At first glance, you might think the answer to this question is a simple “no.” After all, 1 3 is one-third, while 1 4 is one-fourth. And, as we all know, one-third is less than one-fourth.
However, there is actually a mathematical trick that can be used to show that 1 3 is greater than 1 4.
The Mathematical Trick
The trick is to use the fact that the fraction 1 3 can be written as the repeating decimal 0.3333333…. Similarly, the fraction 1 4 can be written as the repeating decimal 0.25252525….
If we now take the fraction 1 3 and multiply it by 10, we get the decimal 0.33333333…. However, if we now take the fraction 1 4 and multiply it by 10, we get the decimal 0.25000000….
As you can see, the decimal representation of 1 3 is larger than the decimal representation of 1 4. This means that 1 3 is actually greater than 1 4.
Applications of This Trick
This mathematical trick can be used in a variety of applications. For example, it can be used to:
- Convert fractions to decimals.
- Compare the size of fractions.
- Find the least common denominator of two fractions.
- Add and subtract fractions.
Conclusion
The mathematical trick of multiplying a fraction by 10 to convert it to a decimal is a powerful tool that can be used in a variety of applications. By understanding this trick, you can solve a wide range of math problems.
Want to Learn More?
If you found this article helpful, you may be interested in learning more about the following topics:
Worksheets
To practice your skills with fractions and decimals, try the following worksheets:
- Fraction Conversion Worksheet
- Decimal Conversion Worksheet
- Fraction Addition and Subtraction Worksheet
- Decimal Addition and Subtraction Worksheet
FAQs
Q: Why does this trick work?
A: This trick works because multiplication by 10 is equivalent to moving the decimal point one place to the right. When we multiply a fraction by 10, we are essentially converting it to a decimal.
Q: Can this trick be used to compare any two fractions?
A: Yes, this trick can be used to compare any two fractions. However, it is important to note that the fractions must be expressed in their simplest form before using the trick.
Q: What are some other applications of this trick?
A: This trick can be used to find the least common denominator of two fractions, as well as to add and subtract fractions.
Glossary
- Decimal: A number that is written using a decimal point.
- Fraction: A number that is expressed as a quotient of two integers.
- Improper fraction: A fraction whose numerator is greater than or equal to its denominator.
- Mixed number: A number that is expressed as a whole number and a fraction.
- Repeating decimal: A decimal that has a repeating pattern of digits.
- Terminating decimal: A decimal that does not have a repeating pattern of digits.