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Exercise 1.4 class 8 solution – exercise preview
Rational numbers are real numbers that can be expressed as fractions of two integers, where the denominator is not zero. Various operations can be performed on rational numbers, just like on other real numbers. Here are the primary operations performed on rational numbers:
- Addition: To add two or more rational numbers, find a common denominator, express them with the common denominator, add the numerators, and then simplify the result if needed.
- Subtraction: Subtracting rational numbers involves a similar process as addition but subtracting the numerators instead of adding.
- Multiplication: To multiply rational numbers, multiply the numerators together and the denominators together. Simplify the result if necessary.
- Division: To divide rational numbers, take the reciprocal (invert) of the second number and then multiply. In other words, division is the same as multiplying by the reciprocal. Remember that division by zero is undefined.
- Exponentiation: Rational numbers can be raised to integer exponents. For example, (a/b)^n is computed by raising both the numerator and denominator to the power of “n.”
- Simplification: Rational numbers can often be simplified by finding the greatest common
- divisor (GCD) of the numerator and denominator and dividing both by it to reduce the fraction to its simplest form.
- Comparisons: You can compare rational numbers using inequality symbols (<, >, ≤, ≥) to determine which number is larger or smaller.
- Additive Inverse: The additive inverse of a rational number a is -a, such that a + (-a) = 0.
- Multiplicative Inverse: The multiplicative inverse (reciprocal) of a non-zero rational number a is 1/a, such that a * (1/a) = 1.
- Order of Operations: Rational numbers follow the standard order of operations (PEMDAS/BODMAS) for performing operations within expressions.
- These operations are fundamental in mathematics and are used in various mathematical applications, such as solving equations, working with proportions, and performing calculations in science and engineering. Exercise 1.4 class 8 solution with explanation are provided here.
Exercise 1.4 class 8 solution pdf
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Exercise 1.4 class 8 solution-Commutative property of rational number under division
The commutative property does not hold for division with rational numbers, as it does for addition and multiplication. The commutative property of division does not exist for rational numbers. This property specifically refers to the order in which numbers are operated on, and for division, changing the order of numbers does change the result.
In other words, for rational numbers a and b:
a ÷ b is not necessarily equal to b ÷ a.
Division is not commutative; changing the order of the numbers in a division expression can result in different outcomes. For example, if you have the rational numbers 2/3 and 3/4:
(2/3) ÷ (3/4) is not equal to (3/4) ÷ (2/3).
(2/3) ÷ (3/4) = (2/3) * (4/3) = 8/9 (3/4) ÷ (2/3) = (3/4) * (3/2) = 9/8
The results are not the same, so the commutative property does not apply to division for rational numbers. Exercise 1.4 class 8 solution
Exercise 1.4 class 8 solution-Associative property of rational number under division
The associative property of division doesn’t hold for rational numbers (or for real numbers in general). The associative property specifically refers to the ability to group numbers and perform the same operation regardless of how they are grouped. For division, changing the grouping of numbers can significantly change the result, so division is not associative.
In other words, for rational numbers a, b, and c:
(a ÷ b) ÷ c is not necessarily equal to a ÷ (b ÷ c).
Changing the grouping in a division expression can lead to different outcomes. For example, if you have the rational numbers 2/3, 1/4, and 2:
- (2/3 ÷ 1/4) ÷ 2 = (8/3) ÷ 2 = 4/3
- 2/3 ÷ (1/4 ÷ 2) = 2/3 ÷ (1/2) = 4/3
The results are the same in this particular example, but in general, changing the grouping in division expressions can lead to different results. This lack of associativity is an important property to keep in mind when working with division.Exercise 1.4 class 8 solution