Question

1. If 1/2 is added to three times the reciprocal of a number, the result is 1. Find the number.

2. The numerator of the given fraction is 4 less than the denominator. If 5 is added to both numerator and denominator, the resulting fraction is equal to 5/7 . What is the original fraction?

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Answer 1

1. Say the reciprocal of the number is x.

Then:

1/2 + 3x = 1

3x = 1/2
/3 /3

x = 1/6

Since x is the reciprocal of a number, just flip it around to find the real number.

1/6 flipped = 6

So the number is 6.

2. So here we can look at the difference between 5 and 7, because even if you subtract 5 from both numerator and denominator the difference will stay the same.

It's two.

Now you want to find how much you have to multiply two by to get four.

2 * ? = 4

? = 2

So therefore you have to multiply the whole fraction by two to get a fraction with a denominator - numerator equal to 4

5/7 * 2/2 = 10/14

And then just subtract five from the numerator and denominator.

10 - 5 / 14 - 5

5 / 9 was the original fraction