Podcast
Questions and Answers
Which symbol correctly compares the fractions $\frac{3}{5}$ and $\frac{5}{8}$?
Which symbol correctly compares the fractions $\frac{3}{5}$ and $\frac{5}{8}$?
- >
- < (correct)
- $\approx$
- =
What is the correct comparison between $\frac{7}{12}$ and $\frac{5}{9}$?
What is the correct comparison between $\frac{7}{12}$ and $\frac{5}{9}$?
- $\frac{7}{12} < \frac{5}{9}$
- $\frac{7}{12} = \frac{5}{9}$
- $\frac{7}{12} > \frac{5}{9}$ (correct)
- Cannot be determined
Which of the following statements is true?
Which of the following statements is true?
- $\frac{2}{3} < \frac{3}{7}$
- $\frac{3}{4} > \frac{5}{8}$ (correct)
- $\frac{5}{6} > \frac{7}{8}$
- $\frac{4}{9} = \frac{1}{2}$
Which comparison is incorrect?
Which comparison is incorrect?
How would you correctly compare $\frac{11}{15}$ and $\frac{2}{3}$?
How would you correctly compare $\frac{11}{15}$ and $\frac{2}{3}$?
Flashcards
Dissimilar Fractions
Dissimilar Fractions
Fractions with different denominators that cannot directly be compared or simplified easily.
Comparing Fractions
Comparing Fractions
Determining which of the fractions is greater, less, or equal using symbols like >, <, and =.
Symbols of Comparison
Symbols of Comparison
The symbols = (equal), > (greater than), and < (less than) used to compare fractions.
Finding Common Denominators
Finding Common Denominators
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Using Number Lines
Using Number Lines
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Study Notes
Comparing Dissimilar Fractions
- Understand that dissimilar fractions have different denominators.
- To compare dissimilar fractions, they must first be converted to equivalent fractions with a common denominator.
- This process involves finding the least common multiple (LCM) of the denominators.
- The LCM represents the smallest positive integer that is a multiple of two or more integers.
- Once the LCM is determined, rewrite each fraction as an equivalent fraction using the LCM as the new denominator.
- The numerators of the equivalent fractions are adjusted proportionally to maintain the same value as the original fraction.
- After rewriting as equivalent fractions, compare the numerators of the converted fractions.
- The fraction with the larger numerator is the larger fraction.
Using the Symbols =, >, and <
- The symbol "=" indicates equality, meaning the two fractions represent the same value.
- The symbol ">" means "greater than". A fraction is greater than another if its value is larger.
- The symbol "<" means "less than". A fraction is less than another if its value is smaller.
Examples and Steps for Comparison
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Example 1: Compare 2/3 and 3/4
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Find the LCM of 3 and 4. The LCM is 12.
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Rewrite 2/3 as an equivalent fraction with a denominator of 12: (2/3) * (4/4) = 8/12
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Rewrite 3/4 as an equivalent fraction with a denominator of 12: (3/4) * (3/3) = 9/12
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Compare the numerators: 9 > 8. Therefore, 3/4 > 2/3
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Example 2: Compare 5/6 and 7/8
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Find the LCM of 6 and 8. The LCM is 24.
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Rewrite 5/6 as an equivalent fraction with a denominator of 24: (5/6) * (4/4) = 20/24.
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Rewrite 7/8 as an equivalent fraction with a denominator of 24: (7/8) * (3/3) = 21/24
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Compare the numerators: 21 > 20. Therefore, 7/8 > 5/6
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Example 3: Compare 1/2 and 1/2
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The LCM of 2 and 2 is 2.
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Rewrite 1/2 as an equivalent fraction with a denominator of 2: (1/2) * (1/1) = 1/2.
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Compare the numerators: 1 = 1. Therefore, 1/2 = 1/2
Key Concepts
- Identifying fractions as equivalent forms of the same value.
- Finding the LCM efficiently.
- Converting dissimilar fractions to equivalent fractions.
- Using the correct symbol to represent the comparison relationship between fractions ( =, >, < ) based on their values.
- Understanding the significance of a common denominator in the comparison of unlike fractions.
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