Lesson

Unit 3 Lesson 1-3 Review

Unit 3 Lesson 1 Review

• Least Common Multiple (LCM)

• Least Common Denominator (LCD)

• Butterfly Method

Multiple Choice

What do you need first before finding the LCD?

• Numbers

• The LCM

• Fractions

Review on Butterfly Method:

1.) Make sure the two fractions are not written as mixed numbers, and fix that to improper if necessary.

2.) Move any negative symbols ( - ) to the number that is directly behind the symbol.

3.) Multiply on the two diagonals, and add the two products together- placed in the numerator.

4.) Multiply the two denominators together- placed in the denominator.

5.) Simplify and reduce.

Multiple Choice

Simplify:

$$3\frac{6}{7}+\frac{3}{2}$$  

• 11/2

• 7/6

• 75/14

• 115/24

Multiple Choice

Daniel watched a beetle and a spider on the sidewalk. The beetle crawled 7/8 of a yard and the spider crawled 1/6 of a yard.

How much farther did the beetle crawl than the spider?

• 25/24

• 17/24

• 21/24

• 2/3

Multiple Choice

Simplify:

$$\frac{7}{12}+\frac{3}{8}$$  

• $$\frac{10}{20}=\frac{1}{2}$$  

• $$\frac{92}{96}=\frac{23}{24}$$  
  

• $$\frac{96}{20}=\frac{23}{5}$$  

Multiple Choice

Convert the mixed number to an improper fraction:

$$7\ \frac{3}{5}$$  

• 15/5

• 38/5

• 3/35

• 10/5

Multiple Choice

Convert the mixed fraction to a improper fraction.

$$-4\frac{5}{3}$$  

• -17/3

• -7/3

• -12/3

• -23/3

Multiple Choice

A plumber is fitting a water pipe that is 3/4 foot long on to a water pipe that is 2/12 foot long. How long will the finished pipe be?

• 11/12 foot
• 8/16 foot
• 2/12 foot
• 1 foot

Multiple Choice

Sally ran 1/3 of a mile and swam 5/6 of a mile. In simplest form, how much farther did she swim than she ran?

• 1/2  mile

• 5/18 mile

• 4/3 mile

• 3/6 mile

Unit 3 Lesson 2 Review

• Least Common Multiple (LCM)

• Finding LCM long method.

• Cake Method: for finding the LCM short cut method.

Finding the LCM (long method)

1.) Know the two numbers you are trying to find the LCM of.

Example: 6 & 8

2.) List all the multiples of the first number:

Example: Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, ...

3.) Do this process again for the second number:

Example: Multiples of 8: 8,16, 24, 32, 40, 48, 56, 64, 72, 80, ...

4.) Find where the two list of multiples intersect at the same number.

Example: 24

LCM: Cake Method (short method)

1. Draw an L, and place the two integers inside the L box.

2. Pull out the greatest common factor of each number. (GCF is a number that goes INTO both numbers.)

3. Once you find the GCF, divide that into each number and restart the process.

4. When you reach the point where there isn't a GCF that works, you will multiply the outside numbers (GCF numbers) along with the remaining numbers below the line.

5. This number will become your LCM.

Example: Find the LCM of 18x²y³ & 27xy²

1. Find the GCF of 18x²y³ & 27xy², which is 9.

2. Now, there is no more GCF of 2 & 3, which involves the variables.

3. The GCF of x² & x is x.

4. The GCF of y³ & y² is y².

5. This lets 2xy & 3 be the remainders. We multiply everything together.

6. 9 * x * y² * 2xy * 3 = 54x²y

Multiple Choice

Find the LCM of 9 and 6

• 18

• 36

• 38

• 72

Multiple Choice

What is the LCM of 2x²y and 5xy²?

• 2xy

• 10x²y²

• 10xy

• 7x²y²

Multiple Choice

What is the LCM of 4a³b² and 10a²c?

• 40abc

• 20abc

• 20a³bc

• 20a³b²c

Multiple Choice

What is the LCM of 32 and 40?

• 180

• 160

• 140

• 200

Multiple Choice

What is the LCD of 1/7 and 3/6?

• 14

• 21

• 7

• 42

Multiple Choice

What integer is the LCD for these two fractions?

$$\frac{2}{3x}\ \&\ \frac{3}{4}$$  

• 24

• 12

• 7x

• 12x

Multiple Choice

If Juanita runs every third day and swims every fifth day, what is the first day that she will both run and swim again?

• Day 5

• Day 15

• Day 45

• Day 30

Multiple Choice

Choose the correct list of the first five multiples of 10.

• 1, 10, 20, 30, 40

• 10, 20, 30, 40, 50

• 1, 2, 5, 10

Multiple Choice

The multiples of 6 are:

1, 2, 3, 6, 12

• True

• False

Multiple Choice

What is the LCM of 6m⁵x and 8m³x³?

• 48mx

• 24m³x³

• 48m⁵x³

• 24m⁵x³

Unit 3 Lesson 3 Review

• Locate the denominators.

  
  

• Find the LCD. 

  
  

• Multiply the every single numerator by the LCD.

  
  

• Reduce the fractions.

  
  

• Solve for the variable.

For additional review of Clearing Fractions...

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Multiple Choice

What LCD would you use to clear the fraction?

$$\frac{5}{6}=\frac{3}{2}b-\frac{7}{3}b$$  

• LCD: 18

• LCD: 36

• LCD: 6

• LCD: 12

Multiple Choice

What is the first step to solve this equation after locating the denominators?

$$\frac{2}{3}x-7=\frac{1}{2}x+4$$  

• Move all the variables to one side.

• Move all the constants to one side.

• Find the least common denominator.

• Plug in a number for X.

Multiple Choice

How would you rewrite the equation after multiplying the LCD?

$$\frac{1}{2}x+5=\frac{3}{4}x+3$$  

• $$2x+20=3x+12$$  
  

• $$2x+5=3x+3$$  
  

• $$2x+20=4x+12$$  
  

Multiple Choice

Solve the equation for x:

$$\frac{5}{6}=\frac{3}{2}b-\frac{7}{3}b$$  

• b = 4

• b = 6

• b = -1

• b = -2

Multiple Choice

Solve the equation for x:

$$\frac{5}{3}-\frac{2}{8}x=\frac{7}{6}$$  

• x = 2

• x = 4

• x = - 3

• solution not listed

Multiple Choice

Solve the equation for x:

$$\frac{2}{3}x+\frac{1}{2}x=14$$  

• x = 1

• x = -2

• x = 8

• x = 12

Multiple Choice

Solve the equation for x:
$$\frac{4}{3x}+\frac{3}{2x}=\frac{5}{6}$$  

• $$x=\frac{33}{7}$$  
  

• $$x=\frac{16}{5}$$  
  

• $$x=\frac{8}{3}$$  
  

• Solution not listed.

This concludes your

Unit 3 Lesson 1-3 Review.

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