SOLVING AN EQUATION THAT INVOLVES FRACTIONS

About "Solving an equation that involves fractions"

Solving an equation that involves fractions :

To solve an equation with variables on both sides that involves fractions, we can use the least common multiple (LCM) of the denominators to eliminate the fractions from the equation.

Solving an equation that involves fractions - Examples

Example 1 :

Solve : 7n/10 + 3/2  =  3n/5 + 2

Solution :

Step 1 :

Find the least common multiple of the denominators (10, 2 and 5).

LCM  =  5 x 2 x 1 x 1 x 1

LCM  =  10

Step 2 :

Multiply both sides of the equation by 10.

10(7n/10 + 3/2)  =  10(3n/5 + 2)

Use distributive property.

10(7n/10) + 10(3/2)  =  10(3n/5) + 10(2)

Simplify.

7n + 5(3)  =  2(3n) + 20

7n + 15  =  6n + 20

Step 3 :

Use inverse operations to solve for "n".

Subtract 15 from both sides.

aaaaaaaaaaaaaaaa 7n + 15  =  6n + 20 aaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaa - 15           - 15 aaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaa---------------------- aaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaa 7n         =  6n + 5 aaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaa---------------------- aaaaaaaaaaaaaaaa

Subtract 6n from both sides.

aaaaaaaaaaaaaaaa 7n         =  6n + 5 aaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaa -6n            -6n aaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaa  -------------------- aaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaa   n         =          5 aaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaa  -------------------- aaaaaaaaaaaaaaaa

Example 2 :

Solve : k/7 - 6  =  3k/7 + 4

Solution :

Step 1 :

Find the least common multiple of the denominators.

Here, we have the same denominator on both sides. That is 7.

So, LCM  =  7.

Step 2 :

Multiply both sides of the equation by 7.

7(k/7 - 6)  =  7(3k/7 + 4)

Use distributive property.

7(k/7) - 7(6)  =  7(3k/7) + 7(4)

Simplify.

k - 42  =  3k + 28

Step 3 :

Use inverse operations to solve for "k".

Subtract 28 from both sides.

aaaaaaaaaaaaaaaa   k - 42  =  3k + 28 aaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaa - 28           - 28 aaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaa---------------------- aaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaa   k - 70  =  3k  aaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaa---------------------- aaaaaaaaaaaaaaaaaa

Subtract k from both sides.

aaaaaaaaaaaaaaaaaaaa k - 70  =  3k aaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaa - k            - k aaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaa---------------- aaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaa       -70  =  2k aaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaa---------------- aaaaaaaaaaaaaaaaaa

Divide both sides by 2.

-70 / 2  =  2k / 2

-35  =  k

After having gone through the stuff given above, we hope that the students would have understood "Solving an equation that involves fractions".

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