Comparing Shelly and Megan

Oct 13, 2025 by miodeya.com 95 views

Introduction

Comparing fractions is an essential skill in mathematics, and it has numerous real-world applications. In this article, we will explore a scenario where three individuals, Shelly, Megan, and Latoya, drink different amounts of water after a dance practice. We will compare the fractions representing the amount of water each person drank to determine which shows a correct comparison between Shelly and the other two individuals.

The Problem

After dance practice, Shelly drank $\frac{2}{3}$ quart of water. Megan drank $\frac{3}{4}$ quart, and Latoya drank $\frac{5}{8}$ quart. We need to compare the amount of water Shelly drank with the amount of water Megan and Latoya drank.

Comparing Shelly and Megan

To compare the amount of water Shelly and Megan drank, we need to find a common denominator. The least common multiple (LCM) of 3 and 4 is 12. We can rewrite the fractions with a denominator of 12:

Shelly drank $\frac{2}{3} = \frac{8}{12}$
Megan drank $\frac{3}{4} = \frac{9}{12}$

Now we can compare the fractions:

$\frac{8}{12} < \frac{9}{12}$

This means that Megan drank more water than Shelly.

Comparing Shelly and Latoya

To compare the amount of water Shelly and Latoya drank, we need to find a common denominator. The least common multiple (LCM) of 3 and 8 is 24. We can rewrite the fractions with a denominator of 24:

Shelly drank $\frac{2}{3} = \frac{16}{24}$
Latoya drank $\frac{5}{8} = \frac{15}{24}$

Now we can compare the fractions:

$\frac{16}{24} > \frac{15}{24}$

This means that Shelly drank more water than Latoya.

Conclusion

In this article, we compared the fractions representing the amount of water Shelly, Megan, and Latoya drank after a dance practice. We found that Megan drank more water than Shelly, and Shelly drank more water than Latoya. This example illustrates the importance of comparing fractions in real-world scenarios.

Real-World Applications

Comparing fractions has numerous real-world applications, such as:

Measuring ingredients in cooking and baking
Calculating the area and perimeter of shapes
Determining the probability of an event
Comparing the cost of different products

Tips and Tricks

To compare fractions, find a common denominator.
Use the least common multiple (LCM) to find the common denominator.
Rewrite the fractions with the common denominator.
Compare the numerators to determine the relationship between the fractions.

Practice Problems

Compare the fractions $\frac{1}{2}$ and $\frac{3}{4}$ .
Compare the fractions $\frac{2}{3}$ and $\frac{5}{6}$ .
Compare the fractions $\frac{3}{4}$ and $\frac{7}{8}$ .

Answer Key

$\frac{1}{2} < \frac{3}{4}$
$\frac{2}{3} < \frac{5}{6}$
$\frac{3}{4} < \frac{7}{8}$
Frequently Asked Questions: Comparing Fractions =====================================================

Q: What is the best way to compare fractions?

A: The best way to compare fractions is to find a common denominator. This will allow you to compare the numerators and determine the relationship between the fractions.

Q: How do I find a common denominator?

A: To find a common denominator, you can use the least common multiple (LCM) of the denominators. For example, if you want to compare the fractions $\frac{1}{2}$ and $\frac{3}{4}$ , you can find the LCM of 2 and 4, which is 4. Then, you can rewrite the fractions with a denominator of 4: $\frac{1}{2} = \frac{2}{4}$ and $\frac{3}{4}$ .

Q: What is the least common multiple (LCM)?

A: The least common multiple (LCM) is the smallest multiple that two or more numbers have in common. For example, the LCM of 2 and 4 is 4, because 4 is the smallest number that both 2 and 4 can divide into evenly.

Q: How do I compare fractions with different denominators?

A: To compare fractions with different denominators, you can find a common denominator by using the LCM of the denominators. Then, you can rewrite the fractions with the common denominator and compare the numerators.

Q: What if the fractions have different signs?

A: If the fractions have different signs, you can compare them by ignoring the signs and comparing the absolute values. For example, if you want to compare the fractions $\frac{2}{3}$ and $-\frac{3}{4}$ , you can ignore the signs and compare the absolute values: $\frac{2}{3} > \frac{3}{4}$ .

Q: Can I compare fractions with unlike denominators using a calculator?

A: Yes, you can compare fractions with unlike denominators using a calculator. Most calculators have a function that allows you to compare fractions and find the common denominator.

Q: What are some real-world applications of comparing fractions?

A: Comparing fractions has numerous real-world applications, such as:

Measuring ingredients in cooking and baking
Calculating the area and perimeter of shapes
Determining the probability of an event
Comparing the cost of different products

Q: How can I practice comparing fractions?

A: You can practice comparing fractions by using online resources, such as fraction comparison games and worksheets. You can also practice by creating your own fraction comparison problems and solving them.

Q: What are some common mistakes to avoid when comparing fractions?

A: Some common mistakes to avoid when comparing fractions include:

Not finding a common denominator
Not rewriting the fractions with the common denominator
Comparing the denominators instead of the numerators
Ignoring the signs of the fractions

Q: Can I compare fractions with decimals?

A: Yes, you can compare fractions with decimals. To compare a fraction with a decimal, you can convert the fraction to a decimal by dividing the numerator by the denominator. Then, you can compare the decimals.

Q: What is the difference between comparing fractions and comparing decimals?

A: The main difference between comparing fractions and comparing decimals is that fractions have a numerator and a denominator, while decimals have a decimal point. When comparing fractions, you need to find a common denominator, while when comparing decimals, you can simply compare the decimal values.