What should be added to twice the rational number – 7/3 to get 3/7?
Answers
Answer:
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Step-by-step explanation:
Let the rational number be \frac{a}{b}
b
a
.
Now, an equation can be formed.
Solve and find the value of \frac{a}{b}
b
a
.
2( \frac{-7}{3} ) + \frac{a}{b} = \frac{3}{7}2(
3
−7
)+
b
a
=
7
3
\frac{-14}{3} + \frac{a}{b} = \frac{3}{7}
3
−14
+
b
a
=
7
3
- \frac{14}{3} + \frac{a}{b} = \frac{3}{7}−
3
14
+
b
a
=
7
3
\frac{a}{b} = \frac{3}{7} + \frac{14}{3}
b
a
=
7
3
+
3
14
\frac{a}{b} = \frac{107}{21}
b
a
=
21
107
∴ The required rational number is \frac{107}{21}
21
107
.
Step-by-step explanation:
Answer and Explanation:
Let us consider, a number
x
.
We can write
x
added to twice the rational number
−
7
3
to get
3
7
as
x
+
2
(
−
7
3
)
=
3
7
Now we can solve the equation to get the value of the unknown variable,
x
+
2
(
−
7
3
)
=
3
7
⇒
x
−
14
3
=
3
7
Multiply
21
to the both sides:
⇒
21
x
−
21
14
3
=
21
3
7
Simplify:
⇒
21
x
−
98
=
9
Add
98
to the both sides:
⇒
21
x
−
98
+
98
=
9
+
98
⇒
21
x
=
107
Divide both sides by
21
:
⇒
21
x
21
=
107
21
⇒
x
=
107
21
Therefore, the rational number is
107
21