Select The Best Answer For The Question.John Had $\frac{2}{3}$ Of His Homework Complete, Sarah Had $\frac{5}{10}$, Alex Had $\frac{7}{8}$, And Michelle Had $\frac{1}{2}$. Who Completed The Most Of The Homework

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**Select the Best Answer for the Question: Who Completed the Most Homework?**

In this article, we will be discussing a question that involves comparing fractions to determine who completed the most homework. We will go through the steps to solve this problem and provide a clear explanation of the solution.

The problem states that John had 23\frac{2}{3} of his homework complete, Sarah had 510\frac{5}{10}, Alex had 78\frac{7}{8}, and Michelle had 12\frac{1}{2}. We need to determine who completed the most homework.

Step 1: Simplify the Fractions

To compare the fractions, we need to simplify them. We can simplify a fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).

  • John's fraction: 23\frac{2}{3}
  • Sarah's fraction: 510=12\frac{5}{10} = \frac{1}{2}
  • Alex's fraction: 78\frac{7}{8}
  • Michelle's fraction: 12\frac{1}{2}

Step 2: Compare the Fractions

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

  • John's fraction: 23\frac{2}{3}
  • Sarah's fraction: 12\frac{1}{2}
  • Alex's fraction: 78\frac{7}{8}
  • Michelle's fraction: 12\frac{1}{2}

To compare these fractions, we can convert them to equivalent decimals.

  • John's fraction: 23≈0.67\frac{2}{3} \approx 0.67
  • Sarah's fraction: 12=0.5\frac{1}{2} = 0.5
  • Alex's fraction: 78=0.875\frac{7}{8} = 0.875
  • Michelle's fraction: 12=0.5\frac{1}{2} = 0.5

Based on the comparison of the fractions, we can see that Alex completed the most homework with a fraction of 78\frac{7}{8}, which is equivalent to 0.875.

Q: How do I simplify a fraction?

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

Q: How do I compare fractions?

A: To compare fractions, you can convert them to equivalent decimals or find a common denominator.

Q: What is the greatest common divisor (GCD)?

A: The greatest common divisor (GCD) is the largest number that divides both the numerator and the denominator of a fraction.

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.

Q: What is the equivalent decimal of a fraction?

A: The equivalent decimal of a fraction is a decimal number that represents the same value as the fraction.

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: How do I add fractions with different denominators?

A: To add fractions with different denominators, you need to find a common denominator and then add the fractions.

Q: How do I subtract fractions with different denominators?

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

Q: How do I multiply fractions?

A: To multiply fractions, you need to multiply the numerators and the denominators separately.

Q: How do I divide fractions?

A: To divide fractions, you need to invert the second fraction and then multiply.

In conclusion, comparing fractions is an important skill in mathematics that can be used to solve a variety of problems. By simplifying fractions, converting them to decimals, and finding a common denominator, we can compare fractions and determine who completed the most homework.