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Answer :
Sure! Let's break down the steps to evaluate the expression [tex]\(86 \frac{14}{24} + 7 \frac{13}{24}\)[/tex].
1. Convert the mixed numbers to improper fractions:
- First mixed number: [tex]\(86 \frac{14}{24}\)[/tex]
- Convert the fractional part: [tex]\(\frac{14}{24}\)[/tex] simplifies to [tex]\(\frac{7}{12}\)[/tex].
- The mixed number becomes [tex]\(86 + \frac{7}{12}\)[/tex].
- Second mixed number: [tex]\(7 \frac{13}{24}\)[/tex]
- Convert the fractional part: [tex]\(\frac{13}{24}\)[/tex] stays as it is since it's already in its simplest form.
- The mixed number becomes [tex]\(7 + \frac{13}{24}\)[/tex].
2. Add the whole numbers and the fractions separately:
- Add the whole numbers: [tex]\(86 + 7 = 93\)[/tex].
3. Deal with the fractions:
- Add the fractions [tex]\(\frac{7}{12}\)[/tex] and [tex]\(\frac{13}{24}\)[/tex].
- Find a common denominator for the fractions, which is 24 since it's the least common multiple of 12 and 24.
- Convert [tex]\(\frac{7}{12}\)[/tex] to [tex]\(\frac{14}{24}\)[/tex] by multiplying both the numerator and the denominator by 2.
- Now, add [tex]\(\frac{14}{24}\)[/tex] and [tex]\(\frac{13}{24}\)[/tex]:
[tex]\[
\frac{14}{24} + \frac{13}{24} = \frac{27}{24}
\][/tex]
- Simplify [tex]\(\frac{27}{24}\)[/tex] to the mixed number [tex]\(1 \frac{3}{24}\)[/tex], which simplifies further to [tex]\(1 \frac{1}{8}\)[/tex].
4. Combine the results:
- Add the whole part [tex]\(93\)[/tex] and the whole part from the fractions [tex]\(1\)[/tex]:
[tex]\(93 + 1 = 94\)[/tex].
5. Combine the remaining fractions:
- Add [tex]\(94\)[/tex] and [tex]\(\frac{1}{8}\)[/tex]:
The result is [tex]\(94 \frac{1}{8}\)[/tex].
So, the final answer is [tex]\(94 \frac{1}{8}\)[/tex].
1. Convert the mixed numbers to improper fractions:
- First mixed number: [tex]\(86 \frac{14}{24}\)[/tex]
- Convert the fractional part: [tex]\(\frac{14}{24}\)[/tex] simplifies to [tex]\(\frac{7}{12}\)[/tex].
- The mixed number becomes [tex]\(86 + \frac{7}{12}\)[/tex].
- Second mixed number: [tex]\(7 \frac{13}{24}\)[/tex]
- Convert the fractional part: [tex]\(\frac{13}{24}\)[/tex] stays as it is since it's already in its simplest form.
- The mixed number becomes [tex]\(7 + \frac{13}{24}\)[/tex].
2. Add the whole numbers and the fractions separately:
- Add the whole numbers: [tex]\(86 + 7 = 93\)[/tex].
3. Deal with the fractions:
- Add the fractions [tex]\(\frac{7}{12}\)[/tex] and [tex]\(\frac{13}{24}\)[/tex].
- Find a common denominator for the fractions, which is 24 since it's the least common multiple of 12 and 24.
- Convert [tex]\(\frac{7}{12}\)[/tex] to [tex]\(\frac{14}{24}\)[/tex] by multiplying both the numerator and the denominator by 2.
- Now, add [tex]\(\frac{14}{24}\)[/tex] and [tex]\(\frac{13}{24}\)[/tex]:
[tex]\[
\frac{14}{24} + \frac{13}{24} = \frac{27}{24}
\][/tex]
- Simplify [tex]\(\frac{27}{24}\)[/tex] to the mixed number [tex]\(1 \frac{3}{24}\)[/tex], which simplifies further to [tex]\(1 \frac{1}{8}\)[/tex].
4. Combine the results:
- Add the whole part [tex]\(93\)[/tex] and the whole part from the fractions [tex]\(1\)[/tex]:
[tex]\(93 + 1 = 94\)[/tex].
5. Combine the remaining fractions:
- Add [tex]\(94\)[/tex] and [tex]\(\frac{1}{8}\)[/tex]:
The result is [tex]\(94 \frac{1}{8}\)[/tex].
So, the final answer is [tex]\(94 \frac{1}{8}\)[/tex].
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