Question

The numerator of a fraction is 3 less than its denominator. If 1 is added to the denominator, the fraction is decreased by 1/15. Represent the situation .​

Answer 1

Answer:

equation is: p/(q+1)= p/q - 1/15

fraction is: 2/23

Step-by-step explanation:

Let the fraction be: p/q

As per given condition:

• p= q-3
• q+1 ⇒ p/(q+1)= p/q - 1/15  this is the equation to represent the situation

solution:

• (q-3)/(q+1)= (q-3)/q - 1/15
• (q-3)/(q+1)= (15(q-3) - q)/15
• 15(q-3)= (q+1)(14q-45)
• 15q-45= 14q²- 45q+ 14q - 45
• 14q²= 46q
• 7q=23
• q= 23/7
• p= q-3= 23/7 - 3= 23/7 - 21/7= 2/7

The fraction is:

p/q= 2/7 ÷ 23/7 = 2/23