Podcast
Questions and Answers
What is the least common multiple (LCM) of the numbers 10 and 15?
What is the least common multiple (LCM) of the numbers 10 and 15?
What is the least common denominator (LCD) of the fractions 5/3 and 4/5?
What is the least common denominator (LCD) of the fractions 5/3 and 4/5?
When adding the fractions 1/4 and 3/8, what is the resulting value?
When adding the fractions 1/4 and 3/8, what is the resulting value?
Which of the following represents the steps to find the least common denominator (LCD) for the expressions 5/4ab and 3/10bc?
Which of the following represents the steps to find the least common denominator (LCD) for the expressions 5/4ab and 3/10bc?
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What is the result of performing the operation 2/x - 3/5 for the given values of x?
What is the result of performing the operation 2/x - 3/5 for the given values of x?
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Study Notes
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
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5/4ab + 3/10bc = 25/20abc + 6/20abc =31/20abc
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3/8xy - 7/12x2 = 9/24x2y - 14/24x2y = -5/24x2y
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7/15a2 - 3/10ab3 =14/30a2b3 - 9/30a2b3 =5/30a2b3
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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)
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(2a^2-6a+3a-12) / (a-4)(a+4)(a-3)
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2x/5x2 +3x/4xy= (8x/20x^2y) + (15x^2/20x^2y) = 23x^2 / 20x^2y)
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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)
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a/a+3 + 5/a = (a2+5a+15)/(a(a+3))
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Description
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!
