What is the result of adding the following fractions: (1) 2/9 + 2/7, (2) 3/11 + 3/13, (3) 8/15 + 8/17, (4) 7/8 + 7/15, (5) 6/17 + 6/11, (6) 9/10 + 9/11?
Understand the Problem
The question involves adding fractions. The user needs to complete the addition of several pairs of fractions provided in the image. Each pair likely requires finding a common denominator to solve.
Answer
The sum of the fractions is $\frac{189}{110}$ or $1 \frac{79}{110}$.
Answer for screen readers
The answer to question (6) is $\frac{189}{110}$ or $1 \frac{79}{110}$.
Steps to Solve
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Identify the fractions
For question (6), we have the fractions $\frac{9}{10}$ and $\frac{9}{11}$. -
Find the least common denominator (LCD)
The denominators are 10 and 11.
The least common multiple of 10 and 11 is 110. -
Convert the fractions to the common denominator
For $\frac{9}{10}$:
Multiply both the numerator and the denominator by 11:
$$ \frac{9 \times 11}{10 \times 11} = \frac{99}{110} $$
For $\frac{9}{11}$:
Multiply both the numerator and the denominator by 10:
$$ \frac{9 \times 10}{11 \times 10} = \frac{90}{110} $$
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Add the two fractions
Now add the two fractions:
$$ \frac{99}{110} + \frac{90}{110} = \frac{99 + 90}{110} = \frac{189}{110} $$ -
Simplify the result if necessary
The fraction $\frac{189}{110}$ cannot be simplified further, so we can represent it as a mixed number:
$$ 189 \div 110 = 1\ \text{R} 79 $$
This gives us the mixed number:
$$ 1\frac{79}{110} $$
The answer to question (6) is $\frac{189}{110}$ or $1 \frac{79}{110}$.
More Information
The process of adding fractions involves finding a common denominator, converting the fractions, and then performing the addition. The final answer here is an improper fraction that can also be expressed as a mixed number.
Tips
- Forgetting to find the least common denominator.
- Incorrectly multiplying the numerators and denominators when converting fractions.
- Not simplifying the fraction or mixed number correctly.
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