Section 4 4 LCM and Equivalent Fractions Topics

Topics Covered Least Common Multiple Equivalent Fractions

Multiples vs Factors What is a multiple? o Commonly referred to as skip counting

GCF vs. LCM What is a Greatest Common Factor (GCF)? o When comparing numbers,

Finding the LCM with the TI-34 To find the LCM of 15 and 12;

Applications of LCM A patient admitted to the hospital was prescribed a pain medication

Example A tile floor is to be made from 10 -in, 12 -in, and

Equivalent Fractions are equivalent if they all represent the same portion of a whole.

$Cross Product Determines Equiv Fractions One method to show that two fractions are equivalent$

Finding Equiv Fractions Using Cross Products

Comparing Fractions Using Cross Products Example:

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Section 4. 4 LCM and Equivalent Fractions

Topics Covered Least Common Multiple Equivalent Fractions

Multiples vs Factors What is a multiple? o Commonly referred to as skip counting Example: Multiples of 2 (counting by 2’s) 2: 2, 4, 6, 8, … Multiples of 6 (counting by 6’s) 6: 6, 12, 18, 24, … What is a factor? o A number multiplied by another number to create a product Example: Factors of 12 {1, 2, 3, 4, 6, 12}

GCF vs. LCM What is a Greatest Common Factor (GCF)? o When comparing numbers, the GCF is the greatest number that divides evenly into both numbers o Used to reduce fractions What is the Least Common Multiple (LCM)? o When comparing numbers, the LCM is the smallest multiple of both numbers o LCM = LCD o LCM/LCD used to create equivalent fractions What is the GCF and LCM of: 8 and 10? 6 and 15?

Methods to Find LCD

Finding the LCM with the TI-34 To find the LCM of 15 and 12; 1. Press the [math] button 2. Press 1 for lcm( 3. Enter 15 4. Press the [2 nd] button 5. Press the [. ] decimal button 6. Enter 12 7. Press the [ ) ] button 8. Press [enter] Note: If you wish to find the lcm of 3 or more numbers you must first find the lcm of the first two numbers and then find the lcm of the answer and your third number. Find the lcm of; 10, 15, 8

Applications of LCM A patient admitted to the hospital was prescribed a pain medication to be given every 4 hr and an antibiotic to be given every 5 hr. Bandages applied to the patient’s external injuries needed changing every 12 hr. The nurse changed the bandages and gave the patient both medications at 6: 00 am Monday morning. How many hours will pass before the patient is given both medications and his bandages changed at the same time? What day and time will this be?

Example A tile floor is to be made from 10 -in, 12 -in, and 15 -in square tiles. A design is made by alternating rows with different-size tiles. The first row uses only 10 -in tiles, the second row uses only 12 -in tiles, and the third row uses only 15 -in tiles. Neglecting the grout seams, what is the shortest length of floor space that can be 1. 1800 in. covered evenly by each row? 2. 60 in. 3. 120 in. 4. 180 in.

Equivalent Fractions are equivalent if they all represent the same portion of a whole.

$Cross Product Determines Equiv Fractions One method to show that two fractions are equivalent$

Cross Product Determines Equiv Fractions One method to show that two fractions are equivalent is to calculate their cross products.

Finding Equiv Fractions Using Cross Products

Comparing Fractions Using Cross Products Example:

Find Equiv Fractions with Variables