Podcast
Questions and Answers
Which of the following fractions is an improper fraction?
Which of the following fractions is an improper fraction?
- $ rac{5}{9}$
- $ rac{11}{5}$ (correct)
- $ rac{2}{3}$
- $ rac{3}{7}$
Which symbol correctly compares the fractions $\frac{5}{12}$ and $\frac{7}{12}$?
Which symbol correctly compares the fractions $\frac{5}{12}$ and $\frac{7}{12}$?
- $<$ (correct)
- $\approx$
- $>$
- $=$
Which of the following statements is true regarding the comparison of $\frac{4}{9}$ and $\frac{4}{9}$?
Which of the following statements is true regarding the comparison of $\frac{4}{9}$ and $\frac{4}{9}$?
- $\frac{4}{9} > \frac{4}{9}$
- $\frac{4}{9} = \frac{4}{9}$ (correct)
- $\frac{4}{9} \neq \frac{4}{9}$
- $\frac{4}{9} < \frac{4}{9}$
Which of the following pairs of fractions is correctly compared?
Which of the following pairs of fractions is correctly compared?
Identify the proper fraction from the following list:
Identify the proper fraction from the following list:
Flashcards
What is a fraction?
What is a fraction?
A number representing a part of a whole or, more generally, any number of equal parts.
What is a proper fraction?
What is a proper fraction?
A fraction where the numerator (top number) is less than the denominator (bottom number).
What is an improper fraction?
What is an improper fraction?
A fraction where the numerator is greater than or equal to the denominator.
Comparing fractions (same denominator)
Comparing fractions (same denominator)
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Symbols for comparing fractions
Symbols for comparing fractions
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Study Notes
- Fractions are a way to represent parts of a whole.
Fraction
- A fraction is a number that represents a part of a whole.
- It is written as one number over another, separated by a line.
- The number on top is called the numerator, and it represents the number of parts you have.
- The number on the bottom is called the denominator, and it represents the total number of equal parts the whole is divided into.
- For example, if a pizza is cut into 8 slices and you have 3 of those slices, you have 3/8 (three-eighths) of the pizza. Here, 3 is the numerator and 8 is the denominator.
Proper Fraction
- A proper fraction is a fraction where the numerator is less than the denominator.
- This means the fraction represents a value less than 1.
- Examples of proper fractions are 1/2, 3/4, and 5/8.
- In a proper fraction, the top number is smaller than the bottom number.
Improper Fraction
- An improper fraction is a fraction where the numerator is greater than or equal to the denominator.
- This means the fraction represents a value equal to or greater than 1.
- Examples of improper fractions are 5/4, 8/3, and 11/11.
- In an improper fraction, the top number is bigger than or equal to the bottom number.
- Improper fractions can be converted into mixed numbers.
Mixed Number
- A mixed number is a combination of a whole number and a proper fraction.
- For example, 1 1/2 (one and one-half) is a mixed number.
- Improper fractions can be converted to mixed numbers, and vice versa.
- To convert an improper fraction to a mixed number: divide the numerator by the denominator; the quotient is the whole number part and the remainder is the numerator of the fractional part, keeping the same denominator.
- Example: 5/4 = 1 1/4 (5 divided by 4 is 1 with a remainder of 1).
Comparing Fractions with the Same Denominators
- When comparing fractions with the same denominators, you only need to compare the numerators.
- The fraction with the larger numerator is the larger fraction.
- Symbols '' (greater than), '' (less than), and '=' (equal to) are used to compare fractions.
- If two fractions have the same numerator and denominator, they are equal.
- If two fractions have the same denominator, the fraction with the larger numerator is greater.
- For example:
- 3/5 > 2/5 (because 3 is greater than 2)
- 1/4 < 3/4 (because 1 is less than 3)
- 2/7 = 2/7 (because the numerators and denominators are the same)
Examples of Comparing Fractions
- Example 1: Comparing 4/9 and 7/9.
- Both fractions have the same denominator (9).
- Compare the numerators: 4 and 7.
- Since 4 is less than 7, 4/9 < 7/9.
- Example 2: Comparing 5/11 and 3/11.
- Both fractions have the same denominator (11).
- Compare the numerators: 5 and 3.
- Since 5 is greater than 3, 5/11 > 3/11.
- Example 3: Comparing 2/5 and 2/5.
- Both fractions have the same denominator (5).
- Compare the numerators: 2 and 2.
- Since 2 is equal to 2, 2/5 = 2/5.
Using Symbols to Compare Fractions
- The symbol '>' means "greater than".
- The symbol '<' means "less than".
- The symbol '=' means "equal to".
- When comparing fractions with the same denominator, use these symbols based on the comparison of their numerators.
- Examples:
- 5/8 > 3/8 (5 is greater than 3)
- 1/3 < 2/3 (1 is less than 2)
- 4/7 = 4/7 (4 is equal to 4)
Summary
- A fraction represents a part of a whole, with a numerator and a denominator.
- A proper fraction has a numerator less than its denominator.
- An improper fraction has a numerator greater than or equal to its denominator and can be converted to a mixed number.
- When comparing fractions with the same denominators, compare the numerators; the larger numerator means the fraction is greater.
- The symbols '>', '<', and '=' are used to show these relationships.
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Description
Learn about fractions, which represent parts of a whole, with a numerator and denominator. Explore proper fractions, where the numerator is less than the denominator, and improper fractions where numerator is greater than the denominator.
