Comparing Fractions

Question 1: What is meant by comparing fractions?

Answer:

“Comparison of fractions” refers to the determination of the larger and the smaller fraction within a given set of fractions. We can determine the greater, smaller, or equivalent fractions by comparing any two fractions. Based on the numerator and the denominator and the kind of fractions given there are different methods and rules to compare fractions.

Question 2: What is the rule for comparing fractions that have the same denominator?

Answer:

If the given set of fractions has the same denominator, then the fraction that has a smaller numerator is the smaller fraction, and the fraction that has a larger numerator is the larger fraction. If the numerators are equal, then the fractions are considered to be equivalent fractions. For example, if we have to compare 2/3 and 5/3, we just need to check their numerators and compare them. Since 2 < 5, so 2/3 < 5/3.

Question 3: What is the Rule when Comparing Fractions with the Same Numerator?

Answer:

If the given set of fractions has the same numerator, then the fraction that has a smaller denominator is the larger fraction, and the fraction that has a larger denominator is the smaller fraction. For example, if we have to compare 4/3 and 4/9, we just need to check their denominators and compare them. Now, out of 4/3 and 4/9, the fraction with the smaller denominator is 4/3. Hence, 4/3 is the larger fraction of the given fractions.

Question 4: What are Equivalent Fractions?

Answer:

Equivalent fractions are those that have distinct numerators and denominators but have the same values when simplified. For example, 3/12 and 5/20 are equivalent fractions as both of them are equal to 1/4 when simplified.

Question 5: How to Compare Fractions with Different Denominators?

Answer:

To 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. For example, let us compare 1/4 and 2/3.

Step 1: First, observe the denominators of the given fractions, i.e., 1/4 and 2/3. Since the denominators are different make them equal by finding the LCM of 4 and 3. LCM(4,3) = 12.

Step 2: Now, let us convert the given fraction in such a way that they have the same denominators. So, multiply the first fraction with 3/3, i.e., 1/4 × 3/3 = 4/12.

Step 3: Similarly, multiply the second fraction with 4/4, i.e., 2/3 × 4/4 = 8/12. Thus, the first fraction becomes 4/12 and the other becomes 8/12.

Step 4: Compare the obtained new fractions, i.e., 4/12 and 8/12. As the denominators are the same, we will compare the numerators. We can observe that 4 < 8.

Step 5: The fraction that has a large numerator is the larger fraction. So, 8/12 > 4/12. So, 1/4 > 2/3.

“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.