{"id":238,"date":"2023-08-31T21:39:56","date_gmt":"2023-08-31T20:39:56","guid":{"rendered":"https:\/\/mathsworld0123.com\/?p=238"},"modified":"2023-08-31T21:39:56","modified_gmt":"2023-08-31T20:39:56","slug":"fractions-everything-you-need-to-know","status":"publish","type":"post","link":"https:\/\/mathsworld0123.com\/?p=238","title":{"rendered":"Fractions: Everything You Need to Know"},"content":{"rendered":"\n

Fractions are a fundamental part of mathematics that allow us to express and compare quantities that are not whole numbers. They are used to represent ratios, proportions, and part-to-whole relationships, which are all important concepts in everyday life.<\/p>\n\n\n\n

What is a fraction?<\/h2>\n\n\n\n

Fractions are fundamental ways to represent parts of wholes.Fractions are composed of two essential components: the numerator<\/strong> and the denominator<\/strong>.<\/p>\n\n\n\n

Denominator:<\/strong> The bottom part of the fraction, indicating how many equal parts make up the whole.<\/p>\n\n\n\n

Numerator:<\/strong> This is the top part of the fraction, representing how many parts of the whole you have.<\/p>\n\n\n\n

Example 1 : Let’s grasp the concept of fractions with the following illustration: Imagine a set of 6 numbered boxes, out of which 2 boxes are filled with green colour.<\/p>\n\n\n\n

\n
\"\"<\/figure>\n<\/figure>\n\n\n\n

Now, let’s determine the fraction representing the boxes filled with green colour:<\/p>\n\n\n\n

Since a fraction signifies a part of a whole, we can calculate it by dividing the number of boxes filled with green colour by the total number of boxes.<\/p>\n\n\n\n

Fraction of boxes filled with green colour = Number of Boxes filled with green colour \/ Total Number of Boxes<\/p>\n\n\n\n

= 2\/6<\/p>\n\n\n\n

Similarly<\/p>\n\n\n\n

Fraction of boxes without filled colour = Number of Boxes without filled colour \/ Total Number of Boxes<\/p>\n\n\n\n

=. 4\/6<\/p>\n\n\n\n

Example 2 : Imagine a pizza cut into 4 equal parts, and one part has been eaten. This means there are 3 parts of the pizza remaining.<\/p>\n\n\n\n

\n
\"\"<\/figure>\n<\/figure>\n\n\n\n

So, if we want to express the fraction of the remaining part, it will be:<\/p>\n\n\n\n

Fraction of the remaining part of the pizza = 3\/4<\/p>\n\n\n\n

Similarly, the fraction of the eaten part would be:<\/p>\n\n\n\n

Fraction of the eaten part = 1\/4<\/p>\n\n\n\n

Question & Solutions<\/h2>\n\n\n\n

Question:<\/strong> Mary has a pizza divided into 8 equal slices. She has eaten 3 of those slices. What fraction of the pizza has Mary eaten, and how many slices are left?<\/p>\n\n\n\n

Solution :<\/strong> <\/p>\n\n\n\n

let’s solve the question:<\/p>\n\n\n\n

Mary has a pizza divided into 8 equal slices, and she has eaten 3 of those slices.<\/p>\n\n\n\n

Fraction of pizza eaten by Mary:<\/strong> To find this, we can use the following formula:<\/p>\n\n\n\n

Fraction eaten = (Number of slices eaten) \/ (Total number of slices)<\/p>\n\n\n\n

In this case, Mary has eaten 3 slices out of a total of 8 slices:<\/p>\n\n\n\n

Fraction eaten = 3 \/ 8<\/p>\n\n\n\n

So, Mary has eaten 3\/8<\/strong> of the pizza.<\/p>\n\n\n\n

Number of slices left:<\/strong> To find this, we subtract the slices Mary ate from the total number of slices:<\/p>\n\n\n\n

Number of slices left = Total number of slices – Number of slices eaten<\/p>\n\n\n\n

Number of slices left = 8 – 3 = 5 slices<\/p>\n\n\n\n

So, Mary has 5 slices of pizza left.<\/p>\n\n\n\n

Types of Fractions :<\/h2>\n\n\n\n

Fractions are more than just numbers; they come in various forms, each with its unique characteristics. In this exploration of fractions, let’s delve into the different types:<\/p>\n\n\n\n

1. Proper <\/strong>Fractions:<\/strong><\/p>\n\n\n\n

Definition: Proper fractions are those where the numerator (the top number) is smaller than the denominator (the bottom number).<\/p>\n\n\n\n

Example: Consider 1\/2, 3\/5, and 7\/9; all are proper fractions.<\/p>\n\n\n\n

2. Improper <\/strong>Fractions:<\/strong><\/p>\n\n\n\n

Definition: In improper fractions, the numerator is greater than or equal to the denominator.<\/p>\n\n\n\n

Example: Think of 4\/3, 5\/4, and 9\/9 as examples of improper fractions.<\/p>\n\n\n\n

3. Mixed <\/strong>Numbers:<\/strong><\/p>\n\n\n\n

Definition: Mixed numbers combine whole numbers with fractions.<\/p>\n\n\n\n

Example: 2 1\/2 is a mixed number, which equals 2 + 1\/2.<\/p>\n\n\n\n

4. Equivalent <\/strong>Fractions:<\/strong><\/p>\n\n\n\n

Definition: Fractions are equivalent if they represent the same portion of a whole.<\/p>\n\n\n\n

Example: Both 1\/2 and 2\/4 are equivalent fractions as they both signify half.<\/p>\n\n\n\n

5. Like <\/strong>Fractions:<\/strong><\/p>\n\n\n\n

Definition: Like fractions have identical denominators.<\/p>\n\n\n\n

Example: 1\/4, 2\/4, and 3\/4 are like fractions, all sharing a denominator of 4.<\/p>\n\n\n\n

6. Unlike <\/strong>Fractions:<\/strong><\/p>\n\n\n\n

Definition: Unlike fractions have different denominators.<\/p>\n\n\n\n

Example: 1\/4 and 1\/3 are unlike fractions due to their differing denominators.<\/p>\n\n\n\n

7. Unit Fractions:<\/strong><\/p>\n\n\n\n

Definition: Unit fractions have 1 as their numerator.<\/p>\n\n\n\n

Example: 1\/2, 1\/3, and 1\/10 are unit fractions, each representing one part of a whole.<\/p>\n\n\n\n

8. Complex <\/strong>Fractions:<\/strong><\/p>\n\n\n\n

Definition: Complex fractions feature numerators and denominators that are fractions themselves.<\/p>\n\n\n\n

Example: An example is (1\/2)\/(1\/3), a complex fraction within fractions.<\/p>\n\n\n\n

Understanding these types of fractions is vital for tackling various mathematical problems. Whether you’re baking, budgeting, or dealing with intricate calculations, fractions play a significant role in making sense of real-world scenarios. Embrace the diversity of fractions; they are the building blocks of mathematical versatility.<\/p>\n\n\n\n

Exercise on Equivalent Fraction<\/h2>\n\n\n\n

How to Find Equivalent Fractions<\/h3>\n\n\n\n

To find equivalent fractions, you need to multiply or divide both the numerator and the denominator by the same nonzero number. Here are some example :-<\/p>\n\n\n\n

Example 1. Find the 3 equivalent fraction of 3\/4?<\/strong><\/p>\n\n\n\n

Solution :<\/p>\n\n\n\n

3\/4 X 2\/2 = 6\/8 <\/p>\n\n\n\n

3\/4 X 3\/3 = 9\/12<\/p>\n\n\n\n

3\/4 X 4\/4 = 12\/16<\/p>\n\n\n\n

Example 2. Find the 3 equivalent fraction on 4\/5 ?<\/strong><\/p>\n\n\n\n

Solution :<\/p>\n\n\n\n

4\/5 X 5\/5 = 20\/25<\/p>\n\n\n\n

4\/5 X 6\/6 = 24\/30<\/p>\n\n\n\n

4\/5 X 8\/8 = 32\/ 40<\/p>\n\n\n\n

Example3: Find an equivalent fraction to 2\/5 with a denominator of 15.<\/strong><\/p>\n\n\n\n

Explanation:<\/strong> To find an equivalent fraction with a denominator of 15 for the fraction 2\/5, <\/p>\n\n\n\n

you need to determine what you can multiply the denominator (5) by to get 15. <\/p>\n\n\n\n

In this case, you can multiply both the numerator (2) and the denominator (5) by 3:<\/p>\n\n\n\n

(2\/5) X (3\/3) = 6\/15<\/p>\n\n\n\n

So, the equivalent fraction to 2\/5 with a denominator of 15 is 6\/15.<\/p>\n\n\n\n

Example 4 :<\/strong> You have the fraction 3\/4, and we want to find an equivalent fraction with a denominator of 12.<\/p>\n\n\n\n

Solution:<\/strong><\/p>\n\n\n\n

    \n
  1. Start with the original fraction: 3\/4.<\/li>\n\n\n\n
  2. To get a denominator of 12, think about what you can multiply 4 by to make it 12. In this case, you need to multiply it by 3 because 4 X 3 = 12.<\/li>\n\n\n\n
  3. Now, to keep the fraction equivalent, you should also multiply the numerator (3) by the same number you multiplied the denominator by, which is 3.<\/li>\n\n\n\n
  4. Multiply the numerator and denominator:Numerator: 3 X 3 = 9 Denominator: 4 X3 = 12 <\/li>\n<\/ol>\n\n\n\n

    3\/4 X 3\/3 = 9\/12<\/p>\n\n\n\n

    So, the equivalent fraction to 3\/4 with a denominator of 12 is 9\/12.<\/p>\n\n\n\n

    You successfully found an equivalent fraction: 3\/4 is the same as 9\/12 when the denominator is 12<\/p>\n\n\n\n

    Conversion of Unlike fraction to like fraction<\/h2>\n\n\n\n

    Unlike Fractions<\/strong><\/p>\n\n\n\n

    Unlike fractions are fractions that have different denominators. For example, 1\/2 and 3\/4 are unlike fractions.<\/p>\n\n\n\n

    Like Fractions<\/strong><\/p>\n\n\n\n

    Like fractions are fractions that have the same denominator. For example, 1\/2 and 2\/2 are like fractions.<\/p>\n\n\n\n

    Converting Unlike Fractions to Like Fractions<\/strong><\/p>\n\n\n\n

    Converting Unlike Fractions to Like Fractions: To add or subtract fractions with different denominators, we need to make them like fractions, which means having the same denominator. <\/p>\n\n\n\n

    Here’s how you can do it:<\/p>\n\n\n\n

    Step 1: Find a Common Denominator<\/strong><\/p>\n\n\n\n