Question

the denominator of a rational numbers is greater than its numerator by 7. If the numerator is increased by 4 and denominator is decreased by 8 the new rational numbers is 8/3​

Answer 1

Answer:

The answer is 4/11

Step-by-step explanation:

The steps are shown in the attachment.

Hope it helps!!

Answer 2

✯ The rational number = 4/11 ✯

Step-by-step explanation:

Given:

• The denominator of a rational number is greater than its numerator by 7.
• If the numerator is increased by 4 and denominator is decreased by 8, the new rational number is 8/3.

To find:

• The rational number.

Solution:

Let the numerator of the rational number be x .

✯ The denominator of a rational number is greater than its numerator by 7.

Then,

• Denominator = (x+7)

${\underline{\sf{According\:to\:the\: question,}}}$

• If the numerator is increased by 4 and denominator is decreased by 8, the new rational number is 8/3.

$: \implies \sf \: \dfrac{x + 4}{x + 7 - 8} = \dfrac{8}{3} \\ \\ : \implies \sf \: \dfrac{x + 4}{x - 1} = \dfrac{8}{3} \\ \\ : \implies \sf \: 8x - 8 = 3x + 12 \\ \\ : \implies \sf \: 8x - 3x = 12 + 8 \\ \\ : \implies \sf \: 5x = 20 \\ \\ : \implies \sf \: x = \dfrac{20}{5} \\ \\ : \implies \sf \: x = 4$

• Numerator = 4
• Denominator = (4+7) = 11

Therefore,

${\boxed{\sf{The\: rational\: number=\dfrac{4}{11}}}}$

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