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Comparing Fractions Calculator
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Comparing Fractions Calculator
This calculator compares two fractions and finds out which fraction is larger, which is smaller, or if both are equal. In addition, it is also useful for comparing decimals, integers, and improper fractions, whether positive or negative.
Comparing Fractions
It would be helpful to learn about fractions before discussing the comparison of two fractions. Wikipedia says, “Fractions represent the part of a whole”. The top number (numerator) represents how many parts we have, while the bottom number (denominator) represents how many parts make up a whole.
Comparing fractions is determining which fraction is larger or smaller, or both are equal in value. For instance, 1/3 is greater than 1/6, 1/7 is smaller than 2/3. The equality or inequality symbols can be used to compare the fractions.
How to Compare Fractions?
When fractions have an equal denominator, compare their numerators. The fraction containing the biggest numerator is greater than the other.
For example, 4/6 is greater than 1/6 because both fractions have the same denominator but numerator 4 is larger than 1.
In cases where fractions have equal numerators but different denominators, the fraction with the greater denominators is smaller than the other fraction.
For instance, fraction 7/9 is greater than 7/11.
Comparing Unlike Fractions
To compare unlike fractions, follow the given steps.
Step 1: Calculate the least common multiple (LCM) of the denominator of both fractions.
Step 2: Convert the given fraction into an equivalent fraction such that their denominators are equal.
Step 3: Next, compare the numerators of obtained equivalent fractions. The fraction with the largest numerator (top number) is greater.
5 | 5, 7 |
7 | 1, 7 |
| 1, 1 |
Let’s consider an example for a better understanding of the above step.
Example:
Compare the fractions 2/5 and 4/7.
Solution
Step 1: Find the least common multiple of 5 and 7.
LCM of 5 & 7 = 5 × 7 = 35
Step 2: Multiply the numerator and denominator by 7 to Convert 2/5 to an equivalent fraction with denominator 35.
(2/5) x (7/7) = 14/35
Similarly, multiply the numerator and denominator by 5 to Convert 4/7 to an equivalent fraction with denominator 35.
(4/7) x (5/5) = 20/35
Step 3: Now, Compare the numerators of the equivalent fractions. 20 is greater than 14, so:
20/35 > 14/35 ⟺ 4/7 > 2/5
Thus, 4/7 is larger than 2/5.
Comparing Fractions with the Decimal method
The first step is to divide the numerator by the denominator for each fraction to convert them into decimal form. Identify the whole part of the decimals. The fraction with the greater whole number part is larger. If the whole parts are the same, compare the decimal parts of the decimal numbers.
The corresponding fraction is larger if one decimal part is greater than the other.
Example:
Compare 3/8 and 7/5 by decimal method.
Solution
3/8 = 0.375 (By dividing 3 by 8)
7/12 ≈ 0.583 (By dividing 7 by 12)
0.583 is greater than 0.375, so we can conclude that 7/12 > 3/8.
Comparing Fractions using Cross-multiplication method
This method involves the multiplication of the numerator of one fraction with the denominator of the other fraction and vice versa. A greater product indicates a larger fraction.
For example, to compare 3/4 and 5/6:
Fraction Comparison Table
Here is a table with more values comparing fractions.
Fractions | Comparisons |
1/2 and 1/3 | 1/2 > 1/3 |
3/4 and 2/5 | 3/4 > 2/5 |
2/3 and 3/4 | 2/3 < 3/4 |
5/8 and 3/7 | 5/8 > 3/7 |
8/9 and 8/9 | 8/9 = 8/9 |
4/9 and 5/11 | 4/9 < 5/11 |
7/12 and 5/9 | 7/12 > 5/9 |