write the equivalent fraction of 78 /158 with denominator 39

write the equivalent fraction of 78 /158 with denominator 39

The Correct Answer and Explanation is:

To find an equivalent fraction for 78158\frac{78}{158}15878​ with a denominator of 39, we need to follow these steps:

1. Simplify the given fraction:
   We first simplify 78158\frac{78}{158}15878​. To do this, we need to find the greatest common divisor (GCD) of 78 and 158. The factors of 78 are:
   • 78 = 1, 2, 3, 6, 13, 26, 39, 78
   The factors of 158 are:
   • 158 = 1, 2, 79, 158
   The greatest common divisor (GCD) is 2, so we divide both the numerator and denominator by 2: 78158=78÷2158÷2=3979\frac{78}{158} = \frac{78 \div 2}{158 \div 2} = \frac{39}{79}15878​=158÷278÷2​=7939​
2. Rewrite with denominator 39:
   Now, we need to convert 3979\frac{39}{79}7939​ into a fraction with the denominator 39. To achieve this, we multiply the numerator and denominator of 3979\frac{39}{79}7939​ by a factor that makes the denominator 39. Since the denominator is 79 and we want to reduce it to 39, we need to find the factor by which 79 can be multiplied to get 39. This factor is: 3979\frac{39}{79}7939​ and multiplying the numerator and denominator both by 39 will give