Practice the questions given in the worksheet on properties of multiplication of rational numbers. The questions are based on different properties of multiplication of rational numbers i.e. closure property, associative property, commutative property, existence of multiplicative inverse property, existence of multiplicative identity property, distributive property of multiplication over addition and multiplicative property of 0.
1. Multiply the rationals:
(i) 5/17 by 51/(60)
(ii) 6/11 by 55/36
(iii) 8/25 by 5/16
(iv) 6/7 by 49/36
2. Verify each of the following:
(i) 4/17 × (7)/9 = (7)/9 × 4/17
(ii) (8)/11 × 1/5 = 1/5 × (8)/11
(iii) (12)/5 × 7/(36) = 7/36 × (12)/5
(iv) 8 × (13)/12 = (13)/12 × (8)
3. Verify each of the following:
(i) (3/5 × 12/13) × 7/18 = 3/5 ×(12/13 × 7/8)
(ii) (13)/24 × {(12)/5 × 35/36} = {(13)/24 × (12)/5} × 35/36
(iii) {(9)/5 × (10)/3} × 21/4 = (9)/5 × {(10)/3 × 21/4}
4. Fill in the blanks:
(i) (23)/17 × 18/35 = 18/35 × (_____)
(ii) 38 × (7)/19 = (7)/19 × (_____)
(iii) {15/7 × 21/10} × (5)/6 = (_____) × {(21)/10 × (5)/6}
(iv) (12)/5 × {4/15 × 25/16} = {(12)/5 × (4/15) × (_____)
5. Find the multiplicative inverse of:
(i) 11/15
(ii) 5
(iii) 0/7
(iv) 2/5
(v) (1)/8
6. Verify the following rational numbers using the multiplication
properties:
(i) 3/7 × {5/6 + 12/13} = (3/7 × 5/6) + (3/7 × 12/13)
(ii) 15/4 × (3/7 + (12)/5) = (15/4 × 3/7) + (15/4 × (12)/5)
(iii) (8/3 + 13/12) × 5/6 = (8/3 × 5/6) + (13/12 × 5/6)
(iv) 16/7 × {8/9 + (7)/6} = (16/7 × (8)/9) + ((16)/7 × 7/6)
7. Name the property of multiplication illustrated by the
following statements:
(i) 11/13 × 17/5 = 17/5 × 11/13
(ii) {(2)/3 × 7/9} × (9)/5 = (2)/3 × {7/9 × (9)/5}
(iii) (3)/4 × {(5)/6 + 7/8 = {(3)/4 × (5)/6} + {(3)/4 × 7/8}
(iv) (16)/9 × 1 = 1 × (16)/9 = (16)/9
(v) (11)/15 × 15/11 = 15/11 × (11)/15 = 1
(vi) 7/5 × 0 = 0
Answers for the worksheet on properties of multiplication of rational numbers are given below to check the exact answers of the above questions.
Answers:
1. (i) 1/4
(ii) 5/6
(iii) 1/10
(iv) 7/6
4. (i) 23/17
(ii) 38
(iii) 15/7
(iv) 25/16
5. (i) 15/11
(ii) 1/5
(iii) Does not exist
(iv) 5/2
(v) 8/1
7. (i) Commutative property
(ii) Associative property
(iii) Distributive property
(iv) Property of multiplicative identity
(v) Property of multiplicative inverse
(vi) Multiplicative property of 0
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● Rational Numbers
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Is Every Rational Number an Integer?
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Equivalent form of Rational Numbers
Rational Number in Different Forms
Properties of Rational Numbers
Lowest form of a Rational Number
Standard form of a Rational Number
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Comparison of Rational Numbers
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Rational Numbers in Descending Order
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Rational Numbers on the Number Line
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Subtraction of Rational Number with Different Denominator
Subtraction of Rational Numbers
Properties of Subtraction of Rational Numbers
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Properties of Division of Rational Numbers
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