Solving Equations by Clearing Fractions

​Clearing the Fraction

Pre-Algebra​

Solve each equation.

• Use the "/" symbol on your keyboard to enter your answer as a fraction

​

​Solving Rational Number Equations

​Warm-Up

Fill in the Blanks

$x+\frac{5}{6}=\frac{3}{8}$  

Fill in the Blanks

$-8=\frac{4}{5}x$  

Fill in the Blanks

$\frac{7}{4}m-\frac{1}{10}=-\frac{107}{20}$  

Fill in the Blanks

$\frac{5}{12}=\frac{3}{2}c+\frac{8}{3}$  

... What if there's an easier way to deal with fractions in equations?​

​Example Problems: Clearing the Fractions

​Clearing the Fraction

Multiple Choice

Make your best guess :)

Select the equation that is equivalent to $$\frac{13}{7}x+\frac{4}{7}=-\frac{9}{7}$$  

• $$13x+4=-9$$  

• $$\frac{7}{13}x+\frac{7}{4}=-\frac{9}{7}$$  

Multiple Choice

What is the least common denominator (LCD) in $$\frac{3}{2}a-2=-\frac{13}{4}$$  

• 1

• 2

• 4

• 8

Multiple Choice

Select the equation that is equivalent to $$\frac{3}{2}a-2=-\frac{13}{4}$$

(hint: use the LCD!)

• $$\frac{2}{3}a-\frac{1}{2}=-\frac{4}{13}$$  

• $$3a-2=-13$$  

• $$6a-8=-13$$  

Multiple Choice

What is the LCD of $$\frac{101}{20}=\frac{13}{10}w+\frac{15}{4}$$  ?

• 4

• 10

• 20

• 40

Multiple Choice

What fraction is equivalent to $$\frac{101}{20}=\frac{13}{10}w+\frac{15}{4}$$  ?

(hint: use the LCD)

• $$101=26w+60$$  

• $$101=13w+15$$  

• $$\frac{101}{20}=26w+30$$  

1. Find the LCD

2. Multiply the entire fraction by the LCD

3. Solve the remaining equation​

​Some text here about the topic of discussion.

​To clear the fractions in an equation...

Fill in the Blanks

What is the LCD of $7n-\frac{1}{2}=\frac{20}{9}$  ?

Multiple Choice

After clearing the fractions, the new coefficients and constants of $$7n-\frac{1}{2}=\frac{20}{9}$$   are...

• 7, 1, 20

• 63, 9, 20

• 126, 9, 40

• 126, 18, 360

After clearing the fractions using the LCD, remember to simplify!​

​

ex) 18÷2=9

​Simplifying

​Clearing the Fractions

Clearing the Fractions

Draw

Find the LCD and clear the fractions.

Draw

Find the LCD and clear the fractions.

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​Now try SOLVING the equations after clearing the fractions!

Draw

Solve for x.

Draw

Solve for v.