Zen F. answered • 12/07/20
Middle and High School Math Tutor
The numerator of a fraction is one less than the denominator. If the reciprocal of this fraction is added by 19/4, the answer will be 6. What is the original fraction?
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Translate each fact of the problem one step at a time.....
Use variable to REPRESENT unknown values....
Fact 1......The numerator of a fraction is one less that the denominator...so...
Let N represent the numerator and D represent the denominator...we have.....N=D-1 or D=N+1
Either the word problem is now represented as a math equation....
Fact 2.......If the reciprocal of this fraction is added by 19/4, the answer will be 6...we have...
Reciprocal is D/N....denominator over numerator.....added by 19/4...we have
D/N + 19/4 = 6
...........so from the word problem we have found two facts that represent the classic math problem of 2 equations and 2 unknowns as shown below....you can use various methods to find the unknowns....
D/N + 19/4 = 6
N=D-1
......let us solve this by substituting the N of the 2nd equation into the first like so.....
D / D-1 + 19/4 =6.....just to eliminate the fractions...we can multiply all terms by 4(D-1)...LCD...we get...
4D + 19D - 19 = 24D - 24.........combine like terms...to isolate the unknown to one side of the eqaution...
23D - 19 = 24D - 24.......
-23D -23D
-19 = D - 24
+24 +24
D = 5.........and N=D-1.....N=5-1=4......so D=5 and N=4........check the values with the facts of the equation...
...let's see....
Fact 1......The numerator of a fraction is one less that the denominator...so...N=4 and D=5....so that checks..
Fact 2.......If the reciprocal of this fraction is added by 19/4, the answer will be 6...we have...
5/4 + 19/4 = 24/4 = 6.........that also checks.....so the ORIGINAL fraction is 4/5...right??
