How $\frac{3}{5}$ and $\frac{2}{3}$ is less than $1$.

Academic Mathematics NCERT Class 9

Given: Fractions $\frac{3}{5}$ and $\frac{2}{3}$.

To do: To show how $\frac{3}{5}$ and $\frac{2}{3}$ are less than $1$.

Solution:

Given fractions are: $\frac{3}{5}$ and $\frac{2}{3}$

$\frac{3}{5}=3\div5=0.6>1$

$\frac{2}{3}=2\div3=0.666..>1$

Thus, $\frac{3}{5}>1$ and $\frac{2}{3}>1$.

Tutorialspoint

e

Updated on: 10-Oct-2022

31 Views

Verify:$\frac{-2}{5} + [\frac{3}{5} + \frac{1}{2}] = [\frac{-2}{5} + \frac{3}{5}] + \frac{1}{2}$
Solve(a) \( \frac{2}{3}+\frac{1}{7} \)(b) \( \frac{3}{10}+\frac{7}{15} \)(c) \( \frac{4}{9}+\frac{2}{7} \)(d) \( \frac{5}{7}+\frac{1}{3} \)(e) \( \frac{2}{5}+\frac{1}{6} \)(f) \( \frac{4}{5}+\frac{2}{3} \)(g) \( \frac{3}{4}-\frac{1}{3} \)(h) \( \frac{5}{6}-\frac{1}{3} \)(i) \( \frac{2}{3}+\frac{3}{4}+\frac{1}{2} \)(j) \( \frac{1}{2}+\frac{1}{3}+\frac{1}{6} \)(k) \( 1 \frac{1}{3}+3 \frac{2}{3} \)(l) \( 4 \frac{2}{3}+3 \frac{1}{4} \)(m) \( \frac{16}{5}-\frac{7}{5} \)(n) \( \frac{4}{3}-\frac{1}{2} \)
Simplify:\( 5 \frac{1}{4} \p 2 \frac{1}{3}-4 \frac{2}{3} \p 5 \frac{1}{3} \times 3 \frac{1}{2} \)
Find:(i) $\frac{2}{5}\div\frac{1}{2}$(ii) $\frac{4}{9}\div\frac{2}{3}$(iii) $\frac{3}{7}\div\frac{8}{7}$(iv) $2\frac{1}{3}\div\frac{3}{5}$(v) $3\frac{1}{2}\div\frac{8}{3}$(vi) $\frac{2}{5}\div1\frac{1}{2}$(vii) $3\frac{1}{5}\div1\frac{2}{3}$(viii) $2\frac{1}{5}\div1\frac{1}{5}$
Solve: $-\frac{2}{3}\ \times\ \frac{3}{5}\ +\ \frac{5}{2}\ -\ \frac{3}{5}\ \times\ \frac{1}{6}$
Simplify:$\frac{-2}{3}\times\frac{3}{5}+\frac{5}{2}-\frac{3}{5}\times\frac{1}{6}$.
$3\frac{1}{3} \ -\ \frac{2}{3}\left\{\frac{3}{10} \ +\ \frac{1}{2}\left( 3\ -\ \frac{3}{5}\right)\right\}$$$
Simplify: $[ ( \frac{3}{2})^{-2}-( \frac{1}{3})^{2}]\times( \frac{5}{3})^{-2}$.
Solve $7\frac{1}{3}\div \frac{2}{3}$ of $2\frac{1}{5}+1\frac{3}{8}\div 2\frac{3}{4}-1 \frac{1}{2}$.
Take away:(i) \( \frac{6}{5} x^{2}-\frac{4}{5} x^{3}+\frac{5}{6}+\frac{3}{2} x \) from \( \frac{x^{3}}{3}-\frac{5}{2} x^{2}+ \) \( \frac{3}{5} x+\frac{1}{4} \)(ii) \( \frac{5 a^{2}}{2}+\frac{3 a^{3}}{2}+\frac{a}{3}-\frac{6}{5} \) from \( \frac{1}{3} a^{3}-\frac{3}{4} a^{2}- \) \( \frac{5}{2} \)(iii) \( \frac{7}{4} x^{3}+\frac{3}{5} x^{2}+\frac{1}{2} x+\frac{9}{2} \) from \( \frac{7}{2}-\frac{x}{3}- \) \( \frac{x^{2}}{5} \)(iv) \( \frac{y^{3}}{3}+\frac{7}{3} y^{2}+\frac{1}{2} y+\frac{1}{2} \) from \( \frac{1}{3}-\frac{5}{3} y^{2} \)(v) \( \frac{2}{3} a c-\frac{5}{7} a b+\frac{2}{3} b c \) from \( \frac{3}{2} a b-\frac{7}{4} a c- \) \( \frac{5}{6} b c \)
Prove that:\( \frac{2^{\frac{1}{2}} \times 3^{\frac{1}{3}} \times 4^{\frac{1}{4}}}{10^{\frac{-1}{5}} \times 5^{\frac{3}{5}}} \p \frac{3^{\frac{4}{3}} \times 5^{\frac{-7}{5}}}{4^{\frac{-3}{5}} \times 6}=10 \)
Solve the following :$\frac{-2}{3} \times \frac{3}{5} + \frac{5}{2} - \frac{3}{5} \times \frac{1}{6}$
Using appropriate properties find.(i) \( -\frac{2}{3} \times \frac{3}{5}+\frac{5}{2}-\frac{3}{5} \times \frac{1}{6} \)(ii) \( \frac{2}{5} \times\left(-\frac{3}{7}\right)-\frac{1}{6} \times \frac{3}{2}+\frac{1}{14} \times \frac{2}{5} \).
Find five rational numbers between.(i) \( \frac{2}{3} \) and \( \frac{4}{5} \)(ii) \( \frac{-3}{2} \) and \( \frac{5}{3} \)(iii) \( \frac{1}{4} \) and \( \frac{1}{2} \).
Simplify:\( \frac{1}{2+\sqrt{3}}+\frac{2}{\sqrt{5}-\sqrt{3}}+\frac{1}{2-\sqrt{5}} \)

Kickstart Your Career

Get certified by completing the course

Get Started

Advertisements