Worksheet on Properties of Multiplication of Rational Numbers
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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Introduction of Rational Numbers
Is Every Rational Number a Natural Number?
Is Every Rational Number an Integer?
Is Every Rational Number a Fraction?
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
Equality of Rational Numbers using Standard Form
Equality of Rational Numbers with Common Denominator
Equality of Rational Numbers using Cross Multiplication
Comparison of Rational Numbers
Rational Numbers in Ascending Order
Rational Numbers in Descending Order
Representation of Rational Numbers on the Number Line
Rational Numbers on the Number Line
Addition of Rational Number with Same Denominator
Addition of Rational Number with Different Denominator
Properties of Addition of Rational Numbers
Subtraction of Rational Number with Same Denominator
Subtraction of Rational Number with Different Denominator
Subtraction of Rational Numbers
Properties of Subtraction of Rational Numbers
Rational Expressions Involving Addition and Subtraction
Simplify Rational Expressions Involving the Sum or Difference
Multiplication of Rational Numbers
Properties of Multiplication of Rational Numbers
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Reciprocal of a Rational Number
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