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Subtraction of Unlike Fractions

We will learn how to solve subtraction of unlike fractions. In order to subtract unlike fractions first we convert them as like fractions.

To subtract unlike fractions, we first convert them into like fractions. In order to make a common denominator, we find LCM of all the different denominators of given fractions and then make them equivalent fractions with a common denominators.

Let us consider some of the examples of subtracting unlike fractions:

1. Subtract 1/10 from 2/5.

Solution:

2/5 - 1/10

The L.C.M. of the denominators 10 and 5 is 10.

2/5 = (2 × 2)/(5 × 2) = 4/10, (because 10 ÷ 5 = 2)

1/10 = (1 × 1)/(10 × 1) = 1/10, (because 10 ÷ 10 = 1)

Thus, 2/5 - 1/10

= 4/10 - 1/10

= (4 - 1)/10

= 3/10


2. Subtract 38 from 512.

Solution:

Let us find the LCM of denominators 8 and 12. LCM is 24.

38 = 3×38×3 = 924 and

512 = 5×212×2 = 1024

Now, subtract 924 and 1024.

1024 - 924                                    

= 10924

= 124

Let us illustrate the above example pictorially as shown below.

Subtraction of Fractions

The whole strip above has 24 equal parts. The fraction 512 is equal to 1024. So the shaded portion represents 1024. We take away 38 or 924 of the above strip. The remaining part represents 124 of the whole strip.


3. Subtract 4/9 from 5/7.

Solution:

5/7 - 4/9

The L.C.M. of the denominators 9 and 7 is 63.

5/7 = (5 × 9)/(7 × 9) = 45/63, (because 63 ÷ 7 = 9)

4/9 = (4 × 7)/(9 × 7) = 28/63, (because 63 ÷ 9 = 7)

Thus, 5/7 - 4/9

= 45/63 - 28/63

= (45 - 28)/63

= 17/63


4. Subtract 5/8 from 1.

Solution:

1 - 5/8

= 1/1 - 5/8

The L.C.M. of the denominators 1 and 8 is 8.

1/1 = (1 × 8)/(1 × 8) = 8/8, (because 8 ÷ 1 = 8)

5/8 = (5 × 1)/(8 × 1) = 5/8, (because 8 ÷ 8 = 1)

Thus, 1/1 - 5/8

= 8/8 - 5/8

= (8 - 5)/8

= 3/8

 

5. Subtract 19/36 from 23/24.

Solution:

23/24 - 19/36

The L.C.M. of the denominators 24 and 36 is 72.

23/24 = (23 × 3)/(24 × 3) = 69/72, (because 72 ÷ 24 = 3)

19/36 = (19 × 2)/(36 × 2) = 38/72, (because 72 ÷ 36 = 2)

Thus, 23/24 - 19/36

= 69/72 - 38/72

= (69 - 38)/72

= 31/72


6. Subtract 9/35 from 3/7.

Solution:

3/7 - 9/35

The L.C.M. of the denominators 7 and 35 is 35.

3/7 = (3 × 5)/(7 × 5) = 15/35, (because 35 ÷ 7 = 5)

9/35 = (9 × 1)/(35 × 1) = 9/35, (because 35 ÷ 35 = 1)

Thus, 3/7 - 9/35

= 15/35 - 9/35

= (15 - 9)/35

= 6/35 

Subtraction of Unlike Fractions


7. Subtract 25 from 7.

Solution:

71 - 25

= 7×52×15 LCM of 1 and 5 is 5

= 3525

= 335

= 635

Hence, 7 - 25 = 635


Note: We write the whole number in the fraction form by keeping 1 in the denominator.


Subtraction of Fractions having the Different Denominator:

8. Subtract 23 - 14

23 = 812 [2×43×4 = 812]

14 = 312 [1×34×3 = 312]

23 - 14 = 812 - 312

= 8312

= 512

Method 1:

Step I: Find the L.C.M. of the denominators 3 and 4.

L.C.M. of 3 and 4 is 12

Step II: Write the equivalent fractions of 23 and 14 with denominator 12.

Step III: Subtract

Step IV: Write the difference in lowest terms.


9. Subtract 56 - 18

56 - 18 = (24÷6)×5(24÷8)×124

= (4×5)(3×1)24

= 20324

= 1724


Method 2:

L.C.M. of 6 and 8


Subtraction of Mixed Numbers:

Method I:

Subtract 812 - 314

812 - 314 = (8 – 3) + [12 - 14]

= 5 + [12 - 14]

= 5 + [24 - 14]

= 5 + 14

= 514

Method II:

Subtract 812 - 314

L.C.M. of 4 and 2 is 4.

812 - 314 = 172 - 134

= 344 - 134

= 34134]

= 214

= 514


2. What is 145 less than 412?

Find 412 - 145

412 - 145 = 92 - 95            L.C.M. of 2 and 5 is 10.

             = 4510 - 1810

             = 451810

             = 2710

            = 2710



Questions and Answers on Subtraction of Unlike Fractions:

1. Find the difference:

(i) 38 - 18

(ii) 1723 - 623

(iii) 12 - 316

(iv) 514 - 27

(v) 56 - 34

(vi) 23 - 15

(vii) 5 - 34

(viii) 2 - 1521

(ix) 423 - 2



Answers:

1. (i) 14

(ii) 1123

(iii) 516

(iv) 114

(v) 112

(vi) 715

(vii) 174

(viii) 2721

(ix) 223


2. Subtract the following Unlike Fractions:

(i) 47 - 13

(ii) 34 - 12

(iii) 8 - 23

(iv) 156 - 112

(v) 434 - 12

(vi) 213 - 112

(vii) 1347 - 6

(viii) 725 - 312

(ix) 92 - 4

(x) 25 - 310


Answer: 

2. (i) 521

(ii) 14 

(iii) 713

(iv) 13

(v) 414

(vi) 56

(vii) 747

(viii) 3910

(ix) 12

(x) 110

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