3/2b=-14 1/2

Question

ok when there are to fractions and one variable what do u do ?

Answer 1

Hi Grace,

Let's begin by writing out our equation as you typed it in (3 divided by 2b = 14 and 1/2): 

3/2b = 14 1/2

First, we want to convert the mixed number 14 1/2 to an improper fraction:

(whole number x denominator + numerator) / denominator

(14 x 2 + 1) / 2 = (28 + 1) / 2 = 29 / 2

Now our equation becomes:  3/2b = 29/2

Our equation is actually a proportion (2 equal ratios or fractions).

In a proportion the cross products of the proportion (numerator x denominator diagonally across the equal sign in both directions) are equal:

(3)(2) = (29)(2b)

Now we can simplify both sides of the equation by doing the multiplication on each side:

6 = 29b

Lastly, we can find b by dividing both sides of the equation by 29, which will cancel out the multiplication by 29 on the right side of the equation:

6/29 = 29b/29

After the division by 29 on both sides of tbe equation, we arrive at our answer:

b = 6/29

I trust the above stepwise explanation will clarify the solution for you.

Thanks for submitting your question.

Regards, Jordan.

Answer 2

Grace, fractions can be confusing.  But I promise, with a little practice, you will be a master in no time!  Let's take a look at your question ...

You asked how to solve the following equations:  (3/2)*b = -14 (1/2)

I am going to assume, based on how your typed the equation, that the right side is written as a mixed number. 

Step 1:  Change the right side of the equation to its improper form

-14 (1/2) is the same as  -29/2

Step 2:  Rewrite the equation using the improper form of the right side

(3/2)*b = -29/2

Remember, the objective is to get the variable, "b," by itself.  This  means everything else must move to the other side.

Step 3:  Move (3/2) to the right side by multiplying both sides by 2/3, which is the reciprocal of 3/2.  Technically, we are dividing both sides by (3/2), but dividing  fractions is the same as multiplying by the reciprocal.

Step 4:  Write the result

Notice that "b" is by itself after we perform Step 3.  This is exactly what we want and we have, therefore, solved the equation.

b = -(29/2) * (2/3) = (-29*2)/(2*3) = -58/6 = -29/3 

When you multiply fractions, multiply numerator by numerator and denominator by denominator!  Unless your teacher requests otherwise, I would leave the answer expressed as a fraction.

Hope this helps!  :)

 

 

Answer 3

first isolate b by using the reciprocal 2/3. Multiplying both sides by 2/3 yields:

b=-14 1/2 * 2/3

now you need to change 14 1/2 into a fraction. You can do this by multiplying the whole number 14 by the denominator 2 which yields 28 and then add one more from the 1/2 and so you get 29/2.

now you have:

b=-29/2 * 2/3

to multiply fractions multiply the numerators together and also the denominators together so you'd get:

b= (-29 * 2) / (2 * 3)

which is:

b= -58/6 reducible to -29/3 (or -9 2/3)

Answer 4

You want to isolate b. So in this case you need to divide by 3/2 to get b by itself. When you divide the other side by 3/2 (dividing by a fraction is the same as multiplying by its inverse) you can multiply by 2/3.   -(14  1/2)* (2/3)= -29/3 and so b=29/3.