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Answer :
To find out how many hours Paul volunteered altogether, we need to add the hours he volunteered on Saturday and Sunday. Let's break down the problem step by step:
1. Convert the mixed numbers to improper fractions:
- For Saturday, Paul volunteered for [tex]\(3 \frac{9}{10}\)[/tex] hours. This can be converted to an improper fraction by multiplying the whole number [tex]\(3\)[/tex] by [tex]\(10\)[/tex] (the denominator) and adding the numerator [tex]\(9\)[/tex]. So, it becomes [tex]\(\frac{30 + 9}{10} = \frac{39}{10}\)[/tex].
- For Sunday, Paul volunteered for [tex]\(5 \frac{1}{6}\)[/tex] hours. This can be converted to an improper fraction by multiplying the whole number [tex]\(5\)[/tex] by [tex]\(6\)[/tex] (the denominator) and adding the numerator [tex]\(1\)[/tex]. So, it becomes [tex]\(\frac{30 + 1}{6} = \frac{31}{6}\)[/tex].
2. Find a common denominator:
- The denominators 10 and 6 have a least common multiple (LCM) of 30, which we will use as the common denominator.
3. Convert the fractions to have a common denominator:
- For [tex]\(\frac{39}{10}\)[/tex], multiply the numerator and the denominator by 3 to get [tex]\(\frac{117}{30}\)[/tex].
- For [tex]\(\frac{31}{6}\)[/tex], multiply the numerator and the denominator by 5 to get [tex]\(\frac{155}{30}\)[/tex].
4. Add the fractions:
- Now, add the fractions: [tex]\(\frac{117}{30} + \frac{155}{30} = \frac{272}{30}\)[/tex].
5. Convert to a mixed number:
- Divide 272 by 30 to find the whole number part. [tex]\(272 \div 30 = 9\)[/tex] with a remainder.
- The remainder is 2, so the fraction part is [tex]\(\frac{2}{30}\)[/tex].
6. Simplify the fractional part:
- The fraction [tex]\(\frac{2}{30}\)[/tex] can be simplified by dividing the numerator and the denominator by their greatest common divisor, which is 2. So, [tex]\(\frac{2}{30}\)[/tex] simplifies to [tex]\(\frac{1}{15}\)[/tex].
In conclusion, Paul volunteered for [tex]\(9 \frac{1}{15}\)[/tex] hours altogether at the senior center.
1. Convert the mixed numbers to improper fractions:
- For Saturday, Paul volunteered for [tex]\(3 \frac{9}{10}\)[/tex] hours. This can be converted to an improper fraction by multiplying the whole number [tex]\(3\)[/tex] by [tex]\(10\)[/tex] (the denominator) and adding the numerator [tex]\(9\)[/tex]. So, it becomes [tex]\(\frac{30 + 9}{10} = \frac{39}{10}\)[/tex].
- For Sunday, Paul volunteered for [tex]\(5 \frac{1}{6}\)[/tex] hours. This can be converted to an improper fraction by multiplying the whole number [tex]\(5\)[/tex] by [tex]\(6\)[/tex] (the denominator) and adding the numerator [tex]\(1\)[/tex]. So, it becomes [tex]\(\frac{30 + 1}{6} = \frac{31}{6}\)[/tex].
2. Find a common denominator:
- The denominators 10 and 6 have a least common multiple (LCM) of 30, which we will use as the common denominator.
3. Convert the fractions to have a common denominator:
- For [tex]\(\frac{39}{10}\)[/tex], multiply the numerator and the denominator by 3 to get [tex]\(\frac{117}{30}\)[/tex].
- For [tex]\(\frac{31}{6}\)[/tex], multiply the numerator and the denominator by 5 to get [tex]\(\frac{155}{30}\)[/tex].
4. Add the fractions:
- Now, add the fractions: [tex]\(\frac{117}{30} + \frac{155}{30} = \frac{272}{30}\)[/tex].
5. Convert to a mixed number:
- Divide 272 by 30 to find the whole number part. [tex]\(272 \div 30 = 9\)[/tex] with a remainder.
- The remainder is 2, so the fraction part is [tex]\(\frac{2}{30}\)[/tex].
6. Simplify the fractional part:
- The fraction [tex]\(\frac{2}{30}\)[/tex] can be simplified by dividing the numerator and the denominator by their greatest common divisor, which is 2. So, [tex]\(\frac{2}{30}\)[/tex] simplifies to [tex]\(\frac{1}{15}\)[/tex].
In conclusion, Paul volunteered for [tex]\(9 \frac{1}{15}\)[/tex] hours altogether at the senior center.
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