Comparing and Ordering Fractions (Grade 5)

Q: How do I compare fractions with different denominators?

Either find the LCM of the denominators and convert to equivalent fractions, or use cross-multiplication. For a/b and c/d, compute a×d and c×b — whichever product is larger corresponds to the larger fraction.

Q: What is the cross-multiplication method?

To compare a/b and c/d: multiply a × d and c × b. If a × d > c × b, then a/b > c/d. If they are equal, the fractions are equal. Example: 3/4 vs 5/7: 3×7=21, 5×4=20, so 3/4 > 5/7.

Class 5Fractions (Grade 5)

In Class 5, students learn to compare and order fractions that have different numerators and different denominators. Comparing fractions tells us which fraction is larger or smaller, and ordering means arranging fractions from smallest to largest (ascending) or largest to smallest (descending).

There are several methods to compare fractions: making the denominators the same (using LCM), cross-multiplication, and converting to decimals. Each method has its advantages depending on the fractions involved.

What is Comparing and Ordering Fractions - Class 5 Maths (Fractions)?

Comparing fractions means determining which fraction is greater, smaller, or if they are equal.

Methods for comparing fractions:

Same denominator: Compare the numerators directly. The fraction with the larger numerator is greater.
Same numerator: The fraction with the smaller denominator is greater (each part is bigger).
Unlike fractions (different numerators and denominators): Use one of these methods:
1. Find LCM of denominators and make equivalent fractions.
2. Cross-multiplication method.
3. Convert fractions to decimals and compare.

Comparing and Ordering Fractions (Grade 5) Formula

Cross-Multiplication: To compare a/b and c/d, calculate a × d and c × b.
If a × d > c × b, then a/b > c/d

Solved Examples

Example 1: Example 1: Same denominator

Problem: Compare 5/9 and 7/9.

Solution:

Both have denominator 9. Compare numerators: 5 < 7.

Answer: 5/9 < 7/9

Example 2: Example 2: Same numerator

Problem: Compare 3/5 and 3/8.

Solution:

Both have numerator 3. The fraction with the smaller denominator is greater (larger pieces).

5 < 8, so 3/5 > 3/8.

Answer: 3/5 > 3/8

Example 3: Example 3: Using LCM method

Problem: Compare 2/3 and 3/4.

Solution:

Step 1: LCM of 3 and 4 = 12

Step 2: Convert: 2/3 = 8/12 and 3/4 = 9/12

Step 3: Compare numerators: 8 < 9

Answer: 2/3 < 3/4

Example 4: Example 4: Using cross-multiplication

Problem: Compare 5/7 and 4/5.

Solution:

Step 1: Cross-multiply: 5 × 5 = 25 and 4 × 7 = 28

Step 2: Compare: 25 < 28

Answer: 5/7 < 4/5

Example 5: Example 5: Ordering three fractions in ascending order

Problem: Arrange in ascending order: 2/3, 3/5, 5/6.

Solution:

Step 1: LCM of 3, 5, 6 = 30

Step 2: Convert all to denominator 30:

2/3 = 20/30
3/5 = 18/30
5/6 = 25/30

Step 3: Order by numerators: 18 < 20 < 25

Answer: 3/5 < 2/3 < 5/6

Example 6: Example 6: Ordering in descending order

Problem: Arrange in descending order: 1/2, 3/7, 4/9.

Solution:

Step 1: LCM of 2, 7, 9 = 126

Step 2: Convert:

1/2 = 63/126
3/7 = 54/126
4/9 = 56/126

Step 3: Descending: 63 > 56 > 54

Answer: 1/2 > 4/9 > 3/7

Example 7: Example 7: Comparing mixed fractions

Problem: Compare 2 3/4 and 2 5/7.

Solution:

Step 1: Whole parts are equal (both 2), so compare the fraction parts: 3/4 and 5/7.

Step 2: Cross-multiply: 3 × 7 = 21 and 5 × 4 = 20

Step 3: 21 > 20, so 3/4 > 5/7

Answer: 2 3/4 > 2 5/7

Example 8: Example 8: Word problem — Race performance

Problem: Dev ran 3/4 of the track, Arjun ran 5/6 of the track, and Priya ran 2/3 of the track. Who ran the most?

Solution:

LCM of 4, 6, 3 = 12

Dev: 3/4 = 9/12
Arjun: 5/6 = 10/12
Priya: 2/3 = 8/12

10/12 > 9/12 > 8/12

Answer: Arjun ran the most (5/6 of the track).

Example 9: Example 9: Comparing using decimal conversion

Problem: Compare 3/8 and 2/5 using decimal conversion.

Solution:

3/8 = 3 ÷ 8 = 0.375

2/5 = 2 ÷ 5 = 0.4

0.375 < 0.4

Answer: 3/8 < 2/5

Key Points to Remember

Same denominator: Larger numerator = larger fraction.
Same numerator: Smaller denominator = larger fraction.
LCM method: Convert to equivalent fractions with the same denominator, then compare numerators.
Cross-multiplication: Compare a/b and c/d by comparing a×d and c×b.
For mixed fractions: Compare whole parts first; if equal, compare the fraction parts.
Ascending order means smallest to largest; descending means largest to smallest.
Converting to decimals is an alternative method for comparing any fractions.

Practice Problems

Compare 4/7 and 5/9 using cross-multiplication.
Arrange in ascending order: 1/3, 2/5, 3/10.
Compare 3 1/2 and 3 4/9.
Arrange in descending order: 5/8, 7/12, 3/4.
Ria ate 2/5 of a cake and Neha ate 3/8 of the same cake. Who ate more?
Arrange in ascending order: 7/10, 3/4, 4/5, 1/2.
Compare 11/15 and 7/10 using the LCM method.
Which is greater: 5/6 or 7/9? Verify using decimals.

Frequently Asked Questions

Q1. How do I compare fractions with different denominators?

Either find the LCM of the denominators and convert to equivalent fractions, or use cross-multiplication. For a/b and c/d, compute a×d and c×b — whichever product is larger corresponds to the larger fraction.

Q2. What is the cross-multiplication method?

To compare a/b and c/d: multiply a × d and c × b. If a × d > c × b, then a/b > c/d. If they are equal, the fractions are equal. Example: 3/4 vs 5/7: 3×7=21, 5×4=20, so 3/4 > 5/7.

Q3. Why does the fraction with a smaller denominator have bigger pieces?

The denominator tells how many equal parts the whole is divided into. Fewer parts means each part is bigger. 1/3 means dividing into 3 parts (each is big), while 1/8 means 8 parts (each is small). So 1/3 > 1/8.

Q4. Can I always convert fractions to decimals to compare?

Yes, but some fractions produce repeating decimals (like 1/3 = 0.333...), making comparison trickier. The LCM and cross-multiplication methods give exact comparisons without dealing with repeating decimals.

Q5. How do I order more than two fractions?

Find the LCM of all the denominators, convert each fraction to an equivalent fraction with that LCM as the denominator, then arrange by comparing the numerators.

Q6. What if the mixed fractions have different whole parts?

The mixed fraction with the larger whole part is greater. You only need to compare the fraction parts when the whole parts are the same. Example: 3 1/4 > 2 7/8 because 3 > 2.

Q7. Is 1/2 always greater than 1/3?

Yes. When numerators are the same, the fraction with the smaller denominator is greater. Since 2 < 3, we have 1/2 > 1/3. You can verify: 1/2 = 0.5 and 1/3 = 0.333...

Q8. What does ascending and descending order mean for fractions?

Ascending order means arranging from smallest to largest. Descending order means arranging from largest to smallest. First compare the fractions, then list them in the required order.

Comparing and Ordering Fractions (Grade 5)

What is Comparing and Ordering Fractions - Class 5 Maths (Fractions)?

Comparing and Ordering Fractions (Grade 5) Formula

Solved Examples

Example 1: Example 1: Same denominator

Example 2: Example 2: Same numerator

Example 3: Example 3: Using LCM method

Example 4: Example 4: Using cross-multiplication

Example 5: Example 5: Ordering three fractions in ascending order

Example 6: Example 6: Ordering in descending order

Example 7: Example 7: Comparing mixed fractions

Example 8: Example 8: Word problem — Race performance

Example 9: Example 9: Comparing using decimal conversion

Key Points to Remember

Practice Problems

Frequently Asked Questions

Q1. How do I compare fractions with different denominators?

Q2. What is the cross-multiplication method?

Q3. Why does the fraction with a smaller denominator have bigger pieces?

Q4. Can I always convert fractions to decimals to compare?

Q5. How do I order more than two fractions?

Q6. What if the mixed fractions have different whole parts?

Q7. Is 1/2 always greater than 1/3?

Q8. What does ascending and descending order mean for fractions?

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