Intro to Solving Equations with Fractions

Solving Equations with Fractions and Square Roots

Objective: Solve multi-step equations with fractions and square roots.

Multiple Choice

Do you know, if you were given this equation: $$\frac{3}{4}x=\frac{1}{4}$$  , and wanted to remove the fractions, what would you do to both sides?

• Multiply both sides by the numerator

• Multiply both sides by the denominator

Multiply Both Sides by the Denominator

In this case we would multiply both sides by 4.

If the denominators are different numbers it get more complicated but we will keep it simple for right now.

Multiply Both Sides By the Denominator

       $\frac{3}{4}x=\frac{1}{4}$  

 $\left(4\right)\frac{3}{4}x=\frac{1}{4}\left(4\right)$  
  
      $\frac{12}{4}x=\frac{4}{4}$     

         $3x=1$  (which is easy to solve)

Here is an example

This example is a little simpler

Multiple Choice

Solve:  $$-\frac{3}{4}y\ =\ 18$$  

• $$y=24$$  

• $$y=-24$$  

• $$y=-\frac{27}{2}$$  

• $$y=-72$$  

Multiple Choice

Solve:   $$9=\frac{3}{2}x$$  

• $$x=3$$  

• $$x=-6$$  

• $$x=4$$  

• $$x=6$$  

Watch the video

This adds a step.

Multiple Choice

$$\frac{1}{2}x\ +\ 4\ =\ 9$$  

• x = 6.5

• x = -10

• x = 2.5

• x = 10

Multiple Choice

$$\frac{3}{4}x\ -\ 1\ =\ 11$$  

• x = 4

• x = 16

• x = 12

• x = 9

Watch the video

Multi-step.

Multiple Choice

Solve for w:

$$\frac{2w+6}{5}=8$$  

• $$w=17$$  

• $$w=40$$  

• $$w=\frac{7}{2}$$  

• $$w=-\frac{3}{2}$$  

Multiple Choice

Solve for x:

$$-20=\frac{x-3}{6}$$  

• $$x=-123$$  

• $$x=-117$$  

• $$x=-\frac{1}{3}$$  

• $$x=-29$$  

Solving Equations with Square Roots

Multiple Choice

Solve:   $$2x^2=98$$  

• 49

• 9.89

• 7

• -49

Multiple Choice

Solve:   $$k^2-6=43$$  

• $$\sqrt{37}$$  
  

• 37

• 7

• 6.1

• 18.5

Multiple Choice

Solve:   $$x^2-64=0$$  

• 64

• 8

• 8

• 32

Multiple Choice

Solve:   $$-7x^2+21=14$$  

• 0

• -7

• 5

• 1

• 2.2