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Questions and Answers
Which type of fraction has a numerator that is less than the denominator?
How do you create equivalent fractions?
How do you read a decimal such as 2.8?
How do you convert a decimal to a fraction?
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What is the result of converting the fraction 3/4 to a decimal?
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How do you compare decimals?
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What is a characteristic of a mixed number?
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How do you convert an improper fraction to a mixed number?
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What is the purpose of the decimal point in a decimal?
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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 (one half)
- 3/4 (three quarters)
- Equivalent fractions:
- Fractions with the same value, but different numbers
- Example: 1/2 = 2/4 = 3/6
- Comparing fractions:
- Compare the numerators (top numbers) if the denominators (bottom numbers) are the same
- Compare the denominators (bottom numbers) if the numerators (top numbers) are the same
Decimals
- A decimal is a way to represent a fraction using a point and digits
- Examples:
- 0.5 (one half)
- 0.75 (three quarters)
- Converting fractions to decimals:
- Divide the numerator by the denominator
- Example: 3/4 = 3 ÷ 4 = 0.75
- Comparing decimals:
- Compare the digits from left to right
- Compare the number of digits after the point
Basic Geometry
- Points, Lines, and Planes:
- A point has no size, only location
- A line extends infinitely in two directions
- A plane is a flat surface that extends infinitely
- Basic Shapes:
- Square: 4 right angles, 4 sides of equal length
- Rectangle: 4 right angles, opposite sides of equal length
- Triangle: 3 sides, 3 angles
- Measuring Angles:
- Right angle: 90 degrees
- Acute angle: less than 90 degrees
- Obtuse angle: more than 90 degrees
Fractions
- A fraction is a way to represent a part of a whole
- Consists of a numerator (top number) and a denominator (bottom number)
- Examples: 1/2 (one half), 3/4 (three quarters)
- Equivalent fractions have the same value, but different numbers
- Example: 1/2 = 2/4 = 3/6
Comparing Fractions
- Compare numerators (top numbers) if denominators (bottom numbers) are the same
- Compare denominators (bottom numbers) if numerators (top numbers) are the same
Decimals
- A decimal is a way to represent a fraction using a point and digits
- Examples: 0.5 (one half), 0.75 (three quarters)
- To convert a fraction to a decimal, divide the numerator by the denominator
- Example: 3/4 = 3 ÷ 4 = 0.75
Comparing Decimals
- Compare digits from left to right
- Compare the number of digits after the point
Basic Geometry
Points, Lines, and Planes
- A point has no size, only location
- A line extends infinitely in two directions
- A plane is a flat surface that extends infinitely
Basic Shapes
- Square: 4 right angles, 4 sides of equal length
- Rectangle: 4 right angles, opposite sides of equal length
- Triangle: 3 sides, 3 angles
Measuring Angles
- Right angle: 90 degrees
- Acute angle: less than 90 degrees
- Obtuse angle: more than 90 degrees
Fractions
- A fraction represents part of a whole, consisting of a numerator (top number) and a denominator (bottom number)
- Numerator indicates how many equal parts we have, while the denominator indicates how many parts the whole is divided into
- Types of fractions include:
- Proper fractions: numerator is less than the denominator (e.g. 1/2)
- Improper fractions: numerator is greater than or equal to the denominator (e.g. 3/2)
- Mixed numbers: a combination of a whole number and a proper fraction (e.g. 2 1/2)
- Equivalent fractions have the same value and can be created by multiplying or dividing both the numerator and denominator by the same number
- Compare fractions by comparing numerators if denominators are the same, or by comparing denominators if numerators are the same
- Use equivalent fractions to compare fractions with different denominators
Decimals
- A decimal represents part of a whole using a point and digits
- Decimal point separates the whole part from the fractional part
- Decimals can be used to represent fractions and mixed numbers
- Read decimals as "and" (e.g. 3.5 is read as "three and five tenths")
- Write decimals with the correct number of digits after the decimal point
- Compare decimals by comparing digits after the decimal point, following the same rules as comparing whole numbers (e.g. 3.5 is greater than 3.4)
- Convert a fraction to a decimal by dividing the numerator by the denominator
- Convert a decimal to a fraction by finding the equivalent fraction (e.g. 0.5 is equivalent to 1/2)
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Description
Learn about what fractions represent, their components, equivalent fractions, and how to compare them.
