Mathematics solution NCERT
Class 9 - Chapter 3: The World of Numbers
Q1: Represent the rational numbers 2/3, -5/4 and 1 1/2 on a single number line.
Solution:
First convert the rational numbers into comparable forms:
| Rational Number | Decimal Form |
|---|---|
| -5/4 | -1.25 |
| 2/3 | 0.667 (approx.) |
| 1 1/2 | 1.5 |
On the number line:
←────────────────────────────────────────────────────────→
-2 -1 0 1 2
|--------|--------|--------|--------|
● ● ●
-5/4 2/3 1½
Answer: The points -5/4, 2/3 and 1½ are marked on the same number line as shown above.
Q2: Find three distinct rational numbers that lie strictly between -1/2 and 1/4.
Solution:
Write both rational numbers with a common denominator.
-1/2 = -4/8
1/4 = 2/8
Now choose any three fractions lying between -4/8 and 2/8.
-3/8, -2/8, 1/8
Simplifying:
-3/8, -1/4, 1/8
| Number | Value |
|---|---|
| -3/8 | -0.375 |
| -1/4 | -0.25 |
| 1/8 | 0.125 |
Answer: Three rational numbers are:
-3/8, -1/4, 1/8
Q3: Simplify the expression (-1/4) + (5/12).
Solution:
LCM of 4 and 12 = 12
-1/4 = -3/12
(-3/12) + (5/12)
= 2/12
= 1/6
Answer: 1/6
Q4: A tailor has 15 3/4 metres of fine silk. If making one kurta requires 2 1/4 metres of silk, exactly how many kurtas can he make?
Solution:
Convert the mixed fractions into improper fractions.
15 3/4 = 63/4
2 1/4 = 9/4
Number of kurtas = Total silk ÷ Silk required for one kurta
= (63/4) ÷ (9/4)
= (63/4) × (4/9)
= 63/9
= 7
Answer: The tailor can make 7 kurtas.
Q5: Find three rational numbers between 3.1415 and 3.1416.
Solution:
Write the numbers with one more decimal place.
3.1415 = 3.14150
3.1416 = 3.14160
Any numbers between them will be rational numbers.
Examples:
| Rational Numbers Between 3.1415 and 3.1416 |
|---|
| 3.14151 |
| 3.14152 |
| 3.14153 |
Answer:
3.14151, 3.14152, 3.14153
Q6: Can you think of other ways to find a rational number between any two rational numbers?
Solution:
Yes. One simple method is to find the average of the two rational numbers.
If two rational numbers are a and b, then
(a + b)/2
always lies between them.
Example:
Find a rational number between 2 and 4.
(2 + 4)/2
= 6/2
= 3
Therefore, 3 lies between 2 and 4.
Another method is to convert the rational numbers into equivalent fractions with larger denominators and then choose fractions between them.
Answer: Yes. The average method and equivalent-fraction method can be used to find rational numbers between any two rational numbers.