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Questions and Answers
What is the least common denominator (LCD) of the fractions $ rac{1}{2}$ and $ rac{1}{3}$?
What is the least common denominator (LCD) of the fractions $ rac{1}{2}$ and $ rac{1}{3}$?
- 3
- 2
- 1
- 6 (correct)
Which step is necessary to convert the fraction $ rac{1}{2}$ to an equivalent fraction with a denominator of 6?
Which step is necessary to convert the fraction $ rac{1}{2}$ to an equivalent fraction with a denominator of 6?
- Multiply the numerator by 2 and the denominator by 3
- Multiply the numerator and denominator by 6
- Divide the numerator by 2 and the denominator by 3
- Multiply the numerator by 3 and the denominator by 3 (correct)
When subtracting $ rac{3}{6}$ from $ rac{2}{6}$, what is the result?
When subtracting $ rac{3}{6}$ from $ rac{2}{6}$, what is the result?
- 0
- $ rac{1}{2}$
- $ rac{1}{3}$
- $ rac{1}{6}$ (correct)
What should you do after finding a common denominator and subtracting the numerators?
What should you do after finding a common denominator and subtracting the numerators?
What is the first step to subtract mixed numbers with unlike denominators?
What is the first step to subtract mixed numbers with unlike denominators?
Flashcards
Common Denominator
Common Denominator
A number that is divisible by both of the original denominators.
Least Common Denominator (LCD)
Least Common Denominator (LCD)
The smallest number that is divisible by both of the original denominators.
Converting to Equivalent Fractions
Converting to Equivalent Fractions
Multiplying both the numerator and denominator of a fraction by the same number.
Subtracting Fractions with a Common Denominator
Subtracting Fractions with a Common Denominator
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Subtracting Mixed Numbers with Unlike Denominators
Subtracting Mixed Numbers with Unlike Denominators
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Study Notes
Subtracting Fractions with Unlike Denominators
- To subtract fractions with unlike denominators, find a common denominator.
- The common denominator is a number divisible by both original denominators.
- The least common denominator (LCD) is the smallest common denominator, simplifying the process.
Finding a Common Denominator
- List the multiples of each denominator.
- Identify the smallest multiple common to both denominators. This is the LCD.
- If one denominator is a multiple of the other, the larger denominator is the LCD.
Converting Fractions to Equivalent Fractions
- To convert a fraction to an equivalent fraction with a common denominator, multiply both numerator and denominator by the same number.
- This doesn't change the fraction's value, only its representation.
Subtracting Fractions with a Common Denominator
- Once fractions share a common denominator, subtract the numerators.
- Maintain the common denominator.
- Simplify the resulting fraction by dividing both numerator and denominator by their greatest common factor (GCF), if possible.
Example
- Subtract 1/2 - 1/3
- Find the LCD of 2 and 3. Multiples of 2: 2, 4, 6, 8... Multiples of 3: 3, 6, 9, 12... The least common multiple is 6.
- Convert 1/2 to an equivalent fraction with a denominator of 6. Multiply both numerator and denominator by 3: (1 x 3) / (2 x 3) = 3/6
- Convert 1/3 to an equivalent fraction with a denominator of 6. Multiply both numerator and denominator by 2: (1 x 2) / (3 x 2) = 2/6
- Subtract the numerators: 3/6 - 2/6 = 1/6
- The result is 1/6.
Mixed Numbers
- When subtracting mixed numbers with unlike denominators, first subtract the fractional parts. Subtract the whole numbers. Simplify the result if needed.
- For example, 2 1/2 - 1 1/3 =...
- Subtract the fractions: 1/2 - 1/3 = 3/6 - 2/6 = 1/6
- Subtract the whole numbers: 2 - 1 = 1
- Combine the results: 1 1/6
- For example, 2 1/2 - 1 1/3 =...
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