Comparing Fractions Calculator
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How to Compare Fractions
Comparing fractions can present a challenge, resembling the task of comparing apples and oranges. Fortunately, several methods exist for comparing one fraction to another.
Method One: Comparing Fractions by Converting to Decimal First
The initial approach to comparing fractions involves converting them into decimal values. Divide the numerator of each fraction by the denominator, and then compare the resulting decimal values.
Alternatively, you can convert the fraction into a form with a denominator of 100, which simplifies dividing the numerator by the denominator.
Here's a tip: Utilize our fraction-to-decimal calculator to obtain the decimal value for your fraction. Additionally, our decimal equivalents chart provides a quick reference for common fractions.
Method Two: Comparing Fractions by Finding the Common Denominator
Another method for comparing fractions is to rewrite all fractions as equivalent fractions with the same denominator. To achieve this, identify the greatest common denominator and adjust the denominators accordingly.
Start by determining the lowest common denominator (also known as the least common denominator), which is the smallest number that divides evenly into each denominator. If you're unsure how to find it, our lowest common denominator calculator can assist you.
For instance, let's find the lowest common denominator of 6 and 9.
6 × 3 = 18
9 × 2 = 18
LCD = 18
Next, convert each fraction into an equivalent fraction with the common denominator. Multiply both the numerator and denominator of each fraction by the same number, ensuring they share the same denominator.
For example, convert 1/6 into a fraction with a denominator of 18.18 ÷ 6 = 33 × 1 = 31/6 = 3/18(alert-success)
Repeat this step for each fraction until they all possess the same denominator.
You may also utilize an equivalent fractions calculator or our equivalent fraction chart to expedite the process of finding equivalents for common fractions.
Finally, compare the numerators to determine which fraction is the largest or smallest. The fraction with the greater numerator is the larger number.
For example, compare 3/18 to 2/18 to ascertain which fraction is larger.Numerator #1 = 3Numerator #2 = 23 > 2Hence, 3/18 is greater than 2/18.(alert-success)
Method Three: Comparing Fractions With the Same Numerator
When fractions share the same numerator, compare them by examining their denominators. When the numerators are identical, the fraction with the smaller denominator is larger.
Stated differently, the greater the denominator, the smaller the number.
For instance, to compare ⅖ and 2/7:
- Both fractions possess the same numerators.
- The first fraction has a denominator of 5, while the second fraction has a denominator of 7.
- 5 < 7, indicating that 2/5 is larger than 2/7.
Method Four: Cross Multiplication
To compare fractions using cross multiplication, begin by aligning the two fractions side by side and multiplying the numerator of the first fraction by the denominator of the second fraction.
For example, let's compare 2/7 and 3/5.2 × 5 = 102/7 is equivalent to 10/35Then, multiply the numerator of the second fraction by the denominator of the first fraction.3 × 7 = 213/5 is equivalent to 21/35Compare the two products. The fraction with the larger product is the greater fraction!Since 21 is larger than 10, we can conclude that 3/5 is greater than 2/7.(alert-success)
In addition to these methods, our fraction calculator also simplifies the process of comparing fractions.
How to Compare Fractions to Decimals and Percentages
To compare a fraction to a decimal or percentage, convert the fraction to either a decimal or percentage, and then make the comparison.
To convert a fraction to a decimal, divide the numerator by the denominator.
To convert a fraction to a percentage, first convert the fraction to a decimal and then multiply the decimal by 100.
You can also convert both the fraction and percentage into decimals and compare the values as decimals. To convert a percentage into a decimal, divide the percentage value by 100.
Comparing numbers, fractions, and percentages is also a crucial step in sorting a set of numbers from least to greatest.
Frequently Asked Questions
Why do we compare fractions?
We compare fractions for various reasons, including:
- Determining which fraction is larger or smaller to make comparisons between quantities or measurements.
- Simplifying fractions and identifying common factors.
- Adding or subtracting fractions.
- Converting fractions to decimals or percentages.
Why is it easier to compare decimals instead of fractions?
Comparing decimals is simpler than comparing fractions because decimals are based on the base-10 numbering system, which provides a more precise representation of a number's magnitude.
By examining the values to the right of the decimal point, comparing decimals becomes straightforward. In contrast, comparing fractions requires finding common denominators and performing additional calculations.
How do you compare fractions with whole numbers?
To compare a fraction to a whole number, convert the whole number into a fraction with the same denominator as the fraction you wish to compare it to.
Alternatively, you can convert the fraction to a decimal and compare the whole number to the resulting value.
How do you compare more than two fractions at a time?
Comparing more than two fractions simultaneously can be achieved through multiple methods, such as:
- Finding a common denominator: Convert the fractions so that they share a common denominator, and then compare the numerators. The fraction with the larger numerator is the largest fraction.
- Using cross-multiplication: Multiply the numerator of the first fraction by the denominator of the second fraction, and vice versa. Repeat this process for all pairs of fractions. The fraction with the larger product is the larger fraction.
- Ordering the fractions: Arrange the fractions from smallest to largest, and then compare the first and last fractions.
Recommended Fraction Resources
- Least Common Denominator Calculator
- Decimal to Fraction Calculator
- Mixed Number Calculator
- Subtracting Fractions Calculator
- Adding Fractions Calculator
