Equivalent Fraction:
An equivalent fraction is a fraction that represents the same value or quantity as another fraction, but with different numerator and denominator.

Given Fraction:
The given fraction is 45/60.

Equivalent Fraction:
To find an equivalent fraction with a denominator of 240 and a numerator of 135, we need to determine a common factor between 60 and 240 that can be used to multiply both the numerator and denominator of the given fraction.

Common Factor:
To find the common factor, we can list the factors of both 60 and 240.

Factors of 60:
The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.

Factors of 240:
The factors of 240 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, and 240.

Common Factor:
From the list of factors, we can see that the common factor between 60 and 240 is 60.

Multiplying the Fraction:
To find the equivalent fraction, we multiply both the numerator and denominator of the given fraction by the common factor.

Multiplying the Numerator:
The numerator of the given fraction is 45. Therefore, we multiply 45 by the common factor (60).

45 * 60 = 2700

Multiplying the Denominator:
The denominator of the given fraction is 60. Therefore, we multiply 60 by the common factor (60).

60 * 60 = 3600

Equivalent Fraction:
The equivalent fraction with a denominator of 240 and a numerator of 135 is 135/240.

Simplifying the Fraction:
To simplify the fraction, we can find the greatest common divisor (GCD) between the numerator and denominator.

Greatest Common Divisor:
The greatest common divisor (GCD) of 135 and 240 is 15.

Dividing the Numerator and Denominator:
To simplify the fraction, we divide both the numerator and denominator by the greatest common divisor (15).

135 ÷ 15 = 9
240 ÷ 15 = 16

Simplified Fraction:
The simplified equivalent fraction with a denominator of 240 and a numerator of 135 is 9/16.

Therefore, the fraction equivalent to 45/60 with a denominator of 240 and a numerator of 135 is 9/16.

9/16