Classify the following fractions:
a)$\frac{3}{2}$b)$3\frac{4}{5}$c)$\frac{4}{2}$d)$\frac{13}{4}$e)$\frac{7}{3}$f)$\frac{21}{5}$g)$\frac{1}{9}$h)$12\frac{3}{7}$i)$3\frac{39}{56}$
a)$\frac{3}{2}$- Proper Fraction
b)$3\frac{4}{5}$-Mixed Fraction
c)$\frac{4}{2}$-Improper Fraction
d)$\frac{13}{4}$-Improper Fraction
e)$\frac{7}{3}$-Improper Fraction
f)$\frac{21}{5}$-Improper Fraction
g)$\frac{1}{9}$-Proper Fraction
h)$12\frac{3}{7}$-Mixed Fraction
i)$3\frac{39}{56}$-Mixed Fraction
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- Solve:(a) \( \frac{1}{18}+\frac{1}{18} \)(b) \( \frac{8}{15}+\frac{3}{15} \)(c) \( \frac{7}{7}-\frac{5}{7} \)(d) \( \frac{1}{22}+\frac{21}{22} \)(e) \( \frac{12}{15}-\frac{7}{15} \)(f) \( \frac{5}{8}+\frac{3}{8} \)(g) \( 1-\frac{2}{3}\left(1=\frac{3}{3}\right) \)(h) \( \frac{1}{4}+\frac{0}{4} \)(i) \( 3-\frac{12}{5} \)
- Simplify:(i) \( \frac{-3}{2}+\frac{5}{4}-\frac{7}{4} \)(ii) \( \frac{5}{3}-\frac{7}{6}+\frac{-2}{3} \)(iii) \( \frac{5}{4}-\frac{7}{6}-\frac{-2}{3} \)(iv) \( \frac{-2}{5}-\frac{-3}{10}-\frac{-4}{7} \)(v) \( \frac{5}{6}+\frac{-2}{5}-\frac{-2}{15} \)(vi) \( \frac{3}{8}-\frac{-2}{9}+\frac{-5}{36} \)
- Re-arrange suitably and find the sum in each of the following:(i) \( \frac{11}{12}+\frac{-17}{3}+\frac{11}{2}+\frac{-25}{2} \)(ii) \( \frac{-6}{7}+\frac{-5}{6}+\frac{-4}{9}+\frac{-15}{7} \)(iii) \( \frac{3}{5}+\frac{7}{3}+\frac{9}{5}+\frac{-13}{15}+\frac{-7}{3} \)(iv) \( \frac{4}{13}+\frac{-5}{8}+\frac{-8}{13}+\frac{9}{13} \)(v) \( \frac{2}{3}+\frac{-4}{5}+\frac{1}{3}+\frac{2}{5} \)(vi) \( \frac{1}{8}+\frac{5}{12}+\frac{2}{7}+\frac{7}{12}+\frac{9}{7}+\frac{-5}{16} \)
- How quickly can you do this? Fill appropriate sign. ( '')(a) \( \frac{1}{2} \square \frac{1}{5} \)(b) \( \frac{2}{4} \square \frac{3}{6} \)(c) \( \frac{3}{5} \square \frac{2}{3} \)(d) \( \frac{3}{4} \square \frac{2}{8} \)(e) \( \frac{3}{5} \square \frac{6}{5} \)(f) \( \frac{7}{9} \square \frac{3}{9} \)(g) \( \frac{1}{4} \square \frac{2}{8} \)(h) \( \frac{6}{10} \square \frac{4}{5} \)(i) \( \frac{3}{4} \square \frac{7}{8} \)(j) \( \frac{6}{10} \square \frac{3}{5} \)(k) \( \frac{5}{7} \square \frac{15}{21} \)
- Write the following rational numbers in ascending order:$(i)$. $\frac{-3}{5},\ \frac{-2}{5},\ \frac{-1}{5}$$(ii)$. $\frac{1}{3},\ \frac{-2}{9},\ \frac{-4}{3}$$(iii)$. $\frac{-3}{7},\ \frac{-3}{2},\ \frac{-3}{4}$
- Multiply the following fractions:(i) $\frac{2}{5}\times5\frac{1}{4}$(ii) $6\frac{2}{5}\times\frac{7}{9}$(iii) $\frac{3}{2}\times5\frac{1}{3}$(iv) $\frac{5}{6}\times2\frac{3}{7}$(v) $3\frac{2}{5}\times\frac{4}{7}$(vi) $2\frac{3}{5}\times3$(vii) $3\frac{4}{7}\times\frac{3}{5}$
- Which is greater in each of the following:$(i)$. $\frac{2}{3},\ \frac{5}{2}$$(ii)$. $-\frac{5}{6},\ -\frac{4}{3}$$(iii)$. $-\frac{3}{4},\ \frac{2}{-3}$$(iv)$. $-\frac{1}{4},\ \frac{1}{4}$$(v)$. $-3\frac{2}{7\ },\ -3\frac{4}{5}$
- 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 \( \frac{3}{2} a b-\frac{7}{4} a c- \) \( \frac{5}{6} b c \)
- Solve:(i) $3-\frac{2}{5}$(ii) $4+\frac{7}{8}$(iii) $\frac{3}{5}+\frac{2}{7}$(iv) $\frac{9}{11}-\frac{4}{15}$(v) $\frac{7}{10}+\frac{2}{5}+\frac{3}{2}$(vi) $2\frac{2}{3}+3\frac{1}{2}$(vii) $8\frac{1}{2}-3\frac{5}{8}$
- Write each of the following as decimals:(a) \( \frac{5}{10} \)(b) \( 3+\frac{7}{10} \)(c) \( 200+60+5+\frac{1}{10} \)(d) \( 70+\frac{8}{10} \)(e) \( \frac{88}{10} \)(f) \( 4 \frac{2}{10} \)(g) \( \frac{3}{2} \)(h) \( \frac{2}{5} \)(i) \( \frac{12}{5} \)(j) \( 3 \frac{3}{5} \)(k) \( 4 \frac{1}{2} \)
- 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) \( 8 \frac{4}{9} \)
- Evaluate each of the following:(i) \( \frac{2}{3}-\frac{3}{5} \)(ii) \( \frac{-4}{7}-\frac{2}{-3} \)(iii) \( \frac{4}{7}-\frac{-5}{-7} \)(iv) \( -2-\frac{5}{9} \)(v) \( \frac{-3}{-8}-\frac{-2}{7} \)(vi) \( \frac{-4}{13}-\frac{-5}{26} \)(vii) \( \frac{-5}{14}-\frac{-2}{7} \).(viii) \( \frac{13}{15}-\frac{12}{25} \)(ix) \( \frac{-6}{13}-\frac{-7}{13} \)(x) \( \frac{7}{24}-\frac{19}{36} \)(xi) \( \frac{5}{63}-\frac{-8}{21} \)
- Using commutativity and associativity of addition of rational numbers, express each of the following as a rational number:(i) \( \frac{2}{5}+\frac{7}{3}+\frac{-4}{5}+\frac{-1}{3} \)(ii) \( \frac{3}{7}+\frac{-4}{9}+\frac{-11}{7}+\frac{7}{9} \)(iii) \( \frac{2}{5}+\frac{8}{3}+\frac{-11}{15}+\frac{4}{5}+\frac{-2}{3} \)(iv) \( \frac{4}{7}+0+\frac{-8}{9}+\frac{-13}{7}+\frac{17}{21} \)
- Find the value of:$(i)$. $(-4)\div\frac{2}{3}$$(ii)$. $-\frac{3}{5}\div2$$(iii)$. $-\frac{4}{5}\div(-3)$$(iv)$. $-\frac{1}{8}\div\frac{3}{4}$$(v)$. $-\frac{2}{13}\div\frac{1}{7}$$(vi)$. $-\frac{7}{12}\div(-\frac{2}{13})$$(vii)$. $\frac{3}{13}\div(-\frac{4}{65})$
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