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