A Long Jump Athlete Jumps $5 \frac{1}{4}$ Meters. The Athlete's Next Jump Is $5 \frac{1}{8}$ Meters.a) How Far Has The Athlete Jumped Altogether?b) What Is The Difference Between The Two Jumps?

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**A Long Jump Athlete's Record Breaker: Calculating Distance and Difference** ===========================================================

Introduction

Long jump athletes require a combination of speed, strength, and technique to achieve impressive distances. In this article, we will explore the calculations involved in determining the total distance covered by an athlete who jumps $5 \frac{1}{4}$ meters and $5 \frac{1}{8}$ meters. We will also calculate the difference between the two jumps.

Calculating the Total Distance

To find the total distance covered by the athlete, we need to add the two jump distances together.

Step 1: Convert Mixed Numbers to Improper Fractions

First, let's convert the mixed numbers to improper fractions.

514=(5×4)+14=2145 \frac{1}{4} = \frac{(5 \times 4) + 1}{4} = \frac{21}{4}

518=(5×8)+18=4185 \frac{1}{8} = \frac{(5 \times 8) + 1}{8} = \frac{41}{8}

Step 2: Find a Common Denominator

To add the two fractions, we need to find a common denominator. The least common multiple (LCM) of 4 and 8 is 8.

Step 3: Add the Fractions

Now that we have a common denominator, we can add the fractions.

214=21×24×2=428\frac{21}{4} = \frac{21 \times 2}{4 \times 2} = \frac{42}{8}

428+418=838\frac{42}{8} + \frac{41}{8} = \frac{83}{8}

Step 4: Convert the Result to a Mixed Number

To make the result more understandable, let's convert the improper fraction to a mixed number.

838=1038\frac{83}{8} = 10 \frac{3}{8}

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

Calculating the Difference

To find the difference between the two jumps, we need to subtract the smaller jump from the larger jump.

Step 1: Convert Mixed Numbers to Improper Fractions

First, let's convert the mixed numbers to improper fractions.

514=2145 \frac{1}{4} = \frac{21}{4}

518=4185 \frac{1}{8} = \frac{41}{8}

Step 2: Find a Common Denominator

To subtract the fractions, we need to find a common denominator. The least common multiple (LCM) of 4 and 8 is 8.

Step 3: Subtract the Fractions

Now that we have a common denominator, we can subtract the fractions.

418−218=208\frac{41}{8} - \frac{21}{8} = \frac{20}{8}

Step 4: Convert the Result to a Mixed Number

To make the result more understandable, let's convert the improper fraction to a mixed number.

208=212\frac{20}{8} = 2 \frac{1}{2}

Therefore, the difference between the two jumps is $2 \frac{1}{2}$ meters.

Conclusion

In this article, we calculated the total distance covered by a long jump athlete who jumped $5 \frac{1}{4}$ meters and $5 \frac{1}{8}$ meters. We also calculated the difference between the two jumps. The total distance covered by the athlete is $10 \frac{3}{8}$ meters, and the difference between the two jumps is $2 \frac{1}{2}$ meters.

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 find a common denominator for two fractions?

A: To find a common denominator, find the least common multiple (LCM) of the two denominators.

Q: How do I subtract fractions with different denominators?

A: To subtract fractions with different denominators, find a common denominator and then subtract the fractions.

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

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

Q: What is the difference between a mixed number and an improper fraction?

A: A mixed number is a combination of a whole number and a fraction, while an improper fraction is a fraction with a numerator greater than the denominator.