Addition and subtraction of fractions:

We have allready learnt about like fractions and unlike fractions in previous blog.

There are two types of fractions-

Fractions with the same denominator(like fractions).
Fractions without same denominators (unlike fractions).

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Addition of like fractions:

When we add fractions with the same denominator, we just add the Numerators and keep the denominator same.

Example: ³/5 + ⁴/5.

Solution:

Step 1 - in this example we find that denominators are same.

Step 2 - Add the Numerator 3 + 4 =7, and keep the denominator same 5.

Step 3 - So we can write the addition of fraction ⁷/5.

⁷/5= 1 and ²/5.

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Addition of unlike fractions:

Addition of unlike fractions by using LCM.

Example: ³/4 + ⁶/5.

Solution:

Step 1 - find the LCM of denominators 4 and 5, LCM= 20.

Step 2 - devide the LCM 20 by the denominator of the first fraction, 20÷4=5. Multiply quotient 5 by Numerator 3, 5×3 =15.

Step 3 - devide the LCM 20 by the denominator of the second fraction, 20÷5=4. multiply quotient 4 by Numerator 6, 6×4=24.

Step 4 - add the value of both steps 2 and 3, 15+24=39. And keep the denominator 20(LCM).

Step 5 - the solution is 39/20 = 1 and 19/20.

Find the image:

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Subtraction of like fractions:

When we subtract fractions with the same denominator, we just subtract the Numerators and keep the denominator same.

Example: ⁶/13 - ⁴/13.

Solution:

Step 1 - in this example we find that denominators are same.

Step 2 - Subtract the Numerator 6-4 =2, and keep the denominator same 13.

Step 3 - So we can write the subtraction of fraction ²/13.

Find the image:

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Subtraction of unlike fractions:

Subtraction of unlike fraction by using LCM

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Example: ⁶/5 - ³/4

Solution:

Step 1 - find the LCM of denominators 5 and 4, LCM= 20.

Step 2 - devide the LCM 20 by the denominator of the first fraction, 20÷5=4. Multiply quotient 4 by Numerator 6, 6×4 =24.

Step 3 - devide the LCM 20 by the denominator of the second fraction, 20÷4=5. multiply quotient 5 by Numerator 3, 5×3=15.

Step 4 - subtract the value of both steps 2 and 3, 24-15=9, And keep the denominator 20(LCM).

Step 5 - the solution is 9/20.

Find the Image:

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Writing A Fraction in its simplest Form :

A fraction is in its simplest Form when it's Numerator and denominator have no common factors other than 1.

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Fractions such as ¹/7,³/5,⁵/9 are All fractions in their simplest Form.

In ¹/7, there is no common factors of 1 and 7 (except 1). likewise,the only common factors of 3 and 5 in ³/5 is 1 and of 5 and 9 in ⁵/9 is 1.

Example: express fraction ⁶/8 in their simplest Form.

Solution:

Step 1 - find the factors of Numerator 6

The factors are 1,2,3,6.

Step 2 - find the factors of denominator 8

The factors are 1,2,4,8.

Step 3 - find the common factor of 6 and 8

The common factor is 2.

Step 4 - devide both (Numerator 6 and denominator 8) by the common

Factor 2.

Step 5 - We find 6÷2=3 and 8÷2=4.

Step 6 - now check the common factor of 3 and 4 there is no common factor except 1.

Now we can write ³/4 is the simplest Form of ⁶/8.

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Comparing Fractions:

Comparing Fractions with the like Denominators :

Note - if two or more fractions have the same denominator, the fraction with the greater Numerator is the greatest number and the small Numerator ie the smallest number.

Example: compair the Fractions ⁶/13,⁸/13.

Solution:

Step 1 - take note the denominators (13) is same of all fractions.

Step 2 - now see the Numerators we can see that 8 is greater than 3.

So we can express fractions ⁶/13<⁸/13. The fraction ⁸/13 is greater than ³/13.

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Comparing Fractions with unlike denominators :

First we talk about what is "unlike denominators" mean?

Fractions have denominators are not same called unlike denominators.

Example: ¹/3,²/5.

Solution:

Let's comparing by the LCM (lowest common factor) mathod.

Step 1- find the LCM of denominators 3 and 5.

Step 2- the LCM is 3×5=15.

Step 3- in fraction ¹/3 multiply by 5 separately in Numerator and denominator we got ⁵/15.

Step 4- in fraction ²/5 multiply by 3 separately in Numerator and denominator we got ⁶/15.

Step 5- now we find that denominators are same for both fractions ⁵/15,⁶/15.

Since, ⁶/15>⁵/15, therefore, ²/5>¹/3.

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Ordering fractions:

Now that we know how to compare fractions, we can order them in any order increasing or decreasing.

Example: Arrange the Fractions ³/8,⁵/12,³/4 in increasing order.

Solution:

Step 1- find the LCM of the denominators 8,12 and 4. The LCM is 24.

Step 2- find the equivalent fractions with denominator 24.

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Step 3- Compare the equivalent fractions: 19/24,10/24 and 18/24. Arranging the Fractions in increasing order, 10/24<18/24<19/24, therefore 5/12<3/4<3/8.

We can also write the same Fractions in decreasing order as 3/8>3/4>3/8.

Tuesday, 9 August 2022