Question
Reduce the fractions to their lowest terms and write their reciprocals: a. \( \frac{50}{120} \) Reciprocal: b. \( \frac{100}{40} \) Reciprocal:
Ask by Ortiz Lyons. in Canada
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( \frac{50}{120} \) simplifies to \( \frac{5}{12} \), and its reciprocal is \( \frac{12}{5} \).
\( \frac{100}{40} \) simplifies to \( \frac{5}{2} \), and its reciprocal is \( \frac{2}{5} \).
Solution
Calculate or simplify the expression \( \frac{50}{120} \).
Calculate the value by following steps:
- step0: Calculate:
\(\frac{50}{120}\)
- step1: Reduce the fraction:
\(\frac{5}{12}\)
Calculate or simplify the expression \( \frac{100}{40} \).
Calculate the value by following steps:
- step0: Calculate:
\(\frac{100}{40}\)
- step1: Reduce the fraction:
\(\frac{5}{2}\)
The fraction \( \frac{50}{120} \) reduced to its lowest terms is \( \frac{5}{12} \).
The reciprocal of \( \frac{5}{12} \) is \( \frac{12}{5} \).
The fraction \( \frac{100}{40} \) reduced to its lowest terms is \( \frac{5}{2} \).
The reciprocal of \( \frac{5}{2} \) is \( \frac{2}{5} \).
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Simplify this solution The Deep Dive
To reduce \( \frac{50}{120} \) to its lowest terms, we divide both the numerator and the denominator by their greatest common divisor (GCD), which is 10. This gives us \( \frac{50 \div 10}{120 \div 10} = \frac{5}{12} \). The reciprocal is \( \frac{12}{5} \). For \( \frac{100}{40} \), we notice that the GCD is 20. So, dividing both parts by 20 yields \( \frac{100 \div 20}{40 \div 20} = \frac{5}{2} \). The reciprocal here is \( \frac{2}{5} \).
