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Answer :
To find out how many ounces of paint Mary mixed, we need to add the given amounts together. We're working with mixed numbers, so the steps involve converting them to improper fractions, summing them, and simplifying if necessary. Here’s how you can think through the problem:
1. Convert each mixed number to an improper fraction:
- [tex]\(1 \frac{2}{3}\)[/tex] is equivalent to [tex]\(\frac{5}{3}\)[/tex].
- [tex]\(1 \frac{5}{6}\)[/tex] becomes [tex]\(\frac{11}{6}\)[/tex].
- [tex]\(1 \frac{7}{8}\)[/tex] changes to [tex]\(\frac{15}{8}\)[/tex].
- [tex]\(2 \frac{2}{3}\)[/tex] is equivalent to [tex]\(\frac{8}{3}\)[/tex].
2. Find a common denominator to add these fractions.
Since our smallest common multiple of 3, 6, and 8 is 24, use that as the common denominator.
3. Convert each fraction to have the common denominator of 24:
- [tex]\(\frac{5}{3}\)[/tex] becomes [tex]\(\frac{40}{24}\)[/tex].
- [tex]\(\frac{11}{6}\)[/tex] becomes [tex]\(\frac{44}{24}\)[/tex].
- [tex]\(\frac{15}{8}\)[/tex] becomes [tex]\(\frac{45}{24}\)[/tex].
- [tex]\(\frac{8}{3}\)[/tex] becomes [tex]\(\frac{64}{24}\)[/tex].
4. Add all the fractions:
[tex]\[
\frac{40}{24} + \frac{44}{24} + \frac{45}{24} + \frac{64}{24} = \frac{193}{24}
\][/tex]
5. Convert the improper fraction back into a mixed number:
[tex]\(\frac{193}{24}\)[/tex] simplifies to 8 whole parts with a remainder:
- Dividing 193 by 24 gives 8 remainder 1, so [tex]\(8 \frac{1}{24}\)[/tex].
Therefore, Mary mixed [tex]\(8 \frac{1}{24}\)[/tex] ounces of paint in total.
1. Convert each mixed number to an improper fraction:
- [tex]\(1 \frac{2}{3}\)[/tex] is equivalent to [tex]\(\frac{5}{3}\)[/tex].
- [tex]\(1 \frac{5}{6}\)[/tex] becomes [tex]\(\frac{11}{6}\)[/tex].
- [tex]\(1 \frac{7}{8}\)[/tex] changes to [tex]\(\frac{15}{8}\)[/tex].
- [tex]\(2 \frac{2}{3}\)[/tex] is equivalent to [tex]\(\frac{8}{3}\)[/tex].
2. Find a common denominator to add these fractions.
Since our smallest common multiple of 3, 6, and 8 is 24, use that as the common denominator.
3. Convert each fraction to have the common denominator of 24:
- [tex]\(\frac{5}{3}\)[/tex] becomes [tex]\(\frac{40}{24}\)[/tex].
- [tex]\(\frac{11}{6}\)[/tex] becomes [tex]\(\frac{44}{24}\)[/tex].
- [tex]\(\frac{15}{8}\)[/tex] becomes [tex]\(\frac{45}{24}\)[/tex].
- [tex]\(\frac{8}{3}\)[/tex] becomes [tex]\(\frac{64}{24}\)[/tex].
4. Add all the fractions:
[tex]\[
\frac{40}{24} + \frac{44}{24} + \frac{45}{24} + \frac{64}{24} = \frac{193}{24}
\][/tex]
5. Convert the improper fraction back into a mixed number:
[tex]\(\frac{193}{24}\)[/tex] simplifies to 8 whole parts with a remainder:
- Dividing 193 by 24 gives 8 remainder 1, so [tex]\(8 \frac{1}{24}\)[/tex].
Therefore, Mary mixed [tex]\(8 \frac{1}{24}\)[/tex] ounces of paint in total.
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