Is the product always greater than the numbers multiplied?
We know that, when a number multiplied by \(1\), the product remains unchanged.
Similarly we have some suituation as follows,
When we multiply two numbers which are greater than \(1\), the product is greater than both the numbers being multiplied.
Consider a number between \(0\) and \(1\) and one number is greater than \(1\), then their product is greater than the number between \(0\) and \(1\), and lesser than the number greater than \(1\).
Consider two numbers between \(0\) and \(1\), then their product is lesser than those two numbers
| Situation | Example | Relationship |
| Two numbers greater than \(1\) |
\(5\) and \(3\)
\(5 \times 3 = 15\)
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Here \(15 > 5\) and \(3\)
The product is greater than both the numbers being multiplied.
|
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One number is between \(0\) and \(1\) and
another number is greater \(1\)
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\(\frac{1}{4}\) and \(8\)
\(\frac{1}{4} \times 8 = \frac{8}{4} = 2\)
|
Here \(2>\frac{1}{4}\) and \(2<8\)
The product is greater than the number
taken between \(0\) and \(1\), and the
product is lesser than the number greater than \(1\).
|
| Two numbers between \(0\) and \(1\) |
\(\frac{3}{4}\) and \(\frac{2}{5}\)
\(\frac{3}{4} \times \frac{2}{5}\)
\(= \frac{3 \times 2}{4 \times 5}\)
\(= \frac{6}{20}\)
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Let us compare than taken numbers and the product
\(\frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20}\)
\(\frac{2}{5} = \frac{2 \times 4}{5 \times 4} = \frac{8}{20}\)
\(\frac{15}{20} > \frac{6}{20}\)
\(\frac{8}{20}> \frac{6}{20}\)
Thus, their product is lesser than those two numbers.
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