Equivalent Fractions?

Question

Express each fraction as an equivalent fraction in lowest terms:

1) 9x^2y over 27xy^2

2) 3a + 3b over 6

3) 9c^3 - 3c^2 over 9c^4

4) 4xy + 2y over 20xy

Answer 1

1) 9x^2y / 27xy^2 = x/3y (9xy is the common factor in numerator and denominator and cancels out)

2) 3a + 3b / 6 = a + b / 2 ( 3 is the common factor in numerator and denominator)

3) 9c^3 - 3c^2 / 9c^4 = 3c - 1 / 3c^2 (3c^2 is the common factor and the numerator becomes 3c^2 (3c - 1) and the denominator can be expressed as 3c^2 multiplied by 3c^2)

4) 4xy + 2y / 20xy = 2x + 1 / 10x (2y is the common factor between numerator and denominator)

I hope the solution is clearer now.

Answer 2

1)
9x^2y
____ =
27xy^2

9/27 = 1/3
x^2/x = x
y/y^2 = y^-1 = 1/y

x/3y ==> the answer
2)
3a + 3b / 6 =

(3(a + b))/6
since 3/6 = 1/2

(a + b)/2 ==> the answer

3)
9c^3 - 3c^2 / 9c^4 =

(3c^2(3c - 1))/ 9c^4 =
Since 3c^2/9c^4 = 1/3c^2

(3c - 1)/3c^2 ==> the answer

4)
4xy + 2y / 20xy =

2y(2x + 1)/ 20xy =
Since 2y/20xy = 1/10x
(2x + 1)/10x ==> the answer

Answer 3

1) 9 is the greatest common factor
1x/3y
2) 3 is the greatest common factor
a+b/2
3) 3c^2 is the GCF. 3c-1/3c^2 or -1/c
4) 2y is the GCF. 2x+1/10x or 1/10x