How do you figure `1/4+1/3n=1/2` ?

Expert Answers
lemjay eNotes educator| Certified Educator


To solve, express the fractions with same denominator. Since the LCD is 12, the equation fractions become:

`1/4*3/3 + 1/3n*4/4=1/2*6/6`


Then, bring together the fractions without n. so, subtract 3/12 from both sides.

`3/12 - 3/12 + 4/12n =6/12-3/12`


Then, isolate the n. So, multiply both sides by the reciprocal of 4/12.

`12/4*4/12n = 3/12*12/4`


Therefore, the solution to the given equation is ` n=3/4` .

sid-sarfraz | Student



In order to solve this equation, first we will have to equal the denominators. For equaling denominators we have to find LCD.

LCD is 12 in this, therefore;

`1/4*3/3 +1/3(n)*4/4 = 1/2*6/6`

Isolate the fraction containing n on LHS and the rest on RHS;


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Now 12 will be canceled as it is the denominator of both sides;



Therefore the value of n=3/4.

Hence Solved!

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zumba96 | Student

How do you figure `` ?

Well first of all you need to make this into a common denominator. The common denominator for 4 and 3 equals 12. Therefore, times (1/4)(3) and (1/3)(4) and (1/2)(6) to get 3/12 + 4/12n=6/12. Subtract 3/12 from 6/12 to get 4/12n=3/12

then divide 4/12 and move to the other side to have the final answer of 

n= 3/4

(The 12 will cancel out) 

nisarg | Student

so 3/12+4/12n=6/12




udonbutterfly | Student


Start by finding the LCD of all the Denominators

4 8 12 16

3 6 9 12 15

2 4 6 8 10 12 14

The LCD is 12. So we are going to take 12 and multiply it on both sides of the equation

12(1/4+1/3n)=(1/2)12 Distribute and you will get

12/4 + 12/3n = 12/2 Simplify!

3 + 4n = 6 Subtract the 3 on both sides

4n = 3 Now divide both sides by 4 to get the n alone


mmenon | Student

The first step when solving any problem with a variable, is to take the variable to one side and to put the rest of the problem to the other side (for example take the variable to the left and the rest to the right) and then simplifying the problem.
We will do the same for this equation:

Step 1
Isolate the variable.
Leaving `1/3 n` on the left, we will take `1/4` to the right to get `(1n)/3=1/2-1/4`

Step 2
Make sure all the fractions have the same common denominator to make it easier to add and subtract them. We will take 12 to be the common denominator. 
`(1n)/3 (4/4) = 1/2 (6/6) - 1/4 (3/3)`

`rArr (4n)/12=6/12-3/12` 

Step 3

Step 4
Cross multiply.
`n=3/12 (12/4)`


rachellopez | Student

In order to solve for the variable n, you have to isolate it. To get n by itself, you should start by subtracting 1/4 from both sides.

To subtract two fractions, they have to have a common denominator. The denominators 4 and 2 are both multiples of 8, so you can change both denominators to 8. Remember what ever you do to the denominator you must do to the numerator as well.

1/2(4/4) - 1/4(2/2) = 4/8 - 2/8 = 2/8 or 1/4

Now your equation is 1/3 n = 1/4. The last step to isolate n is to divide by 1/3. Dividing a fraction by a fraction is the same thing as multiplying by a reciprocal (or multiplying by the bottom fraction flipped).

n = 1/4(3/1)     You can multiply fractions straight across.

n = 3/4