Calculating the Total Distance Covered

Oct 13, 2025 by magicalceylontours.com 42 views

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Introduction

Long jump is a popular athletic event where athletes compete to jump the farthest distance. In this article, we will explore the record-breaking jumps of a long jump athlete who jumped $$5 \frac{1}{4}$$ meters and $$5 \frac{1}{8}$$ meters. We will calculate the total distance covered by the athlete and the difference between the two jumps.

Calculating the Total Distance Covered

To calculate the total distance covered by the athlete, we need to add the two jumps together. We can start by converting the mixed numbers to improper fractions.

5 \frac{1}{4} = \frac{(5 \times 4) + 1}{4} = \frac{21}{4}

5 \frac{1}{8} = \frac{(5 \times 8) + 1}{8} = \frac{41}{8}

Now, we can add the two fractions together by finding a common denominator, which is 8.

\frac{21}{4} = \frac{21 \times 2}{4 \times 2} = \frac{42}{8}

\frac{42}{8} + \frac{41}{8} = \frac{83}{8}

So, the total distance covered by the athlete is $$\frac{83}{8}$$ meters.

Converting the Improper Fraction to a Mixed Number

To make the answer more meaningful, we can convert the improper fraction to a mixed number.

\frac{83}{8} = 10 \frac{3}{8}

Therefore, the athlete has jumped a total distance of $$10 \frac{3}{8}$$ meters.

Calculating the Difference Between the Two Jumps

To calculate the difference between the two jumps, we can subtract the smaller jump from the larger jump.

5 \frac{1}{8} - 5 \frac{1}{4} = \frac{41}{8} - \frac{21}{4}

We can simplify the subtraction by finding a common denominator, which is 8.

\frac{21}{4} = \frac{21 \times 2}{4 \times 2} = \frac{42}{8}

\frac{41}{8} - \frac{42}{8} = -\frac{1}{8}

So, the difference between the two jumps is $$-\frac{1}{8}$$ meters, which is equivalent to $$-0.125$$ meters.

Conclusion

In conclusion, the long jump athlete has jumped a total distance of $$10 \frac{3}{8}$$ meters and the difference between the two jumps is $$-0.125$$ meters. The athlete's next jump was slightly shorter than the previous one, but the total distance covered is still impressive.

Frequently Asked Questions

Q: How do I convert a mixed number to an improper fraction? A: To convert a mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator. Then, write the result as an improper fraction.
Q: How do I add two fractions together? A: To add two fractions together, find a common denominator and add the numerators.
Q: How do I subtract two fractions together? A: To subtract two fractions together, find a common denominator and subtract the numerators.

References

[1] Khan Academy. (n.d.). Adding and Subtracting Fractions. Retrieved from https://www.khanacademy.org/math/fractions-and-decimals/fractions-and-decimals-topic/fractions-and-decimals-topic-article
[2] Math Open Reference. (n.d.). Fractions. Retrieved from https://www.mathopenref.com/fractions.html

Introduction

In our previous article, we explored the record-breaking jumps of a long jump athlete who jumped $$5 \frac{1}{4}$$ meters and $$5 \frac{1}{8}$$ meters. We calculated the total distance covered by the athlete and the difference between the two jumps. In this article, we will answer some frequently asked questions related to the topic.

Q&A

Q: What is the total distance covered by the athlete?

A: The total distance covered by the athlete is $$10 \frac{3}{8}$$ meters.

Q: What is the difference between the two jumps?

A: The difference between the two jumps is $$-0.125$$ meters.

Q: How do I convert a mixed number to an improper fraction?

A: To convert a mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator. Then, write the result as an improper fraction.

Q: How do I add two fractions together?

A: To add two fractions together, find a common denominator and add the numerators.

Q: How do I subtract two fractions together?

A: To subtract two fractions together, find a common denominator and subtract the numerators.

Q: What is the formula for calculating the total distance covered by the athlete?

A: The formula for calculating the total distance covered by the athlete is:

\text{Total Distance} = \frac{(\text{Jump 1} \times \text{Denominator 1}) + \text{Numerator 1}}{\text{Denominator 1}} + \frac{(\text{Jump 2} \times \text{Denominator 2}) + \text{Numerator 2}}{\text{Denominator 2}}

Q: What is the formula for calculating the difference between the two jumps?

A: The formula for calculating the difference between the two jumps is:

\text{Difference} = \frac{(\text{Jump 2} \times \text{Denominator 2}) + \text{Numerator 2}}{\text{Denominator 2}} - \frac{(\text{Jump 1} \times \text{Denominator 1}) + \text{Numerator 1}}{\text{Denominator 1}}

Q: How do I simplify a fraction?

A: To simplify a fraction, divide the numerator and denominator by their greatest common divisor (GCD).

Q: What is the GCD of two numbers?

A: The GCD of two numbers is the largest number that divides both numbers without leaving a remainder.

Conclusion

In conclusion, we have answered some frequently asked questions related to the topic of long jump athlete's record breaking jumps. We hope that this article has provided you with a better understanding of the topic and has helped you to improve your math skills.

Frequently Asked Questions

Q: What is the formula for calculating the total distance covered by the athlete? A: The formula for calculating the total distance covered by the athlete is:

\text{Total Distance} = \frac{(\text{Jump 1} \times \text{Denominator 1}) + \text{Numerator 1}}{\text{Denominator 1}} + \frac{(\text{Jump 2} \times \text{Denominator 2}) + \text{Numerator 2}}{\text{Denominator 2}}

Q: What is the formula for calculating the difference between the two jumps? A: The formula for calculating the difference between the two jumps is:

\text{Difference} = \frac{(\text{Jump 2} \times \text{Denominator 2}) + \text{Numerator 2}}{\text{Denominator 2}} - \frac{(\text{Jump 1} \times \text{Denominator 1}) + \text{Numerator 1}}{\text{Denominator 1}}

References

[1] Khan Academy. (n.d.). Adding and Subtracting Fractions. Retrieved from https://www.khanacademy.org/math/fractions-and-decimals/fractions-and-decimals-topic/fractions-and-decimals-topic-article
[2] Math Open Reference. (n.d.). Fractions. Retrieved from https://www.mathopenref.com/fractions.html