26
Represent the following integers
a). A gain af os. 1000
b 10kg below normal weight
Answers
Answered by
3
FRACTIONS AND DECIMALS
(A) Main Concepts and Results
• A fraction is either a proper fraction or an improper fraction.
• A proper fraction is a number representing a part of a whole. This whole may be a single object or a group of objects. An improper fraction is a number in which numerator is greater than denominator.
• A mixed fraction is a combination of a natural number and a proper fraction.
• Two fractions are multiplied by multiplying their numerators and denominators separately and writing the product as
product of numerators 2 3 2×3 6 productofdenominators. Forexample,5×4=5×4=20.
11
• A fraction acts as an operator ‘of ’. For example, 3 of 3 is 3 ×3=1.
• The product of two proper fractions is less than each of the fractions,
1111 11 Forexample, 2×3 = 6 and6 islessthanboth 2and 3.
• The product of a proper and an improper fraction is less than the improper fraction and greater than the proper fraction. For example,
133331 2×2 = 4 and 4 islessthan 2 butgreaterthan 2.
• The product of two improper fractions is greater than the two fractions.
3721 21 3 7 Forexample, 2×4 = 8 and 8 isgreaterthanboth 2 and 4.
15-04-2018
• The reciprocal of a non-zero fraction is obtained by interchanging
3 is 2 its numerator and denominator. For example, reciprocal of 2 3 .
• While dividing a whole number by a fraction, we multiply the whole
12 number with the reciprocal of that fraction. For example, 3 ÷ 2 =3× 1 .
• While dividing a fraction by a natural number, we multiply the fraction
111
by the reciprocal of the natural number. For example, ÷ 2 = ×
• While dividing one fraction by another fraction, we multiply the first
1113 fraction by the reciprocal of the other. For example, 2 ÷ 3 = 2 × 1 .
• While multiplying two decimal numbers, first multiply them as whole numbers. Count the number of digits to the right of the decimal point in both the decimal numbers. Add the number of digits counted. Put the decimal point in the product by counting the number of digits equal to sum obtained from its rightmost place. For example, 1.2 × 1.24 = 1.488.
• To multiply a decimal number by 10, 100 or 1000, we move the decimal point in the number to the right by as many places as many zeros (0) are the right of one. For example, 1.33 × 10 = 13.3.
• To divide a decimal number by a natural number, we first take the decimal number as natural number and divide by the given natural number. Then place the decimal point in the quotient as in the decimal
1.2 number. For example, 4 = 0.3
• To divide a decimal number by 10, 100 or 1000, shift the decimal point in the decimal number to the left by as many places as there
1.34
are zeros over 1, to get the quotient. For example, 100 = 0.0134
• While dividing one decimal number by another, first shift the decimal points to the right by equal number of places in both, to convert the divisor to a natural number and then divide. For example
1.44 = 14.4 = 1.2. 1.2 12
442
.
UNIT 2
FRACTIONS AND DECIMALS 27
15-04-2018
MATHEMATICS
(B) Solved Examples
In Examples 1 to 11, there are four options, out of which one is correct. Write the correct one.
Example 1:
Solution: Example 2:
Solution: Example 3:
Solution: Example 4:
Solution: Example 5:
Solution:
Savita is dividing 13 kg of sweets equally among her 4
seven friends. How much does each friend receive? (a) 3 kg (b) 1 kg (c) 1kg (d) 3 kg
4 4 2 28
Correct answer is (b)
If 34 of a number is 12, the number is (a)9 (b)16 (c)18
Correct answer is (b)
Product of fractions 72 and 59 is
(d) 32
(a) 2×5 (b) 2+5 (c) 2×9
7+9 2+9 5×7 7×9
(d) 2×5 Giventhat0Correct answer is (d)
which of the following is the smallest?
r +s q+r
Correct answer is (a)
The next number of the pattern 60, 30, 15, _______ is
(a) 10 (b) 5 (c) 15 Correct answer is (d)
(a) p+q (b) p+s (c) q+s
(d) r+s p+q
p+r
(d) 15 42
28 EXEMPLAR PROBLEMS
15-04-2018
Example 6:
Solution: Example 7:
Solution: Example 8:
Solution : Example 9:
Solution: Example 10:
Solution: Example 11:
Solution:
The decimal expression for 8 rupees 8 paise (in Rupees) is (a) 8.8 (b) 8.08 (c) 8.008 (d) 88.0
Correct answer is (b)
Each side of a regular hexagon is 3.5cm long. The
perimeter of the given polygon (a) 17.5cm (b) 21cm (c) Correct answer is (b)
2.5 ÷ 1000 is equal to
(a) 0.025 (b) 0.0025 (c) Correct answer is (b)
Which of the following has the
is
18.3cm (d) 20cm
0.2500 (d) 25000
smallest value?
2 (0.2)2 2 ÷0.01 (a) 0.0002 (b) 1000 (c) 2 (d) 100
UNIT 2
Correct answer is (a)
Which of the following has the
(a) 32 (b) 0.320 (c) 0.05 50
Correct answer is (a)
The largest of the following is
(a) 0.0001 (b) 1 (c) 1000
Correct answer is (d)
largest value?
3.2 (d) 3.2
0.05 50
(0.100)2 (d) 1 ÷0.1 10
In Examples 12 to 19, fill in the blanks to make the statement true. Example 12: A fraction acts as an operator___________
Solution: of
FRACTIONS AND DECI
(A) Main Concepts and Results
• A fraction is either a proper fraction or an improper fraction.
• A proper fraction is a number representing a part of a whole. This whole may be a single object or a group of objects. An improper fraction is a number in which numerator is greater than denominator.
• A mixed fraction is a combination of a natural number and a proper fraction.
• Two fractions are multiplied by multiplying their numerators and denominators separately and writing the product as
product of numerators 2 3 2×3 6 productofdenominators. Forexample,5×4=5×4=20.
11
• A fraction acts as an operator ‘of ’. For example, 3 of 3 is 3 ×3=1.
• The product of two proper fractions is less than each of the fractions,
1111 11 Forexample, 2×3 = 6 and6 islessthanboth 2and 3.
• The product of a proper and an improper fraction is less than the improper fraction and greater than the proper fraction. For example,
133331 2×2 = 4 and 4 islessthan 2 butgreaterthan 2.
• The product of two improper fractions is greater than the two fractions.
3721 21 3 7 Forexample, 2×4 = 8 and 8 isgreaterthanboth 2 and 4.
15-04-2018
• The reciprocal of a non-zero fraction is obtained by interchanging
3 is 2 its numerator and denominator. For example, reciprocal of 2 3 .
• While dividing a whole number by a fraction, we multiply the whole
12 number with the reciprocal of that fraction. For example, 3 ÷ 2 =3× 1 .
• While dividing a fraction by a natural number, we multiply the fraction
111
by the reciprocal of the natural number. For example, ÷ 2 = ×
• While dividing one fraction by another fraction, we multiply the first
1113 fraction by the reciprocal of the other. For example, 2 ÷ 3 = 2 × 1 .
• While multiplying two decimal numbers, first multiply them as whole numbers. Count the number of digits to the right of the decimal point in both the decimal numbers. Add the number of digits counted. Put the decimal point in the product by counting the number of digits equal to sum obtained from its rightmost place. For example, 1.2 × 1.24 = 1.488.
• To multiply a decimal number by 10, 100 or 1000, we move the decimal point in the number to the right by as many places as many zeros (0) are the right of one. For example, 1.33 × 10 = 13.3.
• To divide a decimal number by a natural number, we first take the decimal number as natural number and divide by the given natural number. Then place the decimal point in the quotient as in the decimal
1.2 number. For example, 4 = 0.3
• To divide a decimal number by 10, 100 or 1000, shift the decimal point in the decimal number to the left by as many places as there
1.34
are zeros over 1, to get the quotient. For example, 100 = 0.0134
• While dividing one decimal number by another, first shift the decimal points to the right by equal number of places in both, to convert the divisor to a natural number and then divide. For example
1.44 = 14.4 = 1.2. 1.2 12
442
.
UNIT 2
FRACTIONS AND DECIMALS 27
15-04-2018
MATHEMATICS
(B) Solved Examples
In Examples 1 to 11, there are four options, out of which one is correct. Write the correct one.
Example 1:
Solution: Example 2:
Solution: Example 3:
Solution: Example 4:
Solution: Example 5:
Solution:
Savita is dividing 13 kg of sweets equally among her 4
seven friends. How much does each friend receive? (a) 3 kg (b) 1 kg (c) 1kg (d) 3 kg
4 4 2 28
Correct answer is (b)
If 34 of a number is 12, the number is (a)9 (b)16 (c)18
Correct answer is (b)
Product of fractions 72 and 59 is
(d) 32
(a) 2×5 (b) 2+5 (c) 2×9
7+9 2+9 5×7 7×9
(d) 2×5 Giventhat0Correct answer is (d)
which of the following is the smallest?
r +s q+r
Correct answer is (a)
The next number of the pattern 60, 30, 15, _______ is
(a) 10 (b) 5 (c) 15 Correct answer is (d)
(a) p+q (b) p+s (c) q+s
(d) r+s p+q
p+r
(d) 15 42
28 EXEMPLAR PROBLEMS
15-04-2018
Example 6:
Solution: Example 7:
Solution: Example 8:
Solution : Example 9:
Solution: Example 10:
Solution: Example 11:
Solution:
The decimal expression for 8 rupees 8 paise (in Rupees) is (a) 8.8 (b) 8.08 (c) 8.008 (d) 88.0
Correct answer is (b)
Each side of a regular hexagon is 3.5cm long. The
perimeter of the given polygon (a) 17.5cm (b) 21cm (c) Correct answer is (b)
2.5 ÷ 1000 is equal to
(a) 0.025 (b) 0.0025 (c) Correct answer is (b)
Which of the following has the
is
18.3cm (d) 20cm
0.2500 (d) 25000
smallest value?
2 (0.2)2 2 ÷0.01 (a) 0.0002 (b) 1000 (c) 2 (d) 100
UNIT 2
Correct answer is (a)
Which of the following has the
(a) 32 (b) 0.320 (c) 0.05 50
Correct answer is (a)
The largest of the following is
(a) 0.0001 (b) 1 (c) 1000
Correct answer is (d)
largest value?
3.2 (d) 3.2
0.05 50
(0.100)2 (d) 1 ÷0.1 10
In Examples 12 to 19, fill in the blanks to make the statement true. Example 12: A fraction acts as an operator___________
Solution: of
FRACTIONS AND DECI
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