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Place Values

A fraction eq...

Question

A fraction equivalent to $\frac{2}{3}$ is

(a) $\frac{2 + 3}{3 + 3}$
(b) $\frac{2 - 1}{3 - 1}$
(c) $\frac{2 \times 5}{3 \times 5}$
(d) $\frac{2 + 5}{3 + 5}$

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Solution

Fraction equivalent to a given fraction can be obtained by multiplying or dividing its numerator and denominator by a non-zero number.

Therefore, the fraction equivalent to $\frac{2}{3}$ is $\frac{2 \times 5}{3 \times 5}$ .

Hence, the correct option is (c).

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Q. Find the sum of

1^{3} + 2^{3} + \frac{3^{3}}{⌊ 2} + \frac{4^{3}}{⌊ 3} + \frac{5^{3}}{⌊ 4} + . . . .

1^{3} + 2^{3} + 3^{3} + 4^{3} + 5^{3} + . . . . . . . . + n^{3}

\int \frac{1}{5 + 4 \sin x} d x = A \tan^{- 1} (B \tan \frac{x}{2} + \frac{4}{3}) + C,

\frac{2}{3}

\frac{5}{3}

\frac{1}{3}

\frac{2}{3}

- \frac{2}{3}

\frac{5}{3}

\frac{1}{3}

- \frac{5}{3}

2^{3} \times 3^{3} \times 7^{2}

b = 2^{2} \times 3^{2} \times 5^{3},

{(\frac{2}{3})}^{- 5}

is equal to
(a)

{(\frac{- 2}{3})}^{5}

{(\frac{3}{2})}^{5}

\frac{2 x - 5}{3}

\frac{2}{3 \times 5}

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