Clearing Fractions Activity

Clearing Fractions Activity

Unit 3 Lesson 3

There are 5 steps in solving equations with Fractions.

• Step 1: Locate all the denominators of the fraction.

• Step 2: Find the LCD.

• Step 3: Multiply every numerator by the LCD.

• Step 4: Reduce each fraction to an integer.

• Step 5: Solve for the variable.

Multiple Choice

What is step 2 in the process?

• Locate the denominators.

• Find the LCD.

• Multiply every numerator by the LCD.

• Reduce each fraction to an integer.

• Solve for the variable.

How do we solve for the LCD?

• LCD is the least common denominator.

• We need the LCM (least common multiple) to find the LCD.

Multiple Choice

Using the Cake Method, what is the LCM of 4 and 8?

• 2

• 4

• 8

• 32

Multiple Select

We are going to solve this equation step by step.

Step 1: What are the denominators of this equation?

 $\frac{3}{8}+2x=\frac{7}{4}$  

• 1

• 2

• 4

• 8

• 3

Multiple Choice

Step 2: What is the LCD of:

 $\frac{3}{8}+2x=\frac{7}{4}$  

• LCD: 4

• LCD: 8

• LCD: 16

Multiple Choice

Step 3: What is the equation after multiplying the numerators by the LCD.

 $\frac{3}{8}+2x=\frac{7}{4}$  

•  $\frac{24}{8}+2x=\frac{56}{4}$  

•  $\frac{12}{8}+\frac{8x}{1}=\frac{28}{4}$  

•  $\frac{24}{8}+\frac{16x}{1}=\frac{56}{4}$  

•  $\frac{12}{8}+8x=\frac{28}{4}$  

Multiple Choice

Step 4: What is the equation after reducing each fraction from: 

 $\frac{3}{8}+2x=\frac{7}{4}$  

•  $3+2x=14$  

•  $3+16x=14$  

•  $3+16x=52$  

Multiple Choice

Step 5: Last step is solving for the variable. 

 $3+16x=14$  

•  $x=\frac{17}{16}$  

•  $x=\frac{11}{16}$  

•  $x=\frac{2}{3}$  

The answer to the original equation of:

 $\frac{3}{8}+2x=\frac{7}{4}$  is  $x=\frac{11}{16}$  .

Now that we have successfully reviewed an equation in detail, step-by-step, please complete the next 8 problems, graded on correctness. 

Multiple Choice

What is the LCM of:

4 and 6

• LCM: 2

• LCM: 12

• LCM: 24

Multiple Choice

What is the LCM of:

8 and 18

• LCM: 54

• LCM: 36

• LCM: 72

Multiple Choice

What is the LCD of:

 $\frac{5}{4}x+\frac{3}{2}=\frac{5}{3}$  

• LCD: 6

• LCD: 24

• LCD: 12

Multiple Choice

Solve for x:

 $-\frac{2}{3}x+3=\frac{1}{6}$  

•  $x=4$  

•  $x=\frac{17}{4}$  

•  $x=-\frac{9}{4}$  

Multiple Choice

Solve for x:

 $\frac{x}{4}+\frac{11}{12}=\frac{1}{2}-\frac{x}{6}$  

•  $x=1$  

•  $x=-1$  

•  $x=17$  

•  $x=-17$  

Multiple Choice

Solve for x:

 $\frac{5}{8}x+\frac{1}{4}x+\frac{3}{4}=6$  

•  $x=5$  

•  $x=6$  

•  $x=7$  

Multiple Choice

Solve for x:

 $\frac{9}{4}x=\frac{5}{2}$  

•  $x=\frac{10}{9}$  

•  $x=\frac{9}{10}$  

•  $x=-\frac{9}{7}$  

•  $x=-\frac{7}{9}$  

Multiple Choice

Challenge problem: Hint-Use the correct LCD!
Solve for x:

 $\frac{1}{3x}-\frac{3}{4x}=\frac{5}{6}$  

•  $x=-2$  

•  $x=-\frac{1}{2}$  

•  $x=\frac{13}{10}$  

•  $x=2$  

You are done with today's lesson!

You make work on other assignments. Please stay live in Teams until the bell.