simplify each expression . show cancelling and factoring .

Question

18/24

7rs^3/21r^2s

1/4 * 24x

 

Answer 1

18/24             divide both top and bottom by 6 to get 3/4

the factors would be 18 = 2*3*3        24 = 2*3*4

notice we have 2*3 in both numerator and denominator, therefore 6 would be common and the greatest common divisor.

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7rs³/21r²s

take the coefficients (numbers) first to get 1/3

next we have an r common to both top and bottom so we can factor out one(1) r.

that gives us 1s³/3rs

now we have an s common to both so factor out the s.

That leaves us with s²/3  the answer

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1/4 * 24x  Multiply fractions gives us 24x/4. divide top and bottom by 4 and we get 6x the answer

Answer 2

Find the greatest common factor among each expression:

     18/24     ==>     factors of 18:   1, 2, 3, 6, 9, 18

                              factors of 24:   1, 2, 3, 4, 6, 8, 12, 24

     18/24 = ( 6 (3))/( 6 (4)) = 3/4 

 

     7rs³/21r²s   ==>   greatest common factor among the numerator and the denominator is 7rs

     7rs³/21r²s = ( 7rs (s²))/( 7rs (3r)) = s²/3r

 

     (1/4)·(24x) = (1·24x)/4 = 24x/4   ==>   gcf among 24 and 4 is 4

     24x/4 = ( 4 (6x))/( 4 ) = 6x

Answer 3

The basic idea is to divide both numerator and denominator by the factors that they share:

18/24 = (3 * 6) / (4 * 6) = 3/4. Here, 6 is the shared factor.

7rs³/21r²s = (7 * rs * s²) / (3 * 7 * rs * r) = s² / 3r. Here, 7rs is the shared factor.

1/4 * 24x = 24x / 4 = 6x. Here, the shared factor is 4.

Answer 4

18/24 Write the prime factorization of both the numerator and denominator (2)(3)(3)/(2)(2)(2)(3). Eliminate factors that appear in BOTH the numerator and denominator (2)(3)(3)/(2)(2)(2)(3) = 3/4.

7rs³/21r²s  Write the prime factorization of both the numerator and denominator 7 r s s / (3)(7) r r s. Eliminate factors that appear in BOTH the numerator and denominator 7 r s s / (3)(7) r r s  = s/3r

1/4 * 24x Write the prime factorization of and combine 1/(2)(2) * (2)(2)(2)(3)x/1 = (2)(2)(2)(3)x/(2)(2). Eliminate factors that appear in BOTH the numerator and denominator (2)(2)(2)(3)x/(2)(2) = 6x. Remember that when all factors in the denominator are eliminated, the resulting denominator is 1, not 0!