Question

A rational number is such that when you multiply it by 5/ 2 and add 2/3 to the product, you get -7/12 . What is the number?​

Answer 1

Question:

• A rational number is such that when you multiply it by 5/2 and add 2/3 to the product, you get -7/12. What is the number?

Answer:

• Required number is -1/2.

Explanation:

Given that:

• A rational number is such that when you multiply it by 5/2 and add 2/3 to the product, you get -7/12.

To Find:

• What is the number?

Solution:

• Let the number be m.

According to the question,

• If we multiply it by 5/2 and add 2/3 to the product, we get -7/12.

Therefore,

⇒ $\sf \Bigg\{m\:\times\:\dfrac{5}{2}\Bigg\} + \dfrac{2}{3} = \dfrac{-7}{12}$

$\:$

⇒ $\sf \dfrac{5}{2}m + \dfrac{2}{3} = \dfrac{-7}{12}$

$\:$

⇒ $\sf \dfrac{5}{2}m = \dfrac{-7}{12} - \dfrac{2}{3}$

$\:$

⇒ $\sf \dfrac{5}{2}m = \dfrac{-7}{12} - \dfrac{2\:\times\:4}{3\:\times\:4}$

$\:$

⇒ $\sf \dfrac{5}{2}m = \dfrac{-7}{12} - \dfrac{8}{12}$

$\:$

⇒ $\sf \dfrac{5}{2}m = \dfrac{-7 - 8}{12}$

$\:$

⇒ $\sf \dfrac{5}{2}m = {\cancel{\dfrac{-15}{12}}}$

$\:$

⇒ $\sf \dfrac{5}{2}m = \dfrac{-5}{4}$

$\:$

⇒ $\sf m = \dfrac{-\cancel{5}}{\cancel{4}}\:\times\:\dfrac{\cancel{2}}{\cancel{5}}$

$\:$

⇒ $\sf m = \dfrac{-1}{2}\:\times\:\dfrac{1}{1}$

$\:$

⇒ $\sf m = \dfrac{-1\:\times\:1}{2\:\times\:1}$

$\:$

➠ $\bf\red{m = \dfrac{-1}{2}}$

$\large{\boxed{\sf{\therefore\:Required\:number = \dfrac{{\textsf{\textbf{-1}}}}{{\textsf{\textbf{2}}}}}}}$

Let's Verify:

We know that,

↦ $\sf \Bigg\{m\:\times\:\dfrac{5}{2}\Bigg\} + \dfrac{2}{3} = \dfrac{-7}{12}$

$\:$

Put m = -1/2 in above equation we get,

↦ $\sf \Bigg\{\dfrac{-1}{2}\:\times\:\dfrac{5}{2}\Bigg\} + \dfrac{2}{3} = \dfrac{-7}{12}$

$\:$

↦ $\sf \Bigg\{\dfrac{-1\:\times\:5}{2\:\times\:2}\Bigg\} + \dfrac{2}{3} = \dfrac{-7}{12}$

$\:$

↦ $\sf \dfrac{-5}{4} + \dfrac{2}{3} = \dfrac{-7}{12}$

$\:$

↦ $\sf \dfrac{-5\:\times\:3}{4\:\times\:3} + \dfrac{2\:\times\:4}{3\:\times\:4} = \dfrac{-7}{12}$

$\:$

↦ $\sf \dfrac{-15}{12} + \dfrac{8}{12} = \dfrac{-7}{12}$

$\:$

↦ $\sf \dfrac{-15 + 8}{12} = \dfrac{-7}{12}$

$\:$

↦ $\sf \dfrac{-7}{12} = \dfrac{-7}{12}$

$\:$

➦ $\bf\purple{LHS = RHS}$

$\large{\boxed{\sf{Hence,\:Verified\:\checkmark}}}$

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

Answer 2

Answer:

Given :-

• A rational number is such that when you multiply it by 5/2 and add 2/3 to the product, You get -7/12.

♧ To find :-

• What is the number.

♧Solution :-

• Let here the rational number be x .

• According to the given question,

• We verifies that,

• When we multiply it by 5/12 and add 2/3 to the product you get,

• Here we an equation,

• That is,

• $\frac{5}{2} x + \frac{2}{3} = \frac{ - 7}{12}$

♧By solving we get that ,

• $\frac{5}{2} x = \frac{ - 7}{12} - \frac{2}{3}$
• $\frac{5}{2} x = \frac{ - 7}{12} - \frac{8}{12}$
• $\frac{5}{2} x = \frac{ - 15}{12}$
• $x = \frac{ - 15}{ \: \: \: 12} \times \frac{2}{5}$
• $x = \frac{ - 3}{ \: \: \: 6} = \frac{ - 1}{2}$

♧Therefore ,

• The ration number =x=-1/2.

♧Read for more information

• https://brainly.in/question/8574740?
• search on web.

♧Hope it helps u mate .

♧Thank you .