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CBSE Class 10 Mathematics Worksheet

UNIT I: Number systems - Real numbers

1.
Write 5/6 rational number in decimal form.
2.
The LCM of two numbers is 760 and their product is 6080. Find their HCF.
3.
Find the LCM and HCF of the 510 and 92 and verify that LCM × HCF = product of the two numbers.
4.
What number should be added to 3/8 to get -1/24?
5.
What is meant by rational number?
6.
Which of the rational numbers 4/9, -5/6, -7/-12 and 11/-24 is the smallest?
7.
What is meant by Irrational number?
8.
Find the LCM and HCF of the 26 and 91 and verify that LCM × HCF = product of the two numbers.
9.
Fill in the blanks: The union of the sets of all rational & irrational numbers is called the set of ________ numbers.
10.
Fill in the blanks: The decimal representation of the rational number 8/27 is ______.
11.
Fill in the blanks: The value of (- 16/21 ÷ -4/3) is ______.
12.
Fill in the blanks: All terminating decimal fractions represent _______ numbers.
13.
Fill in the blanks: The multiplicative inverse of -5 is ______.
14.

A box contains a total of 400 tickets that come in five colors: blue, green, red, yellow and orange. The ratio of blue to green to red tickets is 1: 2: 4. The ratio of green to yellow to orange tickets is 1 : 3: 6. How many tickets are there of each colour?

A)

32 blue, 16 green, 96 red, 64 yellow, and 192 orange tickets.

 B)

16 blue, 32 green, 64 red, 96 yellow, and 192 orange tickets.

 C)

192 blue, 96 green, 16 red, 64 yellow, and 32 orange tickets.

 D)

64 blue, 96 green, 16 red, 192 yellow, and 32 orange tickets.
15.
Fill in the blanks: 1/6 is a _____ number.
16.
Fill in the blanks: The reciprocal of a negative rational number _______.
17.
Fill in the blanks: Every point on the number line corresponds to a ______ number which may be either _____ or _____.
18.
Fill in the blanks: The decimal form of irrational number is neither _____ or _____
19.
Fill in the blanks: The value of {-8/13 × 26/-3} is _____
20.
Fill in the blanks: The product of conjugate binomial surds is always a ________ number.

CBSE Class 10 Mathematics Worksheet

UNIT I: Number systems - Real numbers

Answers

1.
0.833….
2.
We know that the product of two numbers is equal to the product of HCF and LCM of the numbers. HCF of the numbers × LCM of the numbers = Product of the numbers, HCF of the numbers = Product of the numbers/LCM of the numbers, = 6080/760 =8. Therefore, the HCF of the numbers is 8.



3.
The prime factors of 510 = 2 × 3 × 5 × 17, The prime factors of 92 = 2 × 2 × 23. Therefore, LCM = 2 × 2 × 3 × 5 × 17 × 23 = 23460 And, HCF = 2. LCM × HCF = 23460 × 2 = 46920, Product of given two Numbers = 510 × 92 = 46920, Therefore, LCM × HCF = Product of given two numbers

4.
-0.41666666670000002
5.
A number which can be written in the form a b where a and b are integers and b ? 0 is called a rational number.
6.
-0.83333333330000003
7.
A number which cannot be written in the form a b , where a and b are integers and b ? 0 is called a irrational number.
8.
The prime factors of 26 = 2 × 13, The prime factors of 91 = 7 × 13. Therefore, LCM = 2 × 7 × 13 = 182 And, HCF = 13. Now, LCM × HCF = 182 × 13 = 2366, Product of given numbers = 26 × 91 = 2366. Thus, LCM × HCF = Product of the given two numbers
9.
Real
10.
0.29599999999999999
11.
0.56999999999999995
12.
Rational
13.
-0.2
14.
Option B

Solution:

We denote the number of tickets of each of the five colours by the first letter of the colour. We are given that b : g : r = 1 : 2 : 4 and that g : y : o = 1 : 3 : 6. The first ratio tells us that b g = 1 2 , and so b = g 2 . The first ratio also tells us that g r = 2 4 , and so r = 2g. The second ratio tells us that g y = 1 3 , and so y = 3g. The second ratio also tells us that g o = 1 6 , and so o = 6g. We are given that there are a total of 400 tickets. That is, b + g + r + y + o = 400. Substituting b = g 2 , r = 2g, y = 3g, and o = 6g, this becomes g 2 + g + 2g + 3g + 6g = 400 25 2 g = 400 g = 32 Thus, b = g 2 = 16, r = 2g = 64, y = 3g = 96, and o = 6g = 192. Therefore, there are 16 blue, 32 green, 64 red, 96 yellow, and 192 orange tickets.


15.
Rational
16.
is a negative rational number
17.
Real, Rational, Irrational
18.
Recurring or Terminating
19.
5.33
20.
Rational
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