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Questions and Answers
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?
Which of the following is an example of a Congruent Shape?
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?
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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?
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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.