Elliot scores 65 out of 80 in a Maths test. Write this as a fraction in its simplest form.
The Correct Answer and Explanation is :
The correct answer is: (\frac{13}{16})
To express Elliot’s score of 65 out of 80 as a fraction in its simplest form, we need to simplify the fraction (\frac{65}{80}).
Step 1: Identify the Fraction
The fraction is (\frac{65}{80}).
Step 2: Find the Greatest Common Divisor (GCD)
To simplify a fraction, we divide both the numerator (65) and the denominator (80) by their greatest common divisor (GCD).
- Finding the GCD:
- The factors of 65 are 1, 5, 13, and 65.
- The factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, and 80.
- The common factors are 1 and 5. Thus, the GCD of 65 and 80 is 5.
Step 3: Simplify the Fraction
Now that we have the GCD, we can simplify the fraction by dividing both the numerator and the denominator by 5:
[
\frac{65 \div 5}{80 \div 5} = \frac{13}{16}
]
Conclusion
The fraction (\frac{65}{80}) simplifies to (\frac{13}{16}).
Explanation
Simplifying fractions is an important skill in mathematics as it helps in understanding proportions and comparisons. When a fraction is expressed in its simplest form, it is easier to work with and provides a clearer representation of the relationship between the numerator and the denominator.
In this case, the score of 65 out of 80 can be understood as Elliot having earned 13 parts out of a total of 16 parts when the total score is normalized. This simplification is especially useful in contexts such as grading, where understanding the proportion of points earned can be critical. For instance, a score of (\frac{13}{16}) indicates that Elliot scored approximately 81.25%, which is a useful percentage to assess his performance in relation to the full score. Thus, simplifying fractions not only aids in mathematical computations but also in interpreting and communicating results effectively.