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bagirrra123 [75]
3 years ago
8

19. The numerator of a fraction is 1 less than the denominator.

Mathematics
1 answer:
yulyashka [42]3 years ago
5 0

Let the original fraction be

\dfrac{n-1}{n}

Now let's increase both numerator and denominator by 2:

\dfrac{n+1}{n+2}

This produces a 1/12 increase:

\dfrac{n+1}{n+2}-\dfrac{n-1}{n}=\dfrac{1}{12}

The left hand side can be rearranged as

\dfrac{2}{n^2+2n}=\dfrac{1}{12}

Invert both sides:

\dfrac{n^2+2n}{2}=12 \iff n^2+2n=24

Solve the quadratic equation:

n^2+2n-24=0 \iff n=-6 \lor n=4

So, in the first case, the original fraction is

\dfrac{n-1}{n}=\dfrac{-6-1}{-6}=\dfrac{7}{6}

In the second case, we have

\dfrac{n-1}{n}=\dfrac{4-1}{4}=\dfrac{3}{4}

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Let p: The whole number has one digit.
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The statement "The whole number has one digit if and only if the whole number is less than 10" is true for converse statement. Then the correct option is C.

<h3>What are converse statements?</h3>

A inverse statement is one that is derived by opposing the supposition and result of a relative clause.

Let p: The whole number has one digit.

Let q: The whole number is less than 10.

The statement "The whole number has one digit if and only if the whole number is less than 10" is true for converse statement.

If p → q, then, q → p

Then the correct option is C.

More about the converse statements link is given below.

brainly.com/question/18152035

#SPJ1

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