Solving Multi-Step Equations with Fractions

​How can I eliminate fractions in algebraic expressions and equations?

Multiple Choice

Find the value of d in the equation: $$\frac{1}{5}d\ =\ 10$$

• d = 50

• d = 2

• d = 15

• d = 5

​Did you multiply both sides of the equation by five...?

Multiple Choice

Find the value of n in the equation: $$\frac{1}{12}n\ =\ 4$$

• n = $$3$$  

• n = $$48$$  

• n = $$36$$  

• n = $$\frac{1}{3}$$  

​Did you multiply both sides of the equation by twelve?

Multiple Choice

Which of the equations below is created if I multiply each term by a factor of three in the equation $$\frac{2}{3}t\ +\ 7\ =\ \frac{5}{3}$$ ?

• $$t+7=5$$  

• $$t+21=5$$  

• $$2t+21=5$$  

• $$2t+21=15$$  

​The numerator is left behind!

Multiple Choice

Solve for the value of t in the equation: $$2t\ +\ 21\ =\ 5$$

• $$t\ =\ 13$$  

• $$t\ =\ -8$$  

• $$t\ =\ 8$$  

• $$t\ =\ \frac{10}{21}$$  

• $$t\ =\ -16$$  

​Did you select the correct equation? If not...

​← Step #2: will subtracting twenty-one from five result in a positive or a negative value?

​Just to be safe, let's try two more examples.

​

Hint: have you been taking notes or writing down your work the entire time? Doing so will help with both your memory and your understanding.

Multiple Choice

Solve for the value of k in the equation: $$\frac{5}{3}k\ -3\ =\ 2$$  

• $$k=3$$  

• $$k=\frac{9}{5}$$  

• $$k=15$$  

• $$k=-\frac{6}{5}$$  

• $$k=\frac{3}{5}$$  

Multiple Choice

Solve for the value of g in the equation: $$43=\frac{g+6}{4}+28$$  

• $$g=11$$  

• $$g=81$$  

• $$g=36$$  

• $$g=54$$  

• $$g=-11$$  

​Can I use this strategy with decimals?

​Yeah, you could. To do so, multiply each term in the equation by a value that changes the decimal to a whole number − the number's reciprocal would be ideal.

​

This is simple with coefficients you can easily scale-up to a value of one, like 0.25 and 0.125 (multiply by 4 or 8, respectively). This gets complicated if the coefficient doesn't easily scale, though.

​

For example, what if the coefficient is 0.325? With a little work, we can find that 0.325 times 40 equals 13. This means you would multiply each term in such an equation by 40, and then you would divide everything by 13 toward the end of the equation...

​

You're probably better off leaving these terms as decimals and solving for your variable as it is.