The role of 0 and 1 — lesson. Mathematics State Board, Class 8.

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எங்கள் ஆசிரியர்களுடன் 1-ஆன்-1 ஆலோசனை நேரத்தைப் பெறுங்கள். டாப்பர் ஆவதற்கு நாங்கள் பயிற்சி அளிப்போம்

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Zero \((0)\) is a rational number, and the sum of any rational number with zero\((0)\) results in the same rational number.

Thus,

(\frac{a}{b} + 0) = (0 + \frac{a}{b}) = \frac{a}{b}

, for every rational number

\frac{a}{b}

\(0\) is called the additive identity for rational numbers.

Example:

(i) Consider the rational number

\frac{3}{5}

Then, we have

(\frac{3}{5} + 0) = (0 + \frac{3}{5}) = \frac{3}{5}

(\frac{3}{5} + 0) = (\frac{3}{5} + \frac{0}{5}) = (\frac{3 + 0}{5}) = \frac{3}{5}

Therefore,

(\frac{3}{5} + 0) = (0 + \frac{3}{5}) = \frac{3}{5}

(ii) Consider the rational number

\frac{- 2}{3}

Then, we have

(\frac{- 2}{3} + 0) = (0 + \frac{- 2}{3}) = \frac{- 2}{3}

(\frac{- 2}{3} + 0) = (\frac{- 2}{3} + \frac{0}{3}) = (\frac{- 2 + 0}{3}) = \frac{- 2}{3}

Therefore,

(\frac{- 2}{3} + 0) = (0 + \frac{- 2}{3}) = \frac{- 2}{3}

One \((1)\) is a rational number and the product of any rational number with one \((1)\) result in the same rational number.

For any rational number

\frac{a}{b}

, we have

(\frac{a}{b} \times 1) = (1 \times \frac{a}{b}) = \frac{a}{b}

\(1\) is called the multiplicative identity for rational numbers.

Example:

(i) Consider the rational number

\frac{3}{4}

Then, we have

(\frac{3}{4} \times 1) = (1 \times \frac{3}{4}) = \frac{3}{4}

(\frac{3}{4} \times 1) = (\frac{3}{4} \times \frac{1}{4}) = (\frac{3 \times 1}{4}) = \frac{3}{4}

and

(1 \times \frac{3}{4}) = (\frac{1}{4} \times \frac{3}{4}) = (\frac{1 \times 3}{4}) = \frac{3}{4}

Therefore,

(\frac{3}{4} \times 1) = (1 \times \frac{3}{4}) = \frac{3}{4}

(ii) Consider the rational

\frac{- 9}{13}

Then, we have

(\frac{- 9}{13} \times 1) = (1 \times \frac{- 9}{13}) = \frac{- 9}{13}

(\frac{- 9}{13} \times 1) = (\frac{- 9}{13} \times \frac{1}{13}) = (\frac{- 9 \times 1}{13}) = \frac{- 9}{13}

and

(1 \times \frac{- 9}{13}) = (\frac{1}{13} \times \frac{- 9}{13}) = (\frac{1 \times (- 9)}{13}) = \frac{- 9}{13}

Therefore,

(\frac{- 9}{13} \times 1) = (1 \times \frac{- 9}{13}) = \frac{- 9}{13}

Did you find an error?

5. The role of 0 and 1