Podcast
Questions and Answers
What is the first step in adding the fractions $\frac{20}{50}$ and $\frac{1}{6}$?
What is the first step in adding the fractions $\frac{20}{50}$ and $\frac{1}{6}$?
- Converting $\frac{1}{6}$ to a decimal
- Multiplying the fractions together
- Finding a common denominator (correct)
- Simplifying $\frac{20}{50}$ to $\frac{2}{5}$
What is the sum of the fractions $\frac{20}{50}$ and $\frac{1}{6}$ after finding a common denominator?
What is the sum of the fractions $\frac{20}{50}$ and $\frac{1}{6}$ after finding a common denominator?
- $\frac{7}{15}$
- $\frac{19}{30}$
- $\frac{4}{10}$
- $\frac{31}{75}$ (correct)
What is the simplified form of $\frac{20}{50}$ before adding it to $\frac{1}{6}$?
What is the simplified form of $\frac{20}{50}$ before adding it to $\frac{1}{6}$?
- $\frac{4}{10}$
- $\frac{10}{25}$
- $\frac{1}{2}$ (correct)
- $\frac{2}{5}$
If you convert $\frac{1}{6}$ to an equivalent fraction with a denominator of 75, what will it be?
If you convert $\frac{1}{6}$ to an equivalent fraction with a denominator of 75, what will it be?
Which operation is used to combine $\frac{20}{50}$ and $\frac{1}{6}$ after converting to a common denominator?
Which operation is used to combine $\frac{20}{50}$ and $\frac{1}{6}$ after converting to a common denominator?
Flashcards
Fraction Addition
Fraction Addition
Adding fractions with different denominators.
20/50
20/50
Twenty fiftieths
1/6
1/6
One sixth
Common Denominator
Common Denominator
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Addition of Fractions
Addition of Fractions
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Study Notes
Calculation of the Sum
- To calculate the sum 20/50 + 1/6, we first need to find a common denominator for the two fractions.
Finding the Common Denominator
- The denominators are 50 and 6.
- We need to find the least common multiple (LCM) of 50 and 6.
- The prime factorization of 50 is 2 x 5 x 5.
- The prime factorization of 6 is 2 x 3.
- The LCM of 50 and 6 is found by taking the highest power of each prime factor that appears in either factorization: 2 x 3 x 5 x 5 = 150.
Converting Fractions to Equivalent Fractions with the Common Denominator
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We need to convert both fractions to equivalent fractions with a denominator of 150 to add them.
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For the first fraction (20/50):
- We need to multiply both the numerator and denominator by 3 to get an equivalent fraction with a denominator of 150. 3 x 20 / 3 x 50 = 60/150
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For the second fraction (1/6):
- We need to multiply both the numerator and denominator by 25 to get an equivalent fraction with a denominator of 150. 25 x 1/ 25 x 6 = 25/150
Addition of the Equivalent Fractions
- Now that both fractions have the same denominator, we can add the numerators: 60/150 + 25/150 = (60 + 25)/150 = 85/150
Simplifying the Result
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The fraction 85/150 can be simplified by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 5. 85 / 5 = 17 150 / 5 = 30
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The simplified fraction is 17/30.
Final Answer
- The final answer is 17/30.
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