Gujarat BoardEnglish MediumSTD 7MATHSRational Numbers1 Mark
MCQ
A rational number equal to $\frac{-2}{3}$ is:
A
$\frac{-10}{25}$
✓
$\frac{10}{-15}$
C
$\frac{-9}{6}$
D
None of these.
✓
Answer
Correct option: B.
$\frac{10}{-15}$
We know that two rational numbers are equal if they have the same standard form.
The rational number $\frac{-2}{3}$ is in its standard form.
Consider the rational number $\frac{10}{-15}$
This rational numbner can be expressed in standerd form as follows:
$\frac{10}{-15}=\frac{10\times(-1)}{-15\times(-1)}=\frac{-10}{15}$ (Multiplying numerator and denominator by $-1$ to make denominator positive)
$HCF$ of $10$ and $15 = 5$
Dividing the numeator and denominator of $\frac{-10}{15}$ by $5,$
We have:
$\frac{-10}{15}=\frac{-10\div5}{15\div5}=\frac{-2}{3}$
Thus, the standard form of $\frac{-10}{15}$ is $\frac{-2}{3},$ which is same as the given rational number.
So, the rational number equal to $\frac{-2}{3}$ is $\frac{-10}{15}$
Let us check why options (a) and $(c)$ are not correct.
The standard form of $\frac{-10}{25}\text{ is }\frac{-2}{5}$
$HCF$ of $10$ and $25 = 5$
Dividing the numerator and denominator of $=\frac{-10}{25}$ by $5,$
We have:
$\frac{-10}{25}=\frac{-10\div5}{25\div5}=\frac{-2}{5}$
The standard form of $\frac{-9}{6}\text{ is }\frac{-3}{2}$
$HCF$ of 6 and $9 = 3$
Dividing the numerator and denominator of $\frac{-9}{3}$by $3,$
We have:
$\frac{-9}{6}=\frac{-9\div3}{6\div2}=\frac{-3}{2}$
Hence, the correct answer is option $(b)$
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