Aimathic
Login | English | Deutsch

Free Math Worksheets

Build your own math worksheets from 21,000 problems for grades 3 to 12, from fractions to calculus. Every problem includes step-by-step solutions.

Estimate the size of a product

Click problems to add them to your worksheet.

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, \(\frac{1}{4}\)

All problems may be used, copied and printed free of charge for school and tutoring, including paid tutoring. Commercial adaptations as well as publication or redistribution on the internet are not permitted.