John Had 2 3 \frac{2}{3} 3 2 ​ Of His Homework Complete, Sarah Had 5 10 \frac{5}{10} 10 5 ​ , Alex Had 7 8 \frac{7}{8} 8 7 ​ , And Michelle Had 1 2 \frac{1}{2} 2 1 ​ . Who Completed The Most Of The Homework Assignment?A) John B) Sarah C) Alex D) Michelle

When comparing fractions, it's essential to understand that the larger the numerator (the top number) in relation to the denominator (the bottom number), the larger the fraction value. In this scenario, we have four individuals with different fractions representing the amount of homework they completed.

Understanding the Fractions

• John had $\frac{2}{3}$ of his homework complete.
• Sarah had $\frac{5}{10}$ of her homework complete.
• Alex had $\frac{7}{8}$ of his homework complete.
• Michelle had $\frac{1}{2}$ of her homework complete.

Converting Fractions to Decimals

To make it easier to compare these fractions, we can convert them to decimals. This will give us a clearer understanding of the relative sizes of the fractions.

• John's fraction as a decimal: $\frac{2}{3} \approx 0.67$
• Sarah's fraction as a decimal: $\frac{5}{10} = 0.5$
• Alex's fraction as a decimal: $\frac{7}{8} \approx 0.875$
• Michelle's fraction as a decimal: $\frac{1}{2} = 0.5$

Comparing the Decimals

Now that we have the fractions converted to decimals, we can compare them to determine who completed the most homework.

• The largest decimal value is 0.875, which belongs to Alex.
• The next largest decimal value is 0.67, which belongs to John.
• The remaining decimal values are 0.5, which belongs to both Sarah and Michelle.

Conclusion

Based on the comparison of the fractions as decimals, we can conclude that Alex completed the most homework with a fraction value of $\frac{7}{8}$, which is equivalent to 0.875 in decimal form.

In the previous section, we compared fractions to determine who completed the most homework. Here are some frequently asked questions (FAQs) related to comparing fractions:

Q: What is the difference between a numerator and a denominator in a fraction?

A: The numerator is the top number in a fraction, and it represents the number of equal parts being considered. The denominator is the bottom number in a fraction, and it represents the total number of parts being divided.

Q: How do I compare two fractions with different denominators?

A: To compare two fractions with different denominators, you can convert them to equivalent fractions with the same denominator. This can be done by finding the least common multiple (LCM) of the two denominators.

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

A: The LCM of two numbers is the smallest number that is a multiple of both numbers. For example, the LCM of 3 and 4 is 12, because 12 is the smallest number that can be divided by both 3 and 4.

Q: How do I convert a fraction to a decimal?

A: To convert a fraction to a decimal, you can divide the numerator by the denominator. For example, the fraction $\frac{3}{4}$ can be converted to a decimal by dividing 3 by 4, which gives 0.75.

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

A: A proper fraction is a fraction where the numerator is less than the denominator, such as $\frac{1}{2}$. An improper fraction is a fraction where the numerator is greater than or equal to the denominator, such as $\frac{3}{2}$.

Q: How do I add or subtract fractions with different denominators?

A: To add or subtract fractions with different denominators, you need to find the least common multiple (LCM) of the two denominators and convert both fractions to equivalent fractions with the same denominator.

Q: What is the order of operations for comparing fractions?

A: The order of operations for comparing fractions is:

1. Convert all fractions to equivalent fractions with the same denominator.
2. Compare the numerators of the equivalent fractions.
3. The fraction with the larger numerator is the larger fraction.

Q: Can I compare fractions with negative numbers?

A: Yes, you can compare fractions with negative numbers. However, you need to remember that a negative number is less than a positive number, and a negative fraction is less than a positive fraction.

Q: How do I compare fractions with decimals?

A: To compare fractions with decimals, you can convert the fractions to decimals and compare the decimal values.

Q: What is the difference between a fraction and a decimal?

A: A fraction is a way of representing a part of a whole, while a decimal is a way of representing a number as a sum of powers of 10.

Q: Can I compare fractions with mixed numbers?

A: Yes, you can compare fractions with mixed numbers. However, you need to convert the mixed numbers to improper fractions before comparing them.

Q: How do I compare fractions with unlike denominators?

A: To compare fractions with unlike denominators, you can convert them to equivalent fractions with the same denominator, or you can convert them to decimals and compare the decimal values.

Q: What is the rule for comparing fractions with unlike denominators?

A: The rule for comparing fractions with unlike denominators is to convert them to equivalent fractions with the same denominator, or to convert them to decimals and compare the decimal values.

Q: Can I compare fractions with decimals and fractions?

A: Yes, you can compare fractions with decimals and fractions. You can convert the fractions to decimals and compare the decimal values.

Q: How do I compare fractions with decimals and fractions?

A: To compare fractions with decimals and fractions, you can convert the fractions to decimals and compare the decimal values.

Q: What is the difference between a fraction and a percentage?

A: A fraction is a way of representing a part of a whole, while a percentage is a way of representing a part of a whole as a percentage of the total.

Q: Can I compare fractions with percentages?

A: Yes, you can compare fractions with percentages. However, you need to convert the percentages to decimals and compare the decimal values.

Q: How do I compare fractions with percentages?

A: To compare fractions with percentages, you can convert the percentages to decimals and compare the decimal values.

Q: What is the rule for comparing fractions with percentages?

A: The rule for comparing fractions with percentages is to convert the percentages to decimals and compare the decimal values.

Q: Can I compare fractions with decimals and percentages?

A: Yes, you can compare fractions with decimals and percentages. You can convert the fractions to decimals and compare the decimal values.

Q: How do I compare fractions with decimals and percentages?

A: To compare fractions with decimals and percentages, you can convert the fractions to decimals and compare the decimal values.

Q: What is the difference between a fraction and a ratio?

A: A fraction is a way of representing a part of a whole, while a ratio is a way of representing the relationship between two quantities.

Q: Can I compare fractions with ratios?

A: Yes, you can compare fractions with ratios. However, you need to convert the ratios to fractions and compare the fraction values.

Q: How do I compare fractions with ratios?

A: To compare fractions with ratios, you can convert the ratios to fractions and compare the fraction values.

Q: What is the rule for comparing fractions with ratios?

A: The rule for comparing fractions with ratios is to convert the ratios to fractions and compare the fraction values.

Q: Can I compare fractions with decimals and ratios?

A: Yes, you can compare fractions with decimals and ratios. You can convert the fractions to decimals and compare the decimal values.

Q: How do I compare fractions with decimals and ratios?

A: To compare fractions with decimals and ratios, you can convert the fractions to decimals and compare the decimal values.

Q: What is the difference between a fraction and a proportion?

A: A fraction is a way of representing a part of a whole, while a proportion is a way of representing the relationship between two quantities as a ratio.

Q: Can I compare fractions with proportions?

A: Yes, you can compare fractions with proportions. However, you need to convert the proportions to fractions and compare the fraction values.

Q: How do I compare fractions with proportions?

A: To compare fractions with proportions, you can convert the proportions to fractions and compare the fraction values.

Q: What is the rule for comparing fractions with proportions?

A: The rule for comparing fractions with proportions is to convert the proportions to fractions and compare the fraction values.

Q: Can I compare fractions with decimals and proportions?

A: Yes, you can compare fractions with decimals and proportions. You can convert the fractions to decimals and compare the decimal values.

Q: How do I compare fractions with decimals and proportions?

A: To compare fractions with decimals and proportions, you can convert the fractions to decimals and compare the decimal values.

Q: What is the difference between a fraction and a fraction with a negative exponent?

A: A fraction with a negative exponent is a fraction where the exponent is negative, such as $\frac{1}{x^{-2}}$.

Q: Can I compare fractions with negative exponents?

A: Yes, you can compare fractions with negative exponents. However, you need to remember that a negative exponent is equivalent to taking the reciprocal of the fraction.

Q: How do I compare fractions with negative exponents?

A: To compare fractions with negative exponents, you can take the reciprocal of the fraction and compare the resulting fraction.

Q: What is the rule for comparing fractions with negative exponents?

A: The rule for comparing fractions with negative exponents is to take the reciprocal of the fraction and compare the resulting fraction.

Q: Can I compare fractions with decimals and negative exponents?

A: Yes, you can compare fractions with decimals and negative exponents. You can convert the fractions to decimals and compare the decimal values.

Q: How do I compare fractions with decimals and negative exponents?

A: To compare fractions with decimals and negative exponents, you can convert the fractions to decimals and compare the decimal values.

Q: What is the difference between a fraction and a fraction with a variable exponent?

A: A fraction with a variable exponent is a fraction where the exponent is a variable, such as $\frac{1}{x^a}$.

Q: Can I compare fractions with variable exponents?

A: Yes, you can compare fractions with variable exponents. However, you need to remember that a variable exponent is equivalent to taking the reciprocal of the fraction.

Q: How do I compare fractions with variable exponents?

A: To compare fractions with variable exponents, you can take the reciprocal of the fraction and compare the resulting fraction.

Q: What is the rule for comparing fractions with variable exponents?

A: The rule for comparing fractions with variable exponents is to take the reciprocal of the fraction and compare the resulting fraction.

Q: Can I compare fractions with decimals and variable exponents?

A: Yes, you can compare fractions with decimals and variable exponents. You can convert the fractions to decimals and compare the decimal values.

Q: How do I compare fractions with decimals and variable exponents?

A: To compare fractions with decimals and variable exponents, you can convert the fractions to decimals and compare the decimal values.

Q: What is the difference between a fraction and a fraction with a complex number?

A: A fraction with a complex number is a fraction where the numerator or denominator is a