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Comparing rational numbers involves determining which number is greater, lesser, or if they are equal.

• Comparing rational numbers
• Formula
• Solved Examples
• FAQs

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## Comparing Rational Numbers

Comparing rational numbers involves determining which number is greater, lesser, or if they are equal. Here’s how to compare rational numbers:

Find a common denominator for the two numbers.

Convert each fraction to its equivalent fraction with the common denominator.

Compare the numerators of the equivalent fractions. The fraction with the greater numerator is the greater fraction.

If the numerators are equal, compare the denominators. The fraction with the lesser denominator is the greater fraction.

Here’s an example:

Compare 3/4 and 5/6 Make the denominators equal by finding the LCM of the denominators. Then make the given fractions equivalent with LCM as the common denominator

Convert each fraction to an equivalent fraction with the denominator of 12:

3/4 = 9/12 and 5/6 = 10/12

Compare the numerators of the equivalent fractions. 10/12 is greater than 9/12.

Therefore, 5/6 is greater than 3/4.

## Formulae for Comparing Rational Numbers

There is no specific formula for comparing rational numbers, but there are some steps that can be followed to compare two fractions.

Alternatively, you can cross-multiply the fractions to compare them:

Cross-multiply the fractions by multiplying the numerator of one fraction with the denominator of the other fraction.

Compare the resulting products. The fraction with the greater product is the greater fraction.

Whichever method you choose, it’s important to simplify the fractions before comparing them to get the most accurate comparison.

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## Solved Examples

Here are some examples of comparing rational numbers:

Example 1: Compare 2/3 and 3/4

Solution: Convert each fraction to an equivalent fraction with the denominator of 12:

2/3 = 8/12 and 3/4 = 9/12

Compare the numerators of the equivalent fractions.9 is greater than 8 and thus 9/12 is greater than 8/12.

Therefore, 3/4 is greater than 2/3.

Example 2: Compare 1/2 and 5/8

Solution: The common denominator is 8.

Convert each fraction to an equivalent fraction with the denominator of 8.

1/2 = 4/8 and 5/8 is already in the required form.

Compare the numerators of the equivalent fractions. 5/8 is greater than 4/8.

Therefore, 5/8 is greater than 1/2.

Example 3: Compare -2/5 and -3/7

Solution: The common denominator is 35.

Convert each fraction to an equivalent fraction with the denominator of 35:

-2/5 = -14/35 and -3/7 = -15/35

Compare the numerators of the equivalent fractions.The integer -14 is greater than integer -15 -14/35 is greater than -15/35.

Therefore, -2/5 is greater than -3/7.

Two negative rational numbers are compared by disregarding their negative signs and then reversing the order of inequality after making their denominators same

## FAQS

##### How do I compare rational numbers?

To compare rational numbers, you can convert them to a common denominator and then compare their numerators. If the numerators are equal, you can compare the denominators to determine which number is greater or lesser.

##### Can I compare rational numbers with different denominators directly?

Yes, you can compare rational numbers with different denominators directly by finding a common denominator for both numbers. Once the numbers have the same denominator, you can compare their numerators.

##### Is it possible for two rational numbers to be equal even if their numerators and denominators are different?

Yes, it is possible for two rational numbers to be equal even if their numerators and denominators are different. For example, 1/2 is equal to 2/4, even though the numerators and denominators differ.

##### What should I do if the numerators of two rational numbers are equal, but the denominators are different?

If the numerators of two rational numbers are equal, but the denominators are different, the number with the smaller denominator is considered greater. The greater the denominator, the smaller the fraction.

##### Can I use decimal representations to compare rational numbers?

Yes, decimal representations can be used to compare rational numbers. You can convert both rational numbers to decimals and then compare them directly. However, keep in mind that decimal representations may have rounding errors, so they might not always provide an exact comparison. Gloria Mathew writes on math topics for K-12. A trained writer and communicator, she makes math accessible and understandable to students at all levels. Her ability to explain complex math concepts with easy to understand examples helps students master math. LinkedIn

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