Express the following compound fraction in lowest terms:
9r2s
——————
7pq2
—————————
3r3s3
———————
14q5
Write as a division problem:
9r2s 3r3s3
—————— ÷ ———————
7pq2 14q5
Then we invert the second franction and change
the division to multiplication:
9r2s 14q5
—————— × ———————
7pq2 3r3s3
Multiply the tops and bottoms:
9·14r2sq5
————————————
7·3pq2r3s3
Cancel the 7 into the 14 and the 3 into the 9
3 2
9·14r2sq5
————————————
7·3pq2r3s3
1 1
or
6r2sq5
—————————
pq2r3s3
Give both the s on top and the p on the bottom exponents of 1
6r2s1q5
—————————
p1q2r3s3
Use this rule of division of exponentials with like bases:
Subtract exponents LARGER MINUS SMALLER, and place the result
in the numerator or denominator, depending of which contains
the larger exponent:
For the r's, the larger exponent is 3, of r3, and it is in the
bottom so we subtract the exponents 3-2, getting 1 and we place
r1 in the bottom and eliminate r from the top
6s1q5
——————————
p1q2r1s3
For the s's, the larger exponent is 3, of s3, and it is in the
bottom so we subtract the exponents 3-1, getting 2 and we place
s2 in the bottom and eliminate s from the top:
6q5
——————————
p1q2r1s2
For the q's, the larger exponent is 5, of q5, and it is in the
top so we subtract the exponents 5-2, getting 3 and we place
q3 in the top and eliminate q from the bottom:
6q3
————————
p1r1s2
Now we erase the 1 exponents on the p and r in the bottom:
6q3
——————
prs2
Edwin
AnlytcPhil@aol.com
