Are the rational numbers -8-28 and 32-112 equivalent- Give reason-

Given rational numbers are 8/28 and 32/ 112 Standard form of 8/28 = 8 ÷ 4/28 ÷ 4 = 2/7 nbsp; nbsp; [∵ HCF of 8 and 28 = 4] And, Standard form of 32/ 1 ...

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Standard VII

Mathematics

Rational Numbers on a Number Line

Are the ratio...

Question

Are the rational numbers $\frac{- 8}{28}$ and $\frac{32}{- 112}$ equivalent? Give reason.

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Solution

Given rational numbers are $\frac{- 8}{28}$ and $\frac{32}{- 112}$
Standard form of $\frac{- 8}{28} = \frac{- 8 \div 4}{28 \div 4} = \frac{- 2}{7}$ [ $∵$ HCF of 8 and 28 = 4]

And,
Standard form of $\frac{32}{- 112} = \frac{32 \div 16}{- 112 \div 16}$ [ $∵$ HCF of 32 and 112 = 16]
$= \frac{2}{- 7} = \frac{- 2}{7}$
Yes
Since, the standard form of $\frac{- 8}{28}$ and $\frac{32}{- 112}$ are equal.
Hence, they are equivalent.

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Are the rational numbers −828 and 32−112 equivalent? Give reason.

Given rational numbers are −828 and 32−112 Standard form of −828=−8÷428÷4=−27 [∵ HCF of 8 and 28 = 4] And, Standard form of 32−112=32÷16−112÷16 [∵ HCF of 32 and 112 = 16] =2−7=−27 Yes Since, the standard form of −828 and 32−112 are equal. Hence, they are equivalent.

Are the rational numbers $\frac{- 8}{28}$ and $\frac{32}{- 112}$ equivalent? Give reason.