Sum of the numerator and the denominator of a fraction is 3 less than twice the denominator. If the numerator and denominator are both decrease by 1, the numerator become half the denominator. Determine the fraction?

Question

3280 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-07T10:38:38

#4/7#

Let's say the fraction is #a/b#, numerator #a,# denominator #b#.

Sum of the numerator and the denominator of a fraction is 3 less than twice the denominator

#a+b=2b-3#

If the numerator and denominator are both decrease by 1, the numerator become half the denominator.

# a-1 = 1/2 (b-1)#

Now we do the algebra. We start with the equation we just wrote.

#2 a- 2 = b-1#

# b = 2a-1 #

From the first equation,

#a+b=2b-3#

#a=b-3#

We can substitute # b = 2a-1 # into this.

# a = 2a - 1 - 3 #

# -a = -4#

#a = 4#

#b = 2a-1=2(4)-1=7#

Fraction is

#a/b = 4/7#

Check:

*Sum of the numerator (4) and the denominator(7) of a fraction is 3 less than twice the denominator *

# (4)(7) = 2(7)-3 quad sqrt#

If the numerator (4) and denominator (7)are both decrease by 1, the numerator become half the denominator.

# 3 = 1/2 \( 6) quad sqrt#