# ADDING AND SUBTRACTING FRACTIONS USING FORMULA

Adding and Subtracting Fractions using Formula :

In this section, we will see how to add and subtract two fractions using formula.

We may use the formula given below under the certain conditions.

(i)  Check if the fractions are having same denominator or different denominators.

(ii)  If they are having same denominators, then we may use the formula given below to simplify them.

(iii)  If they have different denominators, then we can take L.C.M (Least common multiple) and make them as same.

(iv)  If the denominators are co-primes, then we have to use the formula given below and combine the fractions.

Note :

The formula given above is applicable only for combining two fractions.

## Adding and Subtracting Fractions Using Formula Examples

Question 1 :

Solution :

The denominators are different and they are co primes. So, we have to use the formula and combine the fractions.

=  { 1(7) + 2(8) } / (8 ⋅ 7)

=  (7 + 16) / 56

=  23/56

Question 2 :

Solution :

The denominators are different and they are co primes. So, we have to use the formula and combine the fractions.

=  { 2(7) + 1(5) } / (5 ⋅ 7)

=  (14 + 5) / 35

=  19/35

Question 3 :

Solution :

The denominators are different and they are co primes. So, we have to use the formula and combine the fractions.

=  { 2(11) + 3(7) } / (7 ⋅ 11)

=  (22 + 21) / 77

=  43/77

Question 4 :

Solution :

The denominators are different and they are co primes. So, we have to use the formula and combine the fractions.

=  { 1(5) + 2(2) } / (2 ⋅ 5)

=  (5 + 4) / 10

=  9/10

Question 5 :

Subtract  (1/8) - (2/7)

Solution :

The denominators are different and they are co primes. So, we have to use the formula and combine the fractions.

=  { 1(7) - 2(8) } / (8 ⋅ 7)

=  (7 - 16) / 56

=  -9/56

Question 6 :

Subtract  (3/7) - (2/5)

Solution :

The denominators are different and they are co primes. So, we have to use the formula and combine the fractions.

=  { 3(5) - 2(7) } / (7 ⋅ 5)

=  (15 - 14) / 35

=  1/35

Question 7 :

Subtract  (2/5) - (4/9)

Solution :

The denominators are different and they are co primes. So, we have to use the formula and combine the fractions.

=  { 2(9) - 5(4) } / (5 ⋅ 9)

=  (18 - 20) / 45

=  -2/45

Question 8 :

Subtract  (7/9) - (2/7)

Solution :

The denominators are different and they are co primes. So, we have to use the formula and combine the fractions.

=  { 7(7) - 2(9) } / (9 ⋅ 7)

=  (49 - 18) / 63

=  31/63

After having gone through the stuff given above, we hope that the students would have understood how to add and subtract fractions using formula.

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