Choose The Answer That Shows The Fractions In Order From Least To Greatest.${ \begin{array}{|c|c|c|} \hline \frac{7}{7} & \frac{7}{8} & \frac{7}{10} \ \hline \end{array} } A . A. A . [ \begin{array}{|c|c|c|} \hline \frac{7}{8} & \frac{7}{7} &

Mar 10, 2025 by ADMIN 244 views

**Comparing Fractions: Ordering from Least to Greatest**

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Understanding the Basics of Fractions

Fractions are a way to represent a part of a whole. They consist of a numerator (the top number) and a denominator (the bottom number). The numerator tells us how many equal parts we have, while the denominator tells us how many parts the whole is divided into. When comparing fractions, we need to consider both the numerator and the denominator.

Comparing Fractions with the Same Numerator

When the numerators are the same, the fraction with the smaller denominator is the larger fraction. This is because a smaller denominator means each part is larger, so we have more of the whole. For example, $\frac{3}{4}$ is greater than $\frac{3}{5}$ because the denominator of $\frac{3}{4}$ is smaller.

Comparing Fractions with the Same Denominator

When the denominators are the same, the fraction with the larger numerator is the larger fraction. This is because a larger numerator means we have more of the whole. For example, $\frac{2}{3}$ is greater than $\frac{1}{3}$ because the numerator of $\frac{2}{3}$ is larger.

Comparing Fractions with Different Numerators and Denominators

When the numerators and denominators are different, we need to find a common denominator to compare the fractions. The common denominator is the smallest number that both denominators can divide into evenly. Once we have a common denominator, we can compare the fractions by looking at the numerators.

Ordering Fractions from Least to Greatest

To order fractions from least to greatest, we need to compare each fraction to the others. We can start by comparing the first two fractions, then the second and third fractions, and so on. If we find that one fraction is greater than another, we can eliminate the smaller fraction from the comparison.

Comparing the Given Fractions

Let's compare the given fractions: $\frac{7}{7}$ , $\frac{7}{8}$ , and $\frac{7}{10}$ . We can start by comparing the first two fractions, $\frac{7}{7}$ and $\frac{7}{8}$ . Since the numerator is the same, the fraction with the smaller denominator is the larger fraction. Therefore, $\frac{7}{7}$ is greater than $\frac{7}{8}$ .

Comparing the Remaining Fractions

Next, we can compare the remaining fractions, $\frac{7}{8}$ and $\frac{7}{10}$ . Since the numerator is the same, the fraction with the smaller denominator is the larger fraction. Therefore, $\frac{7}{8}$ is greater than $\frac{7}{10}$ .

Ordering the Fractions from Least to Greatest

Based on our comparisons, we can order the fractions from least to greatest: $\frac{7}{10}$ , $\frac{7}{8}$ , and $\frac{7}{7}$ .

Conclusion

Comparing fractions requires us to consider both the numerator and the denominator. When the numerators are the same, the fraction with the smaller denominator is the larger fraction. When the denominators are the same, the fraction with the larger numerator is the larger fraction. By following these rules, we can order fractions from least to greatest.

Final Answer

The correct order of the fractions from least to greatest is:

$\frac{7}{10}$
$\frac{7}{8}$
$\frac{7}{7}$

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Q: What is the first step in comparing fractions?

A: The first step in comparing fractions is to determine if the fractions have the same numerator or the same denominator. If the numerators are the same, we can compare the denominators. If the denominators are the same, we can compare the numerators.

Q: How do I compare fractions with the same numerator?

A: When the numerators are the same, the fraction with the smaller denominator is the larger fraction. This is because a smaller denominator means each part is larger, so we have more of the whole.

Q: How do I compare fractions with the same denominator?

A: When the denominators are the same, the fraction with the larger numerator is the larger fraction. This is because a larger numerator means we have more of the whole.

Q: What is a common denominator?

A: A common denominator is the smallest number that both denominators can divide into evenly. We need to find a common denominator to compare fractions with different numerators and denominators.

Q: How do I find a common denominator?

A: To find a common denominator, we can list the multiples of each denominator and find the smallest number that appears in both lists. Alternatively, we can use the least common multiple (LCM) of the two denominators.

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

A: The least common multiple (LCM) of two numbers is the smallest number that both numbers can divide into evenly. We can find the LCM by listing the multiples of each number and finding the smallest number that appears in both lists.

Q: How do I compare fractions with different numerators and denominators?

A: To compare fractions with different numerators and denominators, we need to find a common denominator. Once we have a common denominator, we can compare the fractions by looking at the numerators.

Q: Can I compare fractions with different signs?

A: Yes, we can compare fractions with different signs. When comparing fractions with different signs, we need to consider the sign of the numerator and the denominator. A positive numerator and a negative denominator make the fraction negative, while a negative numerator and a positive denominator make the fraction negative.

Q: How do I order fractions from least to greatest?

A: To order fractions from least to greatest, we need to compare each fraction to the others. We can start by comparing the first two fractions, then the second and third fractions, and so on. If we find that one fraction is greater than another, we can eliminate the smaller fraction from the comparison.

Q: Can I use a calculator to compare fractions?

A: Yes, we can use a calculator to compare fractions. Many calculators have a fraction mode that allows us to enter fractions and compare them. Alternatively, we can use a calculator to find the decimal equivalent of each fraction and compare the decimals.

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

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

Comparing fractions with different signs without considering the sign of the numerator and the denominator.
Not finding a common denominator when comparing fractions with different numerators and denominators.
Not considering the sign of the numerator and the denominator when comparing fractions with different signs.
Not ordering fractions from least to greatest by comparing each fraction to the others.

Q: How can I practice comparing fractions?

A: We can practice comparing fractions by working through examples and exercises. We can also use online resources and calculators to help us compare fractions. Additionally, we can practice ordering fractions from least to greatest by comparing each fraction to the others.