Ordering Fractions: Videos & Practice Problems

Insert , $>$, or $=$ to form a true statement.
$\frac{5}{18}?\frac{7}{10}$

• A.
• B. $\frac{5}{18}>\frac{7}{10}$
• C. $\frac{5}{18}=\frac{7}{10}$

Answer: (A)

Insert , $>$, or $=$ to form a true statement.
$-\frac{4}{9}?-\frac{2}{7}$

• A.
• B. $-\frac{4}{9}>-\frac{2}{7}$
• C. $-\frac{4}{9}=-\frac{2}{7}$

Answer: (A)

Insert , $>$, or $=$ to form a true statement.
$-\frac{5}{12}?-\frac{30}{72}$

• A.
• B. $-\frac{5}{12}>-\frac{30}{72}$
• C. $-\frac{5}{12}=-\frac{30}{72}$

Answer: (C)

Here's what students ask on this topic:

How do you compare fractions with different denominators?

To compare fractions with different denominators, the most reliable method is to find a common denominator, preferably the least common denominator (LCD). This involves rewriting each fraction as an equivalent fraction with the same denominator. You do this by multiplying both the numerator and denominator of each fraction by the same number so that the denominators match. Once the denominators are the same, you simply compare the numerators. For example, to compare $\frac{3}{4}$ and $\frac{2}{5}$, find the LCD of 4 and 5, which is 20. Rewrite the fractions as $\frac{15}{20}$ and $\frac{8}{20}$. Since 15 > 8, $\frac{3}{4}$ is greater than $\frac{2}{5}$. This method ensures accurate comparison regardless of the original denominators.

What is the least common denominator (LCD) and why is it important in ordering fractions?

The least common denominator (LCD) is the smallest number that is a multiple of the denominators of two or more fractions. It is important because it allows you to rewrite fractions with different denominators into equivalent fractions with the same denominator, making comparison straightforward. For example, to compare $\frac{1}{3}$ and $\frac{1}{4}$, the LCD of 3 and 4 is 12. Rewriting the fractions as $\frac{4}{12}$ and $\frac{3}{12}$ allows you to compare numerators directly. Since 4 > 3, $\frac{1}{3}$ is greater than $\frac{1}{4}$. Using the LCD simplifies the process and avoids errors that can occur when comparing fractions with unlike denominators.

How do you order negative fractions correctly?

Ordering negative fractions requires careful attention because the more negative a number is, the smaller its value. After finding a common denominator and rewriting the fractions as equivalent fractions, compare the numerators as usual. However, remember that a fraction with a larger numerator (in absolute value) is actually smaller if the fraction is negative. For example, consider $\frac{-3}{5}$ and $\frac{-2}{5}$. Both have the same denominator, so compare numerators: -3 and -2. Since -3 < -2, $\frac{-3}{5}$ is less than $\frac{-2}{5}$. Always remember that on the number line, values further to the left are smaller, even if their numerators look larger in absolute terms.

What are the steps to rewrite fractions with a common denominator?

To rewrite fractions with a common denominator, follow these steps: First, find the least common denominator (LCD) of the fractions' denominators. Second, determine the factor needed to multiply each denominator to reach the LCD. Third, multiply both the numerator and denominator of each fraction by this factor to create equivalent fractions with the LCD as the denominator. For example, to rewrite $\frac{2}{3}$ and $\frac{3}{4}$ with a common denominator, find the LCD of 3 and 4, which is 12. Multiply the first fraction by $\frac{4}{4}$ to get $\frac{8}{12}$, and the second by $\frac{3}{3}$ to get $\frac{9}{12}$. Now both fractions have the same denominator and can be compared easily.

How do inequality symbols relate to ordering fractions?

Inequality symbols such as $<$, $>$, and $=$ are used to express the relationship between fractions after they have been compared. Once fractions are rewritten with a common denominator, you compare their numerators. If the numerator of the first fraction is less than the second, you use the less than symbol ($<$). If it is greater, use the greater than symbol ($>$). If the numerators are equal, the fractions are equal, and you use the equals sign ($=$). For example, after rewriting $\frac{1}{2}$ and $\frac{2}{3}$ with a common denominator, you might find $\frac{3}{6}$ and $\frac{4}{6}$. Since 3 < 4, you write $\frac{1}{2}$ $<$ $\frac{2}{3}$. This notation clearly communicates the order of the fractions.