Class 9
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Mathematics
The World of Numbers
NCERT Solutions
NCERT Solutions
The World of Numbers
12 Solutions
Exercise:
All Exercises
Exercise Set 3.1
Exercise Set 3.2
Exercise Set 3.3
Q1
Exercise Set 3.1
A merchant in the port city of Lothal is exchanging bags of spices for copper ingots. He receives 15 ingots for every 2 bags of spices. If he brings 12 bags of spices to the market, how many copper ingots will he leave with?
Q2
Exercise Set 3.1
Look at the sequence of numbers on one column of the Ishango bone: 11, 13, 17, 19. What do these numbers have in common? List the next three numbers that fit this pattern.
Q3
Exercise Set 3.1
We know that Natural Numbers are closed under addition (the sum of any two natural numbers is always a natural number). Are they closed under subtraction? Provide a couple of examples to justify your answer.
Q4
Exercise Set 3.1
Ancient Indians used the joints of their fingers to count, a practice still seen today. Each finger has 3 joints, and the thumb is used to count them. How many can you count on one hand? How does this relate to the ancient base-12 counting systems?
Q1
Exercise Set 3.2
The temperature in the high-altitude desert of Ladakh is recorded as 4 °C at noon. By midnight, it drops by 15 °C. What is the midnight temperature?
Q2
Exercise Set 3.2
A spice trader takes a loan (debt) of ₹850. The next day, he makes a profit (fortune) of ₹1,200. The following week, he incurs a loss of ₹450. Write this sequence as an equation using integers and calculate his final financial standing.
Q3
Exercise Set 3.2
Calculate the following using Brahmagupta's laws:
(i)
(
−
12
)
×
5
(-12) \times 5
(
−
12
)
×
5
(ii)
(
−
8
)
×
(
−
7
)
(-8) \times(-7)
(
−
8
)
×
(
−
7
)
(iii)
0 - (-14)
(iv)
(
−
20
)
÷
4
(-20) \div 4
(
−
20
)
÷
4
Q4
Exercise Set 3.2
Explain, using a real-world example of debt, why subtracting a negative number is the same as adding a positive number (e.g.,
10
−
(
−
5
)
=
15
10 - (-5) = 15
10
−
(
−
5
)
=
15
).
Q1
Exercise Set 3.3
Prove that the following rational numbers are equal:
(i)
2
3
\frac{2}{3}
3
2
and
4
6
\frac{4}{6}
6
4
(ii)
5
4
\frac{5}{4}
4
5
and
10
8
\frac{10}{8}
8
10
(iii)
−
3
5
-\frac{3}{5}
−
5
3
and
−
6
10
-\frac{6}{10}
−
10
6
(iv)
9
3
\frac{9}{3}
3
9
and 3
Q2
Exercise Set 3.3
Find the sum:
(i)
2
5
+
3
10
\frac{2}{5}+\frac{3}{10}
5
2
+
10
3
(ii)
7
12
+
5
8
\frac{7}{12}+\frac{5}{8}
12
7
+
8
5
(iii)
−
4
7
+
3
14
-\frac{4}{7}+\frac{3}{14}
−
7
4
+
14
3
Q3
Exercise Set 3.3
Find the difference:
(i)
5
6
−
1
4
\frac{5}{6}-\frac{1}{4}
6
5
−
4
1
(ii)
11
8
−
3
4
\frac{11}{8}-\frac{3}{4}
8
11
−
4
3
(iii)
−
7
9
−
(
−
2
3
)
-\frac{7}{9}-\left(-\frac{2}{3}\right)
−
9
7
−
(
−
3
2
)
Q4
Exercise Set 3.3
Find the product:
(i)
2
3
×
3
10
\frac{2}{3} \times \frac{3}{10}
3
2
×
10
3
(ii)
7
11
×
5
8
\frac{7}{11} \times \frac{5}{8}
11
7
×
8
5
(iii)
−
4
7
×
5
14
-\frac{4}{7} \times \frac{5}{14}
−
7
4
×
14
5
More from this chapter
Chapter overview
Important Points
Practice Questions
Flashcards