“Comparison of fractions” refers to the determination of the larger and the smaller fraction within a given set of fractions. While comparing fractions, a set of rules is followed to compare the numerator and denominator of a fraction, where the numerator is the number above the fractional bar and the denominator is the number below the fractional bar. We can determine the greater and smaller fractions by comparing any two fractions. Fractions can be compared even if they have different numerators and denominators. To understand the concept better, let’s go over the various ways to compare fractions. Show
FractionBefore going through the concept of comparing two fractions, let us recall what a fraction is. A fraction is defined as a part of a whole that consists of two parts: the numerator and the denominator, where the numerator is the number above the fractional bar and the denominator is the number below the fractional bar. How to compare two fractions in numbers?In order to determine which of the two fractions is larger or smaller, one has to compare them. Based on the numerator and the denominator and the kind of fractions given there are different methods and rules to compare fractions. They are:
Comparing Fractions with Same DenominatorsIt is easy to find the greater or smaller fraction when the fractions have the same denominators. When comparing fractions, check whether the denominators are the same or not. If the denominators are equal, then the fraction with the bigger numerators is the bigger fraction. The fractions are equal if the numerators and denominators of both fractions are equal. Example: Compare: 5/12 and 17/12. Solution:
Comparing Fractions With Unlike DenominatorsTo compare fractions with unlike denominators, we have to convert them to like denominators for which we have to find the Least Common Multiple (LCM) of the denominators. As the denominators are made equal, we can compare the fractions with ease. Example: Compare: 1/4 and 2/3. Solution:
Note: Make a note that if the given fractions have the same numerators and different denominators, then we can compare them easily by looking at their denominators. The fraction that has a smaller denominator has a greater value, while the fraction that has a larger denominator has a smaller value. For example 6/2 > 6/5. Comparing Fractions using the Decimal MethodIn this method, one can compare fractions by finding the decimal values of the fractions and comparing them. For this, divide the numerator by the denominator, and thus the fraction is converted into a decimal. Finally, compare their decimal values. Let us understand this by going through an example. Example: Compare 3/5 and 2/4. Solution:
Comparing Fractions using VisualizationCompared to any other method, comparing fractions using visualization is easier. Make two boxes such that the length and width of both are the same. The figure is given below shows models A and B, which represent two fractions. Then divide each model into equal parts equivalent to their respective denominators. Now, we can easily find that 2/6 < 2/4, as the 2/4 covers a larger shaded area compared to the 2/6. The smaller fraction occupies a lesser area of the same whole, while the larger fraction occupies a larger area of the same whole. Comparing Fractions using the Cross Multiplication methodTo compare fractions using cross multiplication, we have to multiply the numerator of one fraction with the other fraction’s denominator. Let us understand this by going through an example. Example: Compare 3/8 and 4/5.
Solved Examples on Comparison of FractionsExample 1: Which of the following fractions is larger: 6/11 or 8/15? Solution:
Example 2: Which of the given fractions is smaller: 13/85 or 21/85? Solution:
Example 3: Compare the fractions 4/25 and 33/100. Solution:
Example 4: Mrunal was asked to prove that the given fractions are equal: 30/90 and 25/75. Can you prove the given statement using the LCM method? Solution:
Example 5: Which of the following fractions is larger: 27/41 or 27/67? Solution:
FAQs on Comparing FractionsQuestion 1: What is meant by comparing fractions? Answer:
Question 2: What is the rule for comparing fractions that have the same denominator? Answer:
Question 3: What is the Rule when Comparing Fractions with the Same Numerator? Answer:
Question 4: What are Equivalent Fractions? Answer:
Question 5: How to Compare Fractions with Different Denominators? Answer:
How do you compare fractions with different numerator and different denominators?How to Compare Fractions with Unlike Denominators. Find the first number to appear in the times table of every denominator. This is the common denominator.. Write each fraction as an equivalent fraction that has this common denominator.. The larger the numerator of these fractions, the larger the fraction.. What is the rule for comparing fractions?When comparing fractions, check whether the denominators are the same or not. If the denominators are equal, then the fraction with the bigger numerators is the bigger fraction. The fractions are equal if the numerators and denominators of both fractions are equal.
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