Math Class: LCM and Fractions

Least Common Multiple (LCM)

• Find the LCM of 4 and 5: 20
• Find the LCM of 10 and 15: 30
• Find the LCM of 12 and 18: 36
• Find the LCM of 6 and 15: 30
• Find the LCM of x², y³, xy²: x²y³

Adding and Subtracting Fractions

• 1/4 + 3/8 =5/8
• 5/6 - 3/15 = 17/30
• 4/18 + 5/12 = 17/18
• 2/3 - 7/7 =2/3-1 = -1/3
• 1 1/3=4/3

Finding the Least Common Denominator (LCD)

• Find the LCD for 5/4ab and 3/10bc= 20abc
• Find the LCD for 3/8xy and 7/12x²=24x²y
• Find the LCD for 7/15a² and 3/10ab³= 30a²b³
• Find the LCD for 2a/a²-16 and 3/a²+a-12 = (a+4)(a-4)(a+4)(a-3) or (a+4)(a-4)(a+4)(a-3)=a^2-16 and a^2+a-12 = (a+4)(a-4)(a+4)(a-3) = (a+4)(a+4)(a-4)(a-3)

Procedure for Finding the LCD

• Factor each denominator completely.
• Compare the number of times each unique factor appears in each factorization.
• Write a factored form that includes each factor the greatest number of times it appears in the denominator factorizations.

Operations with Rational Expressions

• 5/4ab + 3/10bc = 25/20abc + 6/20abc =31/20abc

• 3/8xy - 7/12x² = 9/24x²y - 14/24x²y = -5/24x²y

• 7/15a² - 3/10ab³ =14/30a²b³ - 9/30a²b³ =5/30a²b³

• 2a/a²-16 + 3/a²+a-12=2a/(a-4)(a+4) +3/(a+4)(a-3)= 2a(a-3)+3(a-4)/ (a-4)(a+4)(a-3)

• (2a^2-6a+3a-12) / (a-4)(a+4)(a-3)

• 2x/5x² +3x/4xy= (8x/20x^2y) + (15x^2/20x^2y) = 23x^2 / 20x^2y)

• 3/x+2 + x/x²-4 -4/(x²+ 3x+2) =(3(x²-4) + x(x+2)-4(x+2)) /(x²-4)(x+2) = (3x²-12 + x²+2x-4x-8) / (x-2)(x+2)(x+2) = (4x²-2x-20)/(x²-4)(x+2)

• a/a+3 + 5/a = (a²+5a+15)/(a(a+3))

This quiz covers key concepts in mathematics, focusing on Least Common Multiple (LCM), adding and subtracting fractions, and finding the Least Common Denominator (LCD). Students will apply their understanding through various problems and procedures. Test your skills and reinforce your learning in these essential topics!