5108215
a) Give a fraction that, when multiplied by \(\frac{3}{8}\), produces a result greater than \(\frac{3}{8}\).
b) Give a fraction that, when multiplied by \(\frac{3}{8}\), produces a result less than \(\frac{1}{8}\).
Hints
- Consider what happens when a positive number is multiplied by a factor greater than \(1\).
- Find the factor that would produce exactly \(\frac{1}{8}\).
- Choose a smaller positive factor for part b).
Solution
1. For a), multiplying a positive number by a factor greater than \(1\) increases it. For example, \(\frac{3}{2}\times\frac{3}{8}=\frac{9}{16}>\frac{3}{8}\).
2. For b), a factor smaller than \(\frac{1}{3}\) makes the product less than \(\frac{1}{8}\), because \(\frac{1}{3}\times\frac{3}{8}=\frac{1}{8}\). For example, \(\frac{1}{4}\times\frac{3}{8}=\frac{3}{32}<\frac{1}{8}\).
Answer
a) For example, \(\frac{3}{2}\)
b) For example, \(\frac{1}{4}\)
