Which of the following is a smaller fraction?
a) $ \frac{4}{5} $
b) $ \frac{5}{3} $
c) $ \frac{5}{6} $
d) $ \frac{5}{2} $
Given :
Given numbers are $\frac{4}{5}$, $\frac{5}{3}$, $\frac{5}{6}$ and $\frac{5}{2}$.
To do:
We have to compare the given numbers.
Solution :
- To compare two or more rational numbers, convert the denominators of the rational numbers into the same number.
- Then compare the numerators of the rational numbers.
- The rational number in which the numerator is greater is the greater rational number.
L.C.M. of the denominators 5, 3, 6 and 2 is 30.
Therefore,
$\frac{4}{5}=\frac{4\times6}{5\times6}=\frac{24}{30}$
$\frac{5}{3}=\frac{5\times10}{3\times10}=\frac{50}{30}$
$\frac{5}{6}=\frac{5\times5}{6\times5}=\frac{25}{30}$
$\frac{5}{2}=\frac{5\times15}{2\times15}=\frac{75}{30}$
On comparing the numerators 24<25<50<75.
This implies, $\frac{24}{30}<\frac{25}{30}<\frac{50}{30}<\frac{75}{30}$
Therefore,
$\frac{4}{5}<\frac{5}{6}<\frac{5}{3}<\frac{5}{2}$.
a) $\frac{4}{5}$ is the smallest fraction.
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- Take away:\( \frac{6}{5} x^{2}-\frac{4}{5} x^{3}+\frac{5}{6}+\frac{3}{2} x \) from \( \frac{x^{3}}{3}-\frac{5}{2} x^{2}+\frac{3}{5} x+\frac{1}{4} \)
- If $cos\ A = \frac{4}{5}$, then the value of $tan\ A$ is(A) $\frac{3}{5}$(B) $\frac{3}{4}$(C) $\frac{4}{3}$(D) $\frac{5}{3}$
- Solve the following :$\frac{-2}{3} \times \frac{3}{5} + \frac{5}{2} - \frac{3}{5} \times \frac{1}{6}$
- Compare the fractions and put an appropriate sign.(a) \( \frac{3}{6} \square \frac{5}{6} \)(b) \( \frac{1}{7} \square \frac{1}{4} \)(c) \( \frac{4}{5} \square \frac{5}{5} \)(d) \( \frac{3}{5} \square \frac{3}{7} \)
- Express the following as improper fractions:(a) \( 7 \frac{3}{4} \)(b) \( 5 \frac{6}{7} \)(c) \( 2 \frac{5}{6} \)(d) \( 10 \frac{3}{5} \)(e) \( 9 \frac{3}{7} \)(f) \( 8 \frac{4}{9} \)
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- Solve the following:$(\frac{5}{3})^4 \times (\frac{5}{3})^4 \div (\frac{5}{3})^2$.
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- Solve the following:$3 \frac{2}{5} \div \frac{4}{5} of \frac{1}{5} + \frac{2}{3} of \frac{3}{4} - 1 \frac{35}{72}$.
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