10 Questions
What is the purpose of finding the greatest common divisor (GCD) when simplifying fractions?
To divide both numerator and denominator by their GCD
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
How do you convert a fraction to a decimal?
Divide the numerator by the denominator
What is the result of dividing a fraction by another fraction?
A fraction with a numerator that is the product of the numerators and a denominator that is the quotient of the denominators
What is the purpose of percentages?
To represent fractions with a denominator of 100
How do you convert a percentage to a decimal?
Divide by 100
What is the order of operations in algebraic expressions?
Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction
What is an algebraic expression?
A combination of variables and constants with mathematical operations
How do you simplify an algebraic expression?
By combining like terms
What is the result of increasing a value by a percentage?
The original value plus the percentage of the original value
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):
- Parentheses
- Exponents
- Multiplication and Division (from left to right)
- 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
Test your knowledge of fundamental math concepts, including fractions, decimals, percentages, algebraic expressions, and basic geometry calculations such as perimeter and area.
Make Your Own Quizzes and Flashcards
Convert your notes into interactive study material.
Get started for free
