Solving Fractional Equations

Solving Equations with Fractions

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First, let's practice 2 step equations

• Remove the constant first by doing the inverse operation

• Next, divide by the coefficient to get the variable alone

Multiple Choice

Solve  3x - 7 = 32

• 13
• -13
• 12
• -12

Now let's add fractions to the mix! We will review 2 types

• 1 - fraction as a coefficient

• 2 - variable in the numerator

Fraction as a Coefficient

When you need to divide by a fraction, you MULTIPLY by the RECIPROCAL!!!

Reciprocal means to flip the fraction

Multiple Choice

What is the recriprocal of 4/5

• 4/5

• 5/4

• 5/1

• 1/5

Now let's do an equation!

• Remove constant FIRST!

• add 2 to both sides

• Now either divide by the fraction or multiply by the reciprocal

Multiple Choice

Solve for y:

$$\frac{4}{3}y\ +1=-14$$  

• $$y=-21$$  

• $$y=-11.25$$  

• $$y=-16$$  

• $$y=4$$  

Multiple Choice

Solve for x:

$$9=\frac{3}{2}x$$  

• $$x=3$$  

• $$x=-6$$  

• $$x=4$$  

• $$x=6$$  

Variable in the Numerator

Before you can solve you must UNDO the fraction. The inverse of division is multiplication! Multiply by the denominator to undo the fraction

Before you can solve you must UNDO the fraction. The inverse of division is multiplication!

•  first, multiply both sides by 14

•  -28 = b-8

•  then add 8 to both sides

• -20 = b

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:

$$-20=\frac{x-3}{6}$$  

• $$x=-123$$  

• $$x=-117$$  

• $$x=-\frac{1}{3}$$  

• $$x=-29$$  

Finally, let's review adding/subtracting fractions

• Fractions MUST have a common denominator before you can add or subtract.

• Need to find LCM

• Now create equivalent fractions

Multiple Choice

What is the Least Common Multiple of 6 and 10?

• 16

• 60

• 30

• 20

Multiple Choice

What is the LCM of 3 and 4? 

• 4
• 16
• 12
• 24

Multiple Choice

What must you have to add and subtract fractions?

• Common numerators
• Different numerators
• Different denominators
• Common denominators

3/4 + 1/6

• Find LCM to create common denominators

• LCM = 12

• Now, decide what to multiply each denominator by to equal LCM

• Multiply numerator by same number

• Once you have equivalent fraction, you can proceed

• 9/12 + 2/12 = 11/12

Multiple Choice

8/9 - 1/3 =

• 7/6

• 5/9

• 2/3

• 8/27

Multiple Choice

Solve for x

Just like a normal equation - do the inverse operation

• 6/10

• 1

• 0

• 9/25

Poll

I understand how to solve equations that contain fractions:

• Yes, I can ace a test on this topic.

• Yes, I just need more practice.

• Almost, I need more practice and have some questions.

• No, I am completely lost.