Question
(b) \( \frac{5}{6}-\frac{2}{3}+\left(\frac{8}{9}\right) \)
Ask by Rodriguez Warren. in Malaysia
Mar 17,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The result is \( \frac{19}{18} \) or \( 1\frac{1}{18} \) or \( 1.0\dot{5} \).
Solution
Calculate or simplify the expression \( 5/6-2/3+8/9 \).
Calculate the value by following steps:
- step0: Calculate:
\(\frac{5}{6}-\frac{2}{3}+\frac{8}{9}\)
- step1: Reduce fractions to a common denominator:
\(\frac{5\times 3}{6\times 3}-\frac{2\times 2\times 3}{3\times 2\times 3}+\frac{8\times 2}{9\times 2}\)
- step2: Multiply the numbers:
\(\frac{5\times 3}{18}-\frac{2\times 2\times 3}{3\times 2\times 3}+\frac{8\times 2}{9\times 2}\)
- step3: Multiply the terms:
\(\frac{5\times 3}{18}-\frac{2\times 2\times 3}{18}+\frac{8\times 2}{9\times 2}\)
- step4: Multiply the numbers:
\(\frac{5\times 3}{18}-\frac{2\times 2\times 3}{18}+\frac{8\times 2}{18}\)
- step5: Transform the expression:
\(\frac{5\times 3-2\times 2\times 3+8\times 2}{18}\)
- step6: Multiply the numbers:
\(\frac{15-2\times 2\times 3+8\times 2}{18}\)
- step7: Multiply the terms:
\(\frac{15-12+8\times 2}{18}\)
- step8: Multiply the numbers:
\(\frac{15-12+16}{18}\)
- step9: Calculate:
\(\frac{19}{18}\)
The result of \( \frac{5}{6}-\frac{2}{3}+\left(\frac{8}{9}\right) \) is \( \frac{19}{18} \) or \( 1\frac{1}{18} \) or \( 1.0\dot{5} \).
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Simplify this solution Extra Insights
To solve \( \frac{5}{6} - \frac{2}{3} + \frac{8}{9} \), we first need a common denominator, which is 18 in this case. First, convert each fraction: - \( \frac{5}{6} = \frac{5 \times 3}{6 \times 3} = \frac{15}{18} \) - \( \frac{2}{3} = \frac{2 \times 6}{3 \times 6} = \frac{12}{18} \) - \( \frac{8}{9} = \frac{8 \times 2}{9 \times 2} = \frac{16}{18} \) Now, substitute back into the equation: \[ \frac{15}{18} - \frac{12}{18} + \frac{16}{18} = \frac{15 - 12 + 16}{18} = \frac{19}{18} \] Thus, the final answer is \( \frac{19}{18} \) or \( 1 \frac{1}{18} \).
