Answer: Several expressions equal to \(\tfrac{7}{8}\). Examples:
- \(\tfrac{14}{16},\ \tfrac{21}{24},\ \tfrac{35}{40},\ \tfrac{56}{64}\)
- \(0.875\)
- \(87.5\%\)
- \(1 - \tfrac{1}{8}\)
- \(\tfrac{3}{8} + \tfrac{4}{8}\)
- More generally, \(\dfrac{7k}{8k}\) for any nonzero integer \(k\).
Explanation:
- Equivalent fractions: multiplying numerator and denominator of \(\tfrac{7}{8}\) by the same nonzero integer \(k\) gives \(\dfrac{7k}{8k}\). For example with \(k=2\) we get \(\tfrac{14}{16}\); with \(k=3\) we get \(\tfrac{21}{24}\), etc. These represent the same rational number because you have multiplied by 1 (\(k/k\)).
- Simplest form: \(\tfrac{7}{8}\) is already in lowest terms because 7 and 8 have no common factors besides 1. You cannot reduce it further.
- Decimal and percent: divide \(7\) by \(8\): \(7 \div 8 = 0.875\). Converting the decimal to percent gives \(0.875 \times 100\% = 87.5\%\).
- Other expressions: rewriting using subtraction/addition also works: \(1-\tfrac{1}{8}=\tfrac{8}{8}-\tfrac{1}{8}=\tfrac{7}{8}\), and \(\tfrac{3}{8}+\tfrac{4}{8}=\tfrac{7}{8}\).
Any expression obtained by these valid algebraic manipulations (multiplying numerator and denominator by the same nonzero number, converting to decimal/percent, or adding/subtracting equivalent fractions) will equal \(\tfrac{7}{8}\).