbers does not change the result of an operation (e.g., 2 + 3 = 3 + 2).
- Associative Property: The order of operations does not change the result of an operation (e.g., (2 + 3) + 4 = 2 + (3 + 4)).
- Distributive Property: Multiplying a number by a sum is the same as multiplying by each addend (e.g., 2 × (3 + 4) = 2 × 3 + 2 × 4).
Geometric Shapes
Points, Lines, and Planes
- Point: A location in space, represented by a set of coordinates (x, y, z).
- Line: A set of points extending infinitely in two directions.
- Plane: A flat surface extending infinitely in all directions.
Types of Angles
- Acute Angle: Less than 90 degrees.
- Right Angle: Exactly 90 degrees.
- Obtuse Angle: Greater than 90 degrees.
- Straight Angle: Exactly 180 degrees.
Properties of Shapes
- Congruent Shapes: Same size and shape (e.g., two identical triangles).
- Similar Shapes: Same shape but different sizes (e.g., two triangles with same angles but different side lengths).
- Regular Shapes: All sides and angles are equal (e.g., equilateral triangle, square).
Basic Shapes
- Triangle: A polygon with three sides and three angles.
- Quadrilateral: A polygon with four sides and four angles.
- Polygon: A shape with five or more sides and angles.
- Circle: A set of points equidistant from a central point (center).
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Description
Test your understanding of basic arithmetic concepts, including numbers, operations, and properties. Covers whole numbers, fractions, decimals, and percentages.
