Exercise 1E
Question 1
The product of two rational numbers is $-12$. If one of the number is $-8$, find the other.
Sol :
Question 2
Divide the sum of $\frac{3}{8}$ and $\frac{-5}{12}$ by the reciprocal of $\frac{-15}{8} \times \frac{16}{27}$.
Sol :
Question 3
By what rational number should $\frac{-15}{56}$ be divided to get $\frac{-5}{7}$ ?
Sol :
Question 4
The perimeter of an isosceles triangle is $10 \frac{3}{4} \mathrm{~cm}$. If one of its equal sides is $2 \frac{5}{6} \mathrm{~cm}$, find the third side.
Sol :
Question 5
The area of a rectangular table top is $5 \frac{3}{8} \mathrm{~m}^{2}$. If one of the sides measures $2 \frac{1}{4} \mathrm{~m}$, find the length of the other side.
Sol :
Question 6
A train covers $80 \frac{4}{5} \mathrm{~km}$ in 1 hour. How much distance will it cover is $4 \frac{3}{4}$ hours ?
Sol :
Question 7
What is the perimeter of a quadrilateral whose four sides measure $3 \frac{1}{6} \mathrm{~cm}, 2 \frac{3}{4} \mathrm{~cm}, 4 \frac{5}{12} \mathrm{~cm}$ and $2 \frac{1}{2} \mathrm{~cm}$.
Sol :
Question 8
If $\frac{1}{3}$ of a number exceeds its $\frac{2}{7}$ by 1 , find the number.
Sol :
Question 9
Rohit travelled $1 \frac{1}{8} \mathrm{~km}$ from home to school, $\frac{5}{6} \mathrm{~km}$ from school to skating rink, $\frac{2}{3} \mathrm{~km}$ from skating rink to work and $\frac{5}{16} \mathrm{~km}$ from work to his home. How many km did Rohit travel?
Sol :
Question 10
Concert tickets usually cost ₹ $120 \frac{4}{5}$ per person. For students they are priced at $\frac{1}{4}$ of the normal cost. How much will 6 tickets cost for students?
Sol :
Multiple Choice Questions (MCQs)
Question 11
If a triangle has a base of $10 \frac{3}{4} \mathrm{~cm}$ and a height of $15 \frac{3}{4} \mathrm{~cm}$, what is its area?
(a) $150 \frac{9}{16} \mathrm{~cm}^{2}$
(b) $75 \frac{9}{32} \mathrm{~cm}^{2}$
(c) $84 \frac{21}{32} \mathrm{~cm}^{2}$
(d) $150 \frac{9}{32} \mathrm{~cm}^{2}$
Sol :
Question 12
In the last three months Mr. Sharma lost $5 \frac{1}{2} \mathrm{~kg}$. gained $2 \frac{1}{4} \mathrm{~kg}$ and then lost $3 \frac{3}{4} \mathrm{~kg}$. If he now weighs $95 \mathrm{~kg}$, how much did Mr. Sharma weigh to begin with ?
(a) $100 \mathrm{~kg}$
(b) $102 \mathrm{~kg}$
(c) $106.5 \mathrm{~kg}$
(d) $104 \mathrm{~kg}$
Sol :
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