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Questions and Answers
What is the simplified form of the fraction 6/8?
0.5 is a decimal representation of the fraction 1/2.
True
What is the percentage representation of the fraction 3/4?
75%
A ______________ is a location in space, represented by coordinates (x, y).
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What is the equation to find the perimeter of a rectangle?
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In algebra, variables are numbers without unknown values.
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Match the following types of angles with their descriptions:
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Study Notes
Fractions
- A fraction represents a part of a whole
- Consists of a numerator (top number) and a denominator (bottom number)
- Examples: 1/2, 3/4, 2/3
- Equivalent fractions: fractions with the same value, e.g. 1/2 = 2/4 = 3/6
- Simplifying fractions: dividing both numerator and denominator by their greatest common divisor (GCD)
- Operations with fractions:
- Addition: add numerators, keep denominator the same
- Subtraction: subtract numerators, keep denominator the same
- Multiplication: multiply numerators and denominators
- Division: invert and multiply
Decimals
- A decimal is a way to represent a fraction with a denominator of 10, 100, 1000, etc.
- Examples: 0.5, 0.25, 3.14
- Converting fractions to decimals: divide numerator by denominator
- Operations with decimals:
- Addition and subtraction: same as with whole numbers
- Multiplication: same as with whole numbers
- Division: same as with whole numbers, but be careful with place value
Percentages
- A percentage is a way to represent a fraction with a denominator of 100
- Examples: 25%, 50%, 75%
- Converting fractions to percentages: divide numerator by denominator, multiply by 100
- Converting decimals to percentages: multiply by 100
- Operations with percentages:
- Increase: multiply by (1 + percentage)
- Decrease: multiply by (1 - percentage)
Geometry
- Points: locations in space, represented by coordinates (x, y)
- Lines: sets of points extending infinitely in two directions
- Line segments: parts of lines with a fixed length
- Angles: formed by two lines or line segments
- Types of angles:
- Acute: less than 90°
- Right: 90°
- Obtuse: greater than 90°
- Basic geometry formulas:
- Perimeter: distance around a shape
- Area: size of a shape
- Volume: amount of space inside a 3D shape
Basic Algebra
- Variables: letters or symbols representing unknown values
- Constants: numbers without variables
- Expressions: combinations of variables, constants, and operations
- Equations: statements with equal values, e.g. 2x + 3 = 5
- Solving equations:
- Addition and subtraction: inverse operations
- Multiplication and division: inverse operations
- Basic algebra formulas:
- Linear equation: ax + b = c
- Quadratic equation: ax^2 + bx + c = 0
分数
- 分数表示一个整体的一部分
- 由分子（上面的数字）和分母（下面的数字）组成
- 例如：1/2、3/4、2/3
- 等值分数：具有相同值的分数，例如 1/2 = 2/4 = 3/6
- 简化分数：将分子和分母同时除以它们的最大公约数（GCD）
- 分数运算：
- 加法：加分子，保持分母不变
- 减法：减分子，保持分母不变
- 乘法：相乘分子和分母
- 除法：倒数然后相乘
小数
- 小数是以10、100、1000等为分母的分数的表示方式
- 例如：0.5、0.25、3.14
- 将分数转换为小数：将分子除以分母
- 小数运算：
- 加法和减法：与整数运算相同
- 乘法：与整数运算相同
- 除法：与整数运算相同，但要注意小数点的位置
百分数
- 百分数是以100为分母的分数的表示方式
- 例如：25%、50%、75%
- 将分数转换为百分数：将分子除以分母，乘以100
- 将小数转换为百分数：乘以100
- 百分数运算：
- 增加：乘以（1 + 百分数）
- 降低：乘以（1 - 百分数）
几何
- 点：空间中的位置，用坐标（x、y）表示
- 线：无限延伸的点集
- 线段：有限长度的线的一部分
- 角：由两条线或线段形成
- 角的类型：
- 锐角：小于90°
- 直角：90°
- 钝角：大于90°
- 基本几何公式：
- 周长：形状周围的距离
- 面积：形状的大小
- 体积：三维形状内部的空间
初等代数
- 变量：表示未知数值的字母或符号
- 常数：不含变量的数字
- 表达式：变量、常数和运算的组合
- 方程：具有相同值的语句，例如 2x + 3 = 5
- 解方程：
- 加法和减法：逆运算
- 乘法和除法：逆运算
- 基本代数公式：
- 线性方程：ax + b = c
- 二次方程：ax^2 + bx + c = 0
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