## Skill Check IX: IITJEE Foundation Math

A) Arrange all the fractions in descending order:

i) $2\frac{3}{7}, \frac{5}{8}, 1 \frac{6}{11}, 3 \frac{2}{5}, \frac{1}{2}$

ii) $\frac{3}{4}, \frac{1}{2}, \frac{5}{6}, \frac{7}{12}, \frac{2}{3}$

iii) $2\frac{1}{10}, 2\frac{1}{5}, 2\frac{4}{5}, 3\frac{1}{2}, \frac{14}{15}$

iv) $3\frac{2}{7}, 3\frac{1}{5}, 3\frac{5}{16}, 3\frac{4}{11}, 3\frac{3}{11}$

v) $\frac{6}{13}, \frac{4}{7}, \frac{5}{9}, \frac{11}{20}, \frac{12}{25}$

B) Arrange the following fractions in ascending order:

i) $3 \frac{1}{8}, \frac{1}{3}, 2\frac{3}{5}, 1\frac{4}{13}, \frac{5}{7}$

ii) $\frac{3}{5}, \frac{7}{10}, \frac{11}{15}, \frac{2}{3}, \frac{1}{2}$

iii) $\frac{24}{25}, 1\frac{5}{7}, 1 \frac{1}{7}, 1 \frac{1}{3}. 1 \frac{1}{5}$

iv) $\frac{24}{25},1 \frac{5}{7}, 1 \frac{1}{7}, 1 \frac{1}{3}, 1 \frac{1}{5}$

v) $1\frac{3}{7}, 1 \frac{2}{5}, 1\frac{4}{9}, 1\frac{5}{11}, 1\frac{7}{11}$

vi) $\frac{1}{2}, \frac{5}{11}, \frac{4}{9}, \frac{13}{25}$

III) Evaluate the following fractions:

(i) $\frac{3}{11} + \frac{2}{11} + \frac{5}{11}$

(ii) $\frac{2}{7} + \frac{2}{3}$

(iii) $\frac{3}{5} +1 \frac{2}{5}$

(iv) $6\frac{1}{2} + 1\frac{2}{3} + 1\frac{5}{6}$

(v) $\frac{2}{9} = \frac{3}{7} + 1\frac{1}{3}$

(vI) $\frac{4}{11} + 2\frac{1}{2} + 3\frac{1}{4} + 2\frac{5}{11} + \frac{7}{44}$

IV) Evaluate the following fractions:

(i) $\frac{8}{13} -\frac{3}{13}$

(ii) $\frac{5}{7} - \frac{1}{2}$

(iii) $2\frac{2}{3} - 1\frac{1}{2}$

(iv) $\frac{7}{9} - \frac{3}{4}$

(v) $1\frac{3}{5} - \frac{4}{7}$

(vi) $2\frac{2}{6} - 1\frac{3}{5}$

V) Evaluate the following fractions:

(i) $\frac{3}{4} \times \frac{1}{2}$

(ii) $\frac{6}{11} \times 1\frac{2}{9}$

(iii) $\frac{2}{5} \times \frac{15}{16} \times \frac{8}{9}$

(iv) $\frac{6}{7} \times 3\frac{1}{2} \times 2\frac{1}{3}$

(v) $1\frac{5}{7} \times 2\frac{1}{10} \times 6\frac{1}{4}$

(vi) $5 \frac{1}{4} \times 3 \frac{1}{7} \times 2 \frac{2}{11}$

VI) Evaluate the following fractions:

(i) $\frac{3}{8} \div 1\frac{1}{2}$

(ii) $\frac{1}{4} \div \frac{1}{2}$

(iii) $\frac{3}{5} \div \frac{5}{3}$

(iv) $6\frac{3}{7} \div 1\frac{2}{7}$

(v) $3\frac{4}{7} \div \frac{5}{7}$

(vi) $4\frac{2}{3} \div \frac{4}{9}$

VII) Find the HCF of the following fractions:

(i) $\frac{1}{3}$ and $\frac{1}{2}$

(ii) $\frac{3}{4}$ and $\frac{2}{5}$

(iii) $\frac{3}{7}$ and $1\frac{5}{7}$

(iv) $\frac{15}{22}$ and $\frac{10}{11}$

(v) $1\frac{5}{7}$ and $1\frac{1}{35}$ and $2\frac{2}{5}$

(vi) $\frac{15}{16}, \frac{21}{40}$ and $\frac{9}{20}$

IX) Find the LCM of the following fractions:

(i) $\frac{1}{4}$ and $\frac{2}{3}$

(ii) $\frac{2}{3}$ and $\frac{4}{5}$

(iii) $\frac{2}{7}$ and $\frac{5}{14}$

(iv) $\frac{6}{11}$ and $\frac{9}{11}$

(v) $\frac{6}{5}, \frac{3}{5}, \frac{3}{4}, \frac{1}{3}$

(vi) $1\frac{1}{6}, 1\frac{5}{9}, \frac{21}{24}, 1\frac{9}{12}$

IX) Find the greatest fraction that divides $\frac{1}{6}$ and $2\frac{1}{2}$ exactly and also find the smallest fraction that can be divided by the given fractions.

X) Simplify the following expressions:

(i) $2\frac{3}{5} - [ \frac{2}{3} + \{ 2\frac{1}{3}-(1\frac{1}{2}- \overline{\frac{3}{5}-\frac{1}{2}})\}]$

(ii) $\frac{5}{8} \div 1 \frac{3}{7} \times \frac{2}{7} \div (3\frac{1}{6}-2\frac{1}{2})$

(iii) $\frac{7}{11} of (1\frac{3}{5}-\overline{1\frac{2}{5}-\frac{3}{7}})$

(iv) $7(\frac{3}{8} \div \frac{1}{4} - \frac{3}{7} - 1\frac{3}{4} of \frac{6}{7} \div 1\frac{1}{2})$

(v) $1\frac{4}{7} - \frac{6}{7}[1\frac{2}{3}-\frac{3}{4} \{ \frac{2}{3} \div (\frac{5}{9}-\frac{1}{3})\}]$

(vi) $\frac{1\frac{1}{2}}{1\frac{13}{14}} - \frac{1\frac{2}{11}}{1\frac{17}{22}}$

(vii) $\frac{2\div 1\frac{5}{7}-1\frac{3}{4}}{3\div 2\frac{1}{2}-\frac{4}{15}} + \frac{3 \hspace{0.1in} of \hspace{0.1in} 1\frac{1}{4}-3\frac{1}{8}}{2 \hspace{0.1in} of \hspace{0.1in} 2 \frac{2}{5}-4\frac{1}{5}}$

XI) In a village consisting of 150 females and 100 males, $\frac{1}{15}$ of all females and $\frac{1}{10}$ of all males are graduates. What fraction of all the villagers are graduates?

XII) $\frac{7}{11}$ of all the money in Mr Ghoshn’s bank account is Rs 98000/-. How much money does Mr Ghoshn have in his bank account?

XIII) A $116\frac{2}{3}$ m long cable is cut into equal pieces measuring $8\frac{1}{3}$ m each. How many such small pieces are there?

XIV) $\frac{1}{6}$ of a ship’s crew are deck officers, $\frac{1}{4}$ are engineers and stewards, and the rest are sailors. If there are 48 crew members in all, how many sailors are on board the ship?

XV) $\frac{2}{7}$ part of a road was paved on the first day, $\frac{1}{5}$ part on the second day, and $\frac{1}{3}$ part was paved on the third day. If $443\frac{1}{3}$ m was paved on the fourth day to complete the road, what is the total length of the road paved?

XVI) The perimeter of an isosceles trapezium measures $13\frac{7}{30}$ cm. If its unequal sides measure $3\frac{2}{5}$ cm and $5\frac{1}{6}$ cm, find the measure of its equal sides.

XVII) A father and his two sons construct a house for INR 525,000. The elder son contributes $\frac{3}{5}$ of his father’s contributions while the younger son contributes $\frac{1}{2}$ of his father’s contributions. How much do the three contribute individually?

XVIII) Ramu inherited $\frac{2}{9}$ of the money his grandfather left behind while his cousin Rakesh’s share was $\frac{1}{7}$. If Ramu’s share was Rs 60000/- more than Rakesh’s share, find how much money their grandfather left behind.

XIX) A, B and C receive a total of Rs 2016 as monthly allowance from their dad such that C gets $\frac{1}{2}$ of what A gets, and B gets $1\frac{2}{3}$ times C’s share. How much money do the three brothers get individually?

XX) $\frac{1}{4}$ studentts of a school come by school bus while $\frac{2}{5}$ students ride a bicycle to school. All the other students walk to school, of which $\frac{1}{3}$ walk on their own and the rest are escorted by an elder. If 196 students come to school walking on their own, how many students study in that school?

Regards,

Nalin Pithwa

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