Comparison of Rational Numbers by Cross Multiplication
Comparison of Rational Numbers by Cross Multiplication
Comparison:
Comparison means to analyse the relation between two numbers. There can be three situations
1. Both the numbers are equal
2. First number is less than the second number
3. First number is more than the second number.
Cross Multiplication:
The method of cross multiplication means multiplying the numerator of one number with the denominator of the other number. For two rational numbers
Cross multiplication means multiplying the numerator of first number with the denominator of second number and the denominator of first number with the numerator of second number and we get
Comparison of Rational Numbers by Cross Multiplication:
When ever we are given two rational numbers and we have to check whether the given rational numbers are equal, less than or greater than, the comparison is done by the method of cross multiplication.
For two rational numbers there can be three situations
Case 1. They are equal if:
i.e. ,
Numerator of first Denominator of second = Numerator of second
Denominator of first.
Case 2. The first rational number is greater than the second rational number if:
i.e. ,
Numerator of first Denominator of second > Numerator of second
Denominator of first.
Case 3. The first rational number is less than the second rational number if:
i.e. ,
Numerator of first Denominator of second < Numerator of second
Denominator of first.
Illustration: Compare the rational numbers for equality.
Solution:To compare the rational numbers for equality we will perform cross multiplication
63 = 63
Hence, these rational numbers are equal.
Illustration: Compare the rational numbers , for equality.
Solution: To compare the rational numbers for equality we will perform cross multiplication
140 = 140
Hence, these rational numbers are equal.
Illustration: Do represent the same rational number?
Solution: To compare the rational numbers for equality we will perform cross multiplication
4 x 36 = 144
(-9) x (-16) = 144
These rational numbers are equal.
Illustration: Compare the rational numbers
Solution: To compare the rational numbers for equality we will perform cross multiplication
: 2 x 8 = 16 and 3 x 5 = 15
Hence,
Which of the following relation holds for | |||
| Right Option : A | |||
| View Explanation | |||
Which of the following relation holds for | |||
| Right Option : B | |||
| View Explanation | |||
For two rational numbers that are in standard form | |||
| Right Option : D | |||
| View Explanation | |||
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