Math Basics: Fractions, Decimals, Percentages, Algebra, and Geometry
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Questions and Answers

What is the purpose of finding the greatest common divisor (GCD) when simplifying fractions?

  • To multiply fractions by the same value
  • To find the decimal equivalent of a fraction
  • To divide both numerator and denominator by their GCD (correct)
  • To add fractions with different denominators

    • What is the result of multiplying two fractions?

  • A fraction with a numerator that is the product of the numerators and a denominator that is the product of the denominators (correct)
  • A fraction with a denominator that is the product of the denominators
  • A decimal number
  • A fraction with a numerator that is the sum of the numerators

    • How do you convert a fraction to a decimal?

  • Divide the numerator by the denominator (correct)
  • Subtract the denominator from the numerator
  • Multiply the numerator and denominator
  • Add the numerator and denominator

    • What is the result of dividing a fraction by another fraction?

    <p>A fraction with a numerator that is the product of the numerators and a denominator that is the quotient of the denominators</p> Signup and view all the answers

    What is the purpose of percentages?

    <p>To represent fractions with a denominator of 100</p> Signup and view all the answers

    How do you convert a percentage to a decimal?

    <p>Divide by 100</p> Signup and view all the answers

    What is the order of operations in algebraic expressions?

    <p>Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction</p> Signup and view all the answers

    What is an algebraic expression?

    <p>A combination of variables and constants with mathematical operations</p> Signup and view all the answers

    How do you simplify an algebraic expression?

    <p>By combining like terms</p> Signup and view all the answers

    What is the result of increasing a value by a percentage?

    <p>The original value plus the percentage of the original value</p> Signup and view all the answers

    Study Notes

    Fractions

    • A fraction represents a part of a whole
    • Consists of a numerator (top number) and a denominator (bottom number)
    • Equivalent fractions have the same value but different numbers
    • Simplifying fractions: divide both numerator and denominator by their greatest common divisor (GCD)
    • Adding and subtracting fractions: need same denominator, then add or subtract numerators
    • Multiplying fractions: multiply numerators and multiply denominators
    • Dividing fractions: invert and multiply (i.e., flip the second fraction and multiply)

    Decimals

    • A decimal is a way to represent a fraction as a number with a fractional part
    • Converting fractions to decimals: divide numerator by denominator
    • Comparing decimals: compare digits from left to right
    • Rounding decimals: round to a specific number of decimal places
    • Adding and subtracting decimals: line up decimal points and add or subtract
    • Multiplying and dividing decimals: multiply or divide as with whole numbers, then place decimal point

    Percentages

    • A percentage represents a fraction with a denominator of 100
    • Converting percentages to decimals: divide by 100
    • Converting decimals to percentages: multiply by 100
    • Increasing or decreasing by a percentage: calculate percentage of original value and add or subtract
    • Percentage change: calculate difference as a percentage of original value

    Algebraic Expressions

    • An algebraic expression is a combination of variables, constants, and mathematical operations
    • Simplifying expressions: combine like terms
    • Order of operations (PEMDAS):
      1. Parentheses
      2. Exponents
      3. Multiplication and Division (from left to right)
      4. Addition and Subtraction (from left to right)
    • Evaluating expressions: substitute values for variables and simplify

    Perimeter

    • Perimeter is the distance around a shape
    • Formula for perimeter of a rectangle: P = 2(l + w)
    • Formula for perimeter of a triangle: P = a + b + c (where a, b, and c are side lengths)
    • Perimeter of other shapes: find side lengths and add them up

    Area

    • Area is the amount of space inside a shape
    • Formula for area of a rectangle: A = l × w
    • Formula for area of a triangle: A = (b × h) / 2
    • Formula for area of a circle: A = πr^2
    • Area of other shapes: find formulas or break down into simpler shapes

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