8 Questions
What is the primary purpose of finding the greatest common divisor when simplifying fractions?
To divide both numerator and denominator
What is the result of multiplying a decimal by a power of 10?
The decimal point shifts to the right
What is the result of converting a fraction to a percentage?
Multiplying by 100
What is the effect of multiplying a negative number by -1?
The number becomes positive
What is the result of adding a negative number to a positive number?
The result depends on the numbers
What is the purpose of using a common denominator when adding or subtracting fractions?
To make the fractions comparable
What is the result of increasing a value by a percentage?
The value increases
What is the purpose of using percentages in real-world applications?
To represent proportions, ratios, and rates
Study Notes
Numbers
Fractions
- A fraction is a way to represent a part of a whole
- Consists of a numerator (top number) and a denominator (bottom number)
- Numerator tells how many equal parts are being referred to
- Denominator tells how many parts the whole is divided into
- Examples: 1/2, 3/4, 2/3
- Can be simplified by dividing both numerator and denominator by their greatest common divisor (GCD)
- Can be added and subtracted by finding a common denominator
- Can be multiplied by multiplying numerators and denominators separately
- Can be divided by inverting and multiplying
Decimals
- A decimal is a way to represent a fraction with a denominator of 10, 100, 1000, etc.
- Consists of a whole number part and a fractional part separated by a decimal point
- Examples: 0.5, 3.14, 2.75
- Can be converted from fractions by dividing the numerator by the denominator
- Can be added and subtracted by lining up the decimal points
- Can be multiplied by multiplying by a power of 10
- Can be divided by dividing by a power of 10
Percentages
- A percentage is a way to represent a fraction with a denominator of 100
- Consists of a value with a "%" symbol
- Examples: 25%, 50%, 75%
- Can be converted from fractions by dividing the numerator by the denominator and multiplying by 100
- Can be converted from decimals by multiplying by 100
- Can be increased or decreased by a percentage by multiplying by the percentage as a decimal
- Can be used to represent proportions, ratios, and rates
Negative Numbers
- A negative number is a number that is less than zero
- Examples: -1, -2, -3
- Can be represented on a number line with a negative direction
- Can be added and subtracted by following the rules of addition and subtraction, but with a negative sign
- Can be multiplied by multiplying by -1
- Can be divided by dividing by -1
- Important in real-world applications, such as temperatures, debts, and elevations
Numbers
Fractions
- A fraction represents a part of a whole, consisting of a numerator (top number) and a denominator (bottom number)
- The numerator indicates how many equal parts are being referred to, while the denominator indicates how many parts the whole is divided into
- Examples of fractions include 1/2, 3/4, and 2/3
- Fractions can be simplified by dividing both the numerator and denominator by their greatest common divisor (GCD)
- Fractions can be added and subtracted by finding a common denominator
- Fractions can be multiplied by multiplying the numerators and denominators separately
- Fractions can be divided by inverting and multiplying
Decimals
- A decimal represents a fraction with a denominator of 10, 100, 1000, etc.
- Decimals consist of a whole number part and a fractional part separated by a decimal point
- Examples of decimals include 0.5, 3.14, and 2.75
- Decimals can be converted from fractions by dividing the numerator by the denominator
- Decimals can be added and subtracted by lining up the decimal points
- Decimals can be multiplied by multiplying by a power of 10
- Decimals can be divided by dividing by a power of 10
Percentages
- A percentage represents a fraction with a denominator of 100
- Percentages consist of a value with a "%" symbol
- Examples of percentages include 25%, 50%, and 75%
- Percentages can be converted from fractions by dividing the numerator by the denominator and multiplying by 100
- Percentages can be converted from decimals by multiplying by 100
- Percentages can be used to represent proportions, ratios, and rates
- Percentages can be increased or decreased by multiplying by the percentage as a decimal
Negative Numbers
- A negative number is a number that is less than zero
- Examples of negative numbers include -1, -2, and -3
- Negative numbers can be represented on a number line with a negative direction
- Negative numbers can be added and subtracted by following the rules of addition and subtraction, but with a negative sign
- Negative numbers can be multiplied by multiplying by -1
- Negative numbers can be divided by dividing by -1
- Negative numbers are important in real-world applications, such as temperatures, debts, and elevations
Learn about fractions, including what they are, their components, and how to simplify, add, subtract, and multiply them. Understand the concepts of numerator and denominator, and how to find common denominators.
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