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3/2b=-14 1/2

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4 Answers

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.

Comments

Hi Grace,

Just realize a computation error in my original solution.

Beginning with step that shows equation:  (3)(2) = (29)(2b)

Next step should be:

6 = 58b (correct multiplication result for right side of equation).

All remaining steps below are the same as explained in my original answer save the use of the correct multiplication result (58b instead of 29b):

6/58 = 58b/58 (division of both sides by 58 to cancel out multiplication by 58 on right side).

6/58 = b (division results for both sides of equation).

(6/2) / (58/2) = b (reduce fraction result for b by dividing both numerator and denominator by common factor of 2)

3/29 = b (reduced fraction result for b).

Sorry for the mishap.

Regards, Jordan. 

Comment

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!  :)

 

 

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)

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.