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Associative Property of Rational Numbers Video Lecture | Advance Learner Course: Mathematics (Maths) Class 7
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FAQs on Associative Property of Rational Numbers Video Lecture - Advance Learner Course: Mathematics (Maths) Class 7
| 1. What is the associative property of rational numbers? |  |
Ans. The associative property of rational numbers states that the grouping of numbers in an addition or multiplication operation does not affect the result. For addition, it can be expressed as (a + b) + c = a + (b + c), and for multiplication, it can be expressed as (a * b) * c = a * (b * c).
| 2. How does the associative property apply to rational numbers? | |
Ans. The associative property applies to rational numbers in the same way as it applies to whole numbers or integers. It allows us to change the grouping of numbers in an addition or multiplication operation without changing the sum or product. This property is useful in simplifying calculations and solving equations involving rational numbers.
| 3. Can you provide an example of the associative property of rational numbers in action? | |
Ans. Certainly! Let's consider the addition of three rational numbers: 1/2, 3/4, and 5/6. According to the associative property, (1/2 + 3/4) + 5/6 should give us the same result as 1/2 + (3/4 + 5/6).
Using the first grouping, (1/2 + 3/4) + 5/6, we can find the common denominator, which is 12. Then, we add the fractions: (6/12 + 9/12) + 10/12 = 15/12 + 10/12 = 25/12.
Using the second grouping, 1/2 + (3/4 + 5/6), we again find the common denominator, which is 12. Then, we add the fractions: 1/2 + (9/12 + 10/12) = 1/2 + 19/12 = 13/12.
As we can see, both calculations yield different numerical results. Therefore, the associative property does not hold for addition of rational numbers in this case.
| 4. Does the associative property hold for multiplication of rational numbers? | |
Ans. Yes, the associative property does hold for multiplication of rational numbers. For example, consider the multiplication of three rational numbers: 2/3, 4/5, and 6/7. According to the associative property, (2/3 * 4/5) * 6/7 should give us the same result as 2/3 * (4/5 * 6/7).
Using the first grouping, (2/3 * 4/5) * 6/7, we multiply the fractions: (8/15) * 6/7 = 48/105.
Using the second grouping, 2/3 * (4/5 * 6/7), we multiply the fractions: 2/3 * (24/35) = 48/105.
As we can see, both calculations yield the same result of 48/105. Therefore, the associative property holds for multiplication of rational numbers.
| 5. Can the associative property be applied to both addition and multiplication of rational numbers simultaneously? | |
Ans. No, the associative property cannot be applied to both addition and multiplication of rational numbers simultaneously. While the property holds true for either addition or multiplication individually, it does not hold true when applying both operations simultaneously to a group of rational numbers. The associative property specifically applies to a single operation at a time.
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