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Questions and Answers
What is the least common denominator (LCD) of the fractions $\frac{2}{3}$ and $\frac{5}{12}$?
What is the least common denominator (LCD) of the fractions $\frac{2}{3}$ and $\frac{5}{12}$?
- 12
- 6
- 24 (correct)
- 36
When adding the fractions $\frac{3}{4}$ and $\frac{1}{6}$, which value should be used as the greatest common denominator (GCD) to simplify the result?
When adding the fractions $\frac{3}{4}$ and $\frac{1}{6}$, which value should be used as the greatest common denominator (GCD) to simplify the result?
- 2 (correct)
- 12
- 3
- 24
How do you add the fractions $\frac{1}{8}$ and $\frac{1}{4}$?
How do you add the fractions $\frac{1}{8}$ and $\frac{1}{4}$?
- Convert both to eighths and add: $\frac{1}{8} + \frac{2}{8} = \frac{3}{8}$ (correct)
- Add directly since the denominators are the same.
- Convert both to fourths and add: $\frac{2}{4} + \frac{1}{4} = \frac{3}{4}$
- Convert to sixteenths first: $\frac{2}{16} + \frac{4}{16} = \frac{6}{16}$
Which method correctly determines the least common multiple (LCM) needed to find the least common denominator for the fractions $\frac{2}{5}$ and $\frac{3}{10}$?
Which method correctly determines the least common multiple (LCM) needed to find the least common denominator for the fractions $\frac{2}{5}$ and $\frac{3}{10}$?
What is the sum of the fractions $\frac{7}{12}$ and $\frac{1}{4}$ when correctly added using the least common denominator?
What is the sum of the fractions $\frac{7}{12}$ and $\frac{1}{4}$ when correctly added using the least common denominator?
What is the primary purpose of finding the least common denominator when adding fractions?
What is the primary purpose of finding the least common denominator when adding fractions?
Which of these fractions has the greatest common denominator with $ rac{4}{5}$?
Which of these fractions has the greatest common denominator with $ rac{4}{5}$?
When adding two fractions with different denominators, which step is essential?
When adding two fractions with different denominators, which step is essential?
What happens if you add fractions without finding a common denominator first?
What happens if you add fractions without finding a common denominator first?
Which term describes the largest number that divides two or more numbers evenly?
Which term describes the largest number that divides two or more numbers evenly?
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Study Notes
Least Common Denominator (LCD)
- The LCD of the fractions (\frac{2}{3}) and (\frac{5}{12}) is 12, as it is the smallest multiple of both denominators (3 and 12) that they can both divide into without a remainder.
Greatest Common Denominator (GCD)
- When adding (\frac{3}{4}) and (\frac{1}{6}), use the GCD of the numerators (3 and 1) if simplifying afterwards. The GCD is 1 in this case, meaning the fractions will not simplify further post addition.
Adding Fractions
- To add (\frac{1}{8}) and (\frac{1}{4}), first convert (\frac{1}{4}) to eighths: (\frac{1}{4} = \frac{2}{8}).
- Then, add the numerators: (\frac{1}{8} + \frac{2}{8} = \frac{3}{8}).
Least Common Multiple (LCM) for LCD
- To determine the LCD for the fractions (\frac{2}{5}) and (\frac{3}{10}), find the LCM of the denominators (5 and 10).
- The LCM is 10, as it is the smallest number that both denominators can divide into evenly.
Sum of Fractions
- To add (\frac{7}{12}) and (\frac{1}{4}), find the LCD, which is 12.
- Convert (\frac{1}{4}) to twelfths: (\frac{1}{4} = \frac{3}{12}).
- Add the fractions: (\frac{7}{12} + \frac{3}{12} = \frac{10}{12}).
- Simplifying gives (\frac{5}{6}).
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