Solved Examples on Multiplication of Rational Numbers
Example 1: Multiply the two rational numbers: 15/4, -8/5.
Solution:
Multiply numerators of both rational numbers = 15 × (-8) = -120
Multiply denominators of both rational numbers = 4 × 5 = 20
(15/4) × (-8/5) = [15 × (-8)] / [4 × 5]
(15/4) × (-8/5) = -120 / 20
Simplify the above number we get
(15/4) × (-8/5) = -6 / 1
(15/4) × (-8/5) = -6
Example 2: Find the length of rectangle given the area of rectangle is 63/ 50 sq. units and breadth of rectangle is 3/ 100 units.
Solution:
Area of rectangle = length × breadth
Let L be the length of rectangle.
63 / 50 = L × (3/10)
L = (63/50) × (10/3)
L = 21 / 5 units
The length of given rectangle is 21/ 5 units.
Example 3: If the product of two rational numbers is -24/25 and one rational Number is – 6/5. Find the second rational number.
Solution:
Let second number be y.
The multiplication of given rational numbers is:
(-6/5) × y = -24 / 25
y = (-24/25) × (-5/6)
y = 4 / 5
So, the second number is 4/5.
Example 4: Prove that: (1/9 × 5/ 3) = 5/3 × 1/9.
Solution:
LHS = (1/9 × 5/ 3)
(1/9 × 5/ 3) = (1 × 5) / (9 × 3) = 5 / 27
RHS = 5/3 × 1/9
5/3 × 1/9 = (5 × 1) / (3 × 9) = 5/ 27
LHS = RHS
Hence Proved
Example 5: Prove the associative law for multiplication of rational numbers (-21/2 × 3/ 5) × -7/ 6 = -21/2 × (3/ 5 × -7/ 6).
Solution:
LHS = (-21/2 × 3/ 5) × -7/ 6
(-21/2 × 3/ 5) × -7/ 6 = [(-21 × 3) / (2 × 5)] × -7/ 6
(-21/2 × 3/ 5) × -7/ 6 = (-63 / 10) × -7/ 6
(-21/2 × 3/ 5) × -7/ 6 = [(-63 × -7) / (10 × 6)]
(-21/2 × 3/ 5) × -7/ 6 = 441 / 60
RHS = -21/2 × (3/ 5 × -7/ 6)
-21/2 × (3/ 5 × -7/ 6) = -21/2 × [(3 × -7) / (6 × 5)]
-21/2 × (3/ 5 × -7/ 6) = -21/2 × (-21/ 30)
-21/2 × (3/ 5 × -7/ 6) = (-21 × -21) / (2 × 30)
-21/2 × (3/ 5 × -7/ 6) = 441 / 60
LHS = RHS
Hence Proved
Example 6: Calculate the multiplication of rational numbers given the multiplication of their numerators is 10 and the multiplication of denominators is -32.
Solution:
To calculate the multiplication of rational numbers we use formula:
Multiplication of Rational numbers = Multiplication of numerators / Multiplication of denominators
Multiplication of Rational numbers = 10 / (-32)
Multiplication of Rational numbers = -10 / 32
On simplifying we get,
Multiplication of Rational numbers = -5 / 16
Multiplication of Rational Numbers
For the multiplication of rational numbers, we take the numerators multiplication and the denominators multiplication and divide the numerator multiplication by denominator multiplication. Simplify the obtained result to get the multiplication of rational numbers. In this article we will cover the multiplication of rational numbers with basics of rational number. Also, we will discuss how to multiply rational numbers and solve some examples related to it.
Table of Content
- What are Rational Numbers?
- Multiplication of Rational Numbers
- Multiplication of Rational Numbers Formula
- How to Multiply Rational Numbers
- Solved Examples on Multiplication of Rational Numbers
- Practice Questions on Multiplication of Rational Numbers
- FAQs on Multiplication of Rational Numbers
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