11 Plus Fractions
Fractions are considered as representing a part of a whole quantity. Fractions are usually represented in the form of a/b where a, b are ≠ 0. The terminologies of fractions are generally used while dividing a thing into smaller parts, like sharing a pizza among friends.
The pizza shown in the above picture has been divided into eight pieces. When the pizza is considered a whole, each part is given by 1/8, which is a fraction.
A fraction consists of 2 parts they are Numerator and Denominator.
Types of fractions:
Generally, fractions can be divided into three types they are
- Proper Fractions
- Improper fractions
- Mixed Fractions
The fractions in which the denominator is greater than the numerator, then such fractions are considered as the Proper Fractions. Examples are ½, ¼, ¾, etc.
The fractions in which the denominator is greater than the numerator, then such fractions are considered as the Improper Fractions. Examples are 11/4, 5/2, 10/7 etc.
The other form of representing an improper fraction is in terms of Mixed Fractions. It is a combination of a whole number and a proper fraction. Examples are 3 ½, 5 ¼, 7 ¾, etc.
Some important facts about fractions are
- The fractions with the same denominator are said to be Like Fractions else, they are said as, Unlike Fractions.
- A fraction in which numerator and denominator are equal, then its value will be equal to One. Eg 2/2 = 1.
- A fraction in which the numerator = 0, then the value of the fraction will be Zero. Eg 0/100 = 0.
- A fraction in which the denominator = 0, then the fraction is said to be undefined.
Example: Jason brings a cake and cuts it into 6 equal parts and distributes among his friend, what fraction does each friend get?
Sol: No. of pieces = 6, then each one will be getting 1/6 part of the cake.
Arithmetic operations on fractions
To perform addition or subtraction, we need to check if the fractions have the same denominator or not. We will know about them in detail through some interesting and easy examples.
Consider two fractions, a/b and c/b, and then their sum will be (a + c)/b, similarly in subtraction also, it will be (a-c)/b. Here denominators of both the fractions are equal.
Now Consider two fractions, a/b and c/d. Then, to find their sum or difference, we must make their denominators equal. For this, we must find the LCM of the denominators, and based on it, and we must make the fractions like or we follow another method, in which the fractions are represented as (ad/bd), (bc/bd) and perform the addition or subtraction.
Example: Add 1/2 and 2/3?
Sol: First, convert them into like fractions. 1/2 can be written as (1x3) / (2x3) = 3/6. Similarly, 2/3 can be written as 2/6. Now we can add both the fractions,
3/6 + 2/6 = 5/6
For multiplication, it is very easy, multiply the numerators and denominators separately. For division, reciprocate the 2nd fraction and multiply.
Multiplication of a / b & c / d = (a x b) / (c x d)
Division of a / b & c / d = (a x d) / (b x c)
Example: Multiply 1/4 and 2/3?
Sol: It is very easy to multiply numerators and denominators separately.
1/4 x 2/3 = (1 x 2) / (4 x 3) = 2 / 12.
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