Common Fraction: Definitions and Examples

Introduction

Common Fractions: Understanding the Basics

Fractions are a fundamental part of mathematics that are used in everyday life. A fraction represents a part of a whole, and is written as two numbers separated by a slash (/). The number on top of the slash is called the numerator, and represents the part of the whole that we are interested in. The number below the slash is called the denominator, and represents the whole itself. In this article, we will explore the basics of common fractions, their properties, and how to perform basic operations on them.

Properties of Fractions

Fractions have several properties that are important to understand. Here are some of the key properties:

Fractions can be equivalent: Two fractions are equivalent if they represent the same part of a whole. For example, 1/2 and 2/4 are equivalent fractions, because they both represent half of a whole.
Fractions can be simplified: A fraction can be simplified by dividing both the numerator and the denominator by the same number. For example, 4/8 can be simplified to 1/2 by dividing both the numerator and the denominator by 4.
Fractions can be added or subtracted: To add or subtract fractions, they must have a common denominator. This means that the denominator must be the same for both fractions. Once the fractions have a common denominator, the numerators can be added or subtracted. For example, to add 1/4 and 1/3, we need to find a common denominator, which is 12. We can then rewrite 1/4 as 3/12 and 1/3 as 4/12. Adding these two fractions gives us 7/12.
Fractions can be multiplied or divided: To multiply or divide fractions, we simply multiply or divide the numerators and denominators. For example, to multiply 1/2 by 2/3, we multiply the numerators (1 x 2 = 2) and the denominators (2 x 3 = 6), giving us 2/6, which can be simplified to 1/3. To divide 1/2 by 1/3, we multiply the first fraction by the reciprocal of the second fraction (the reciprocal of 1/3 is 3/1), giving us 1/2 x 3/1 = 3/2.

Common Fractions

Common fractions are fractions that are used frequently in everyday life. Here are some examples of common fractions:

1/2: This fraction represents one-half of a whole. It is commonly used to represent half of a pizza, half of a cake, or half of a sandwich.
1/4: This fraction represents one-quarter of a whole. It is commonly used to represent a quarter of a pie, a quarter of a sheet of paper, or a quarter of an hour.
3/4: This fraction represents three-quarters of a whole. It is commonly used to represent three-quarters of a cup, three-quarters of a pound, or three-quarters of a gallon.
1/3: This fraction represents one-third of a whole. It is commonly used to represent one-third of a pizza, one-third of a cake, or one-third of a sandwich.
2/3: This fraction represents two-thirds of a whole. It is commonly used to represent two-thirds of a cup, two-thirds of a pound, or two-thirds of a gallon.

Definition of a Common Fraction

A common fraction is a fraction in which the numerator and denominator are both integers. The numerator represents the number of parts being considered, and the denominator represents the total number of parts in the whole or group. Common fractions are also known as vulgar fractions or simple fractions.

The numerator and denominator of a common fraction are separated by a fraction bar, which is also known as a division symbol. The fraction bar indicates that the numerator is to be divided by the denominator to get the value of the fraction.

Working with Common Fractions

Working with common fractions involves several basic operations, including adding, subtracting, multiplying, and dividing. These operations are similar to those used with whole numbers, but they require a slightly different approach.

Adding and Subtracting Common Fractions

To add or subtract common fractions, you must first find a common denominator. A common denominator is a number that is divisible by all the denominators in the fractions being added or subtracted.

Once you have a common denominator, you can add or subtract the numerators and write the result over the common denominator. For example, to add the fractions 1/3 and 1/4, you would first find a common denominator, which in this case is 12. Then you would convert both fractions so that they have a denominator of 12, giving you 4/12 and 3/12. Finally, you would add the numerators to get 7/12.

Multiplying and Dividing Common Fractions

To multiply common fractions, you simply multiply the numerators together and then multiply the denominators together. For example, to multiply 2/3 and 3/4, you would multiply 2 by 3 to get 6 and multiply 3 by 4 to get 12, giving you a result of 6/12, which can be simplified to 1/2.

To divide common fractions, you invert the second fraction (i.e., swap the numerator and denominator) and then multiply the two fractions together. For example, to divide 2/3 by 3/4, you would invert 3/4 to get 4/3 and then multiply it by 2/3, giving you 8/9.

Simplifying Common Fractions

Simplifying common fractions involves reducing the numerator and denominator to their lowest terms. This is done by finding the greatest common factor (GCF) of the numerator and denominator and dividing both by the GCF.

For example, to simplify the fraction 10/20, you would find the GCF of 10 and 20, which is 10, and divide both the numerator and denominator by 10, giving you 1/2.

Another example is the fraction 15/25. The GCF of 15 and 25 is 5, so you would divide both the numerator and denominator by 5, giving you 3/5.

Examples of Common Fractions

Common Fraction: Definitions and Examples

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