Ordering fractions: Definition, Methods, and Solved Examples
Ordering fractions refers to the process of arranging fractions in a specific order based on their numerical values. Fractions represent parts of a whole, and they consist of a numerator (the number above the fraction line) and a denominator (the number below the fraction line). When comparing fractions, it is often necessary to determine which fraction is larger or smaller.
Ordering fractions is an important skill in various mathematical contexts, such as comparing measurements, finding equivalent fractions. It helps us understand the relative sizes of fractions and make meaningful comparisons in mathematical operations.
In this article, we will discuss the definition of ordering fractions, types of ordering fractions, and methods of ordering fractions. In addition, topic will be explained with the help of example.
Also Read : How Can You Explain and Teach Equations to a Child
Ordering Fractions
Ordering fractions is the process of arranging fractions in ascending or descending order based on their numerical values. To order fractions, we consider their numerical values and compare them using various methods.
One commonly used method is finding a common denominator for all the fractions involved, which allows for easier comparison. By expressing fractions with a common denominator, we can compare their numerators directly.
Types of ordering fraction
There are two main types of ordering fractions:
1. Ascending Order:
This type of ordering involves arranging fractions from the smallest to the largest. It helps determine which fraction has the smallest value and which has the largest value among a given set of fractions.
You can use an ascending order calculator to arrange the fractions from least to greatest instead of using manual and time taking methods.
2. Descending Order:
This type of ordering involves arranging fractions from the largest to the smallest. It helps determine which fraction has the largest value and which has the smallest value among a given set of fractions.
Methods use to order the fractions
There are various methods you can use to compare and order fractions like,
a) Common Denominator Method:
Convert each fraction to an equivalent fraction with the common denominator, and then compare the numerators to determine the order.
The main steps involved in using the common denominator method.
- Finding a Common Denominator
- Converting Fractions to Equivalent Fractions
- Comparing Numerators to Determine Order
b) Decimal or Percent Conversion Method:
Convert each fraction to its decimal or percent equivalent. Compare the resulting decimals or percentages to determine the order.
The name of two main methods uses for solving fractions by using the decimal or percent conversion method.
- Converting Fractions to Decimals or Percentages
- Comparing Decimal or Percentage Values to Determine Order
c) Cross-Multiplication Method:
In cross-Multiplication we multiply the one nominator with the denominator of the other fraction then compare the products to determine the order.
The name of two main methods uses for solving fractions using the cross-Multiplication method.
- Understanding Cross-Multiplication
- Applying Cross-Multiplication to Compare Fractions
d) Simplification Method:
Simplify the fractions by finding their lowest common terms. Compare the simplified fractions to determine the order.
The name most useful method for simplification fractions.
- Finding the Lowest Common Terms
- Simplifying Fractions for Comparison
These methods can be used individually or in combination depending on the specific situation and the fractions involved.
How to order the fractions?
Example 1
Consider the fractions 3/8, 5/6, and 1/4. Solve the fraction by using the denominator method.
Solution:
Given fraction 3/8, 5/6, and 1/4.
we can find the step-by-step solution by using the denominator method.
Step 1:
Find a common denominator.
In this case, the common denominator for 8, 6, and 4 is 24.
We can find a common denominator by using LCM methods like
2 | 8- | 6- | 4 |
2 | 4- | 3- | 2 |
2 | 2- | 3- | 1 |
3 | 1- | 3- | 1 |
| 1- | 1- | 1 |
LCM=2×2×2×3 = 24
Step 2:
Convert fractions to equivalent fractions with the common denominator.
Multiply the required number on both sides to make the required condition.
- 3/8 remains the same.
- 5/6 can be multiplied by 4/4 to get 20/24.
- 1/4 can be multiplied by 6/6 to get 6/24.
Now, the fractions become:
3/8, 20/24, and 6/24.
Step 3:
Compare the numerators.
We compare nominator directly because the denominator is same.
3/8 < 6/24 < 20/24.
Therefore, the fractions in ascending order are:
3/8, 6/24, 20/24.
To summarize, when ordering the fractions 3/8, 5/6, and 1/4 in ascending order using the common denominator method, we get 3/8, 6/24, and 20/24.
Example 2:
Consider the fractions 2/9, 5/6, and 3/8. Solve the ordering fraction and also order them in ascending order.
Solution:
Given
2/9, 5/6, and 3/8
We can find the solution of the given ordering fraction in step.
Step 1:
Common Denominator Method:
To compare fractions using the common denominator method, we need to find a common denominator for all the fractions. In this case, we can use 72 as the common denominator because it is divisible by 9, 6, and 8.
To make the denominator equal we convert fractions into equivalent fractions:
2/9 = (2/9) × (8/8) = 16/72
5/6 = (5/6) × (12/12) = 60/72
3/8 = (3/8) × (9/9) = 27/72
Now, we can compare the numerators
16/72, 27/72, 60/72.
The order from smallest to largest is
16/72, 27/72, 60/72.
Step 2:
Decimal or Percent Conversion Method:
Now we convert the given fractions to decimals for compression.
Decimal | Fraction |
2/9 | 0.222 |
5/6 | 0.833
|
3/8 | 0.375 |
Now, we can compare the order from smallest to largest is 0.222, 0.375, 0.833.
Both methods yield the same result: 16/72, 27/72, 60/72 or 0.222, 0.375, 0.833.
Therefore, the fractions in ascending order from smallest to largest are 2/9, 3/8, and 5/6.
Summary
In this article, we have discussed the definition of ordering fractions, types of ordering fractions, and methods of ordering fractions. Also, topic will be explained with the help of example. After studying this article anyone can explain this topic easily.
FAQ's
It is possible to learn Algebra by yourself. However, you’ll need an online course that incorporates the teacher into all aspects of the syllabus. The most effective way to learn Algebra by yourself is to make sure that every lesson includes audio and video explanations of the examples and the problems for practice.
Any Algebra 1 student who wants to achieve an A grade must master the understanding of these concepts and abilities.
- Arithmetic
- Order of Operations
- Integers
- Working with Variables
- Memorizing Formulas
- The Organizing of problems on paper
The following fundamental ideas during Algebra 1.
- Simplifying
- Equations and Inequalities
- Word Problems
- Functions and graphing
- Linear Equations
- Systems of Equations
- Polynomials and Exponents
- Factoring
- Rational Expressions
- Radicals
- Quadratics
If you’re looking for ways to get through Algebra 1, the key is getting individualized instruction. The past was when this was costly private tutoring. Today, however, it is affordable. Algebra online tuition is now available via videos and guided exercises that include audio explanations at home.
Algebra 1 takes about 6 to 12 months to master. The length of time it takes to learn depends on the student’s math knowledge and ability to learn math naturally and what time they have allocated for assistance each day.
FAQ's
Yes, fractions with negative numerators or denominators can be ordered using the same methods mentioned earlier. The negative sign only affects the sign of the resulting decimal or percentage value, but the ordering process remains the same.
Real-life application of ordering fraction are:
- comparing sizes or quantities
- understanding proportions in recipes
- solving word problems involving fractions
- making informed decisions
Working through exercises, solving real-life problems. Also, Online resources, textbooks, and math practice websites often provide interactive exercises and worksheets for practice.
