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Answer :
To solve the problem of finding the value of [tex]29.94 \div 1.45[/tex], given that [tex]2994 \div 14.5 = 172[/tex], we can use a method of scale.
First, let's analyze the given equation:
- [tex]2994 \div 14.5 = 172[/tex]
By observing the numbers, we see that each of the terms in the equation is 100 times larger than the terms in [tex]29.94 \div 1.45[/tex]. This is because dividing or multiplying by a power of 10 shifts the decimal point.
Now, keep in mind:
- When the divisor and dividend are reduced by the same factor of 100 (by moving the decimal point), the quotient remains unchanged.
Thus, if [tex]2994 \div 14.5 = 172[/tex], then similarly:
- [tex]29.94 \div 1.45[/tex] results in the same quotient.
Therefore, [tex]29.94 \div 1.45 = 172[/tex].
This method effectively demonstrates that without changing the relationship between the numbers, we maintain the quotient by adjusting the decimal scale equally for both the dividend and divisor.
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