Express each of the following rational numbers in standard form:

1. $\frac{299}{- 166}$

2. $\frac{- 27}{45}$

3. $\frac{- 14}{- 49}$

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Solution

1. To express $\frac{299}{- 166}$ in standard form.
Dividing the numerator and the denominator by 23,
$\frac{299}{- 166}$ = $\frac{(299 \div 23)}{(- 166 \div 23)}$
= $\frac{13}{- 7}$
Therefore, the standard form of the given number is $\frac{13}{- 7}$ .

2. To express $\frac{- 27}{45}$ in standard form.
Dividing the numerator and the denominator by 9,
$\frac{- 27}{45}$ = $\frac{(- 27 \div 9)}{(45 \div 9)}$
= $\frac{- 3}{5}$
Therefore, the standard form of the given number is $\frac{- 3}{5}$ .

3. To express $\frac{- 14}{- 49}$ in standard form.
The denominator is negative.
Therefore, multiplying the numerator and the denominator by (-1).
= $\frac{(- 14 \times (- 1))}{(45 \times (- 1))}$ = $\frac{14}{49}$
Now, dividing the numerator and the denominator by 7,
$\frac{14}{49}$ = $\frac{(14 \div 7)}{(49 \div 7)}$
= $\frac{2}{7}$
Therefore, the standard form of the given number is $\frac{2}{7}$ .

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\frac{- 14}{- 49}

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\frac{299}{- 161}

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Question 70 (ii)

Express the following rational number in its standard form:
$\frac{14}{- 49}$

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